[1] E. Osayande, K.P. Ayodele, M.A. Komolafe. Development of a robotic hand orthosis for stroke patient rehabilitation. International Journal of Online and Biomedical Engineering, 16(13):142–149, 2020. doi: 10.3991/ijoe.v16i13.13407.
[2] Z. Yue, X. Zhang, and J. Wang. Hand Rehabilitation robotics on poststroke motor recovery. Behavioural Neurology, 2017:3908135, 2017. doi: 10.1155/2017/3908135.
[3] C. Grefkes and G.R. Fink. Recovery from stroke: current concepts and futures perspectives. Neurological Research and Practice, 2(1):17, 2020. doi: 10.1186/s42466-020-00060-6.
[4] R. Gassert and V. Dietz. Rehabilitation robots for the treatment of sensorimotor deficits: a neurophysiological perspective. Journal of NeuroEngineering and Rehabilitation, 15:46, 2018. doi: 10.1186/s12984-018-0383-x.
[5] S.H. Hayes and S.R. Carroll. Early intervention care in the acute stroke patient. Archives of Physical Medicine and Rehabilitation, 67(5):319–321, 1986.
[6] D.U. Jette, R.L. Warren, and C. Wirtalla. The relation between therapy intensity and outcomes of rehabilitation in skilled nursing facilities. Archives of Physical Medicine and Rehabilitation, 86(3):373–379, 2005. doi: 10.1016/j.apmr.2004.10.018.
[7] Z. Zhou and Q. Wang. Concept and prototype design of a robotic ankle-foot rehabilitation system with passive mechanism for coupling motion. 2019 IEEE 9th Annual International Conference on CYBER Technology in Automation, Control, and Intelligent Systems (CYBER), pages 1002–1005, Suzhou, China, 29 July -2 August, 2019. doi: 10.1109/cyber46603.2019.9066745.
[8] C.M. Racu and I. Doroftei. An overview on ankle rehabilitation devices. Advanced Materials Research, 1036:781–786, 2014. doi: 10.4028/www.scientific.net/amr.1036.781.
[9] A.A. Blank, J.A. French, A.U. Pehlivan, and M.K. O'Malley. Rehabilitation: Current trends in robot-assisted upper-limb stroke rehabilitation: promoting patient engagement in therapy. Current Physical Medicine and Rehabilitation Reports, 2(3):184–195, 2014.
[10] Z. Liao, L. Yao, Z. Lu, and J. Zhang. Screw theory based mathematical modeling and kinematic analysis of a novel ankle rehabilitation robot with a constrained 3-PSP mechanism topology. International Journal of Intelligent Robotics and Applications, 2(3):351–360, 2018. doi: 10.1007/s41315-018-0063-9.
[11] C.C.K. Lin, M.S. Ju, S.M. Chen, and B.W. Pan. A specialized robot for ankle rehabilitation and evaluation. Journal of Medical and Biological Engineering, 28(2):79–86, 2008.
[12] Z. Sun et al. Mechanism Design and ADAMS-MATLAB-Simulation of a Novel Ankle Rehabilitation Robot. 2019 IEEE International Conference on Robotics and Biomimetic (ROBIO), pages 425–432, Dali, China, December, 2019. doi: 10.1109/robio49542.2019.8961829.
[13] Q. Liu, A. Liu, W. Meng, Q. Ai, and S.Q. Xie. Hierarchical compliance control of a soft ankle rehabilitation robot actuated by pneumatic muscles. Frontiers in Neurorobotics, 11:64, 2017. doi: 10.3389/fnbot.2017.00064.
[14] T. Yonezawa, K. Nomura, T. Onodera, S. Ishimura, H. Mizoguchi, and H. Takemura. Evaluation of venous return in lower limb by passive ankle exercise performed by PHARAD. 2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pages 3582–3585, Milan, Italia, 25–29 August, 2015. doi: 10.1109/embc.2015.7319167.
[15] Ye Ding, M. Sivak, B. Weinberg, C. Mavroidis, and M.K. Holden. NUVABAT: Northeastern university virtual ankle and balance trainer. 2010 IEEE Haptics Symposium, pages 509–514, Waltham, Massachusetts, USA, 25–26 March, 2010. doi: 10.1109/haptic.2010.5444608.
[16] D. Ao, R. Song, and J. Gao. Movement performance of human–robot cooperation control based on emg-driven hill-type and proportional models for an ankle power-assist exoskeleton robot. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 25(8):1125–1134, 2017. doi: 10.1109/tnsre.2016.2583464.
[17] Y. Ren, Y.-N. Wu, C.-Y. Yang, T. Xu, R. L. Harvey, and L.-Q. Zhang. Developing a wearable ankle rehabilitation robotic device for in-bed acute stroke rehabilitation. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 25(6):589–596, 2017. doi: 10.1109/tnsre.2016.2584003.
[18] G. Aguirre-Ollinger, J.E. Colgate, M.A. Peshkin, and A. Goswami. Design of an active one-degree-of-freedom lower-limb exoskeleton with inertia compensation. The International Journal of Robotics Research, 30(4):486–499, 2011. doi: 10.1177/0278364910385730.
[19] Z. Zhou, Y. Sun, N. Wang, F. Gao, K. Wei, and Q. Wang. Robot-assisted rehabilitation of ankle plantar flexors spasticity: a 3-month study with proprioceptive neuromuscular facilitation. Frontiers in Neurorobotics, 10:16, 2016. doi: 10.3389/fnbot.2016.00016.
[20] I. Doroftei, C.M. Racu, C. Honceriu, and D. Irimia. One-degree-of freedom ankle rehabilitation platform. IOP Conference Series: Materials Science and Engineering, 591:012076, 2019. doi: 10.1088/1757-899x/591/1/012076.
[21] A. Gmerek and E. Jezierski. Admittance control of a 1-DoF robotic arm actuated by BLDC motor. 2012 17th International Conference on Methods & Models in Automation & Robotics (MMAR), pages 633–638, Miedzyzdroje, Poland, 27–30 August, 2012. doi: 10.1109/mmar.2012.6347811.
[22] Ł. Woliński. Comparison of the adaptive and neural network control for LWR 4+ manipulators: simulation study. Archive of Mechanical Engineering, 67(1):111–121, 2020. doi: 10.24425/ame.2020.131686.
[23] Meera C S, M.K. Gupta, and S. Mohan. Disturbance observer-assisted hybrid control for autonomous manipulation in a robotic backhoe. Archive of Mechanical Engineering, 66(2):153–169, 2019. doi: 10.24425/ame.2019.128442.
[24] O. Jedda, J. Ghabi and A. Douik. Sliding mode control of an inverted pendulum. In: Derbel N., Ghommam J., Zhu Q. (eds), Applications of Sliding Mode Control. Studies in Systems, Decision and Control, chapter 6:105–118, 2016, Springer. doi: 10.1007/978-981-10-2374-3_6.
[25] S. Singh, M.S. Qureshi, and P. Swarnkar. Comparison of conventional PID controller with sliding mode controller for a 2-link robotic manipulator. 2016 International Conference on Electrical Power And Energy System (ICEPES), pages 115–119, Bhopal, India, 14-16 December, 2016. doi: 10.1109/icepes.2016.7915916.
[26] P. Boscariol and D. Richiedei. Trajectory design for energy savings in redundant robotic cells. Robotics, 8(1):15, 2019. doi: 10.3390/robotics8010015.
[27] M. Adolphe, J. Clerval, Z. Kirchof, R. Lacombe-Delpech, and B. Zagrodny. Center of mass of human's body segments, Mechanics and Mechanical Engineering, 21(3):485–497, 2017.
[28] T. Eiammanussakul and V. Sangveraphunsiri. A lower limb rehabilitation robot in sitting position with a review of training activities. Journal of Healthcare Engineering, 2018:927807, 2018. doi: 10.1155/2018/1927807.
[29] A. Roy, H.I. Krebs, C.T. Bever, L.W. Forrester, R.F. Macko, and N. Hogan. Measurement of passive ankle stiffness in subjects with chronic hemiparesis using a novel ankle robot. Journal of Neurophysiology, 105(5):2132–2149, 2011. doi: 10.1152/jn.01014.2010.
[30] F. Gao, Y. Ren, E.J. Roth, R. Harvey, and L.-Q. Zhang. Effects of repeated ankle stretching on calf muscle–tendon and ankle biomechanical properties in stroke survivors. Clinical Biomechanics, 26(5):516–522, 2011. doi: 10.1016/j.clinbiomech.2010.12.003.
[31] G. Bucca, A. Bezzolato, S. Bruni and F. Molteni. A Mechatronic Device for the Rehabilitation of Ankle Motor Function. Journal of Biomechanical Engineering, 131(12):125001, 2009. doi: 10.1115/1.4000083.
[32] J. Zhong, Y. Zhu, C. Zhao, Z. Han, and X. Zhang. Position tracking of a pneumatic-muscle-driven rehabilitation robot by a single neuron tuned pid controller. Complexity, 2020:438391, 2020. doi: 10.1155/2020/1438391.

[1] Z. Recebli, S. Selimli, M. Ozkaymak, and O. Gonc. Biogas production from animal manure. Journal of Engineering Science and Technology, 10(6):722–729, 2015.
[2] S. Rasi, A.Veijanen, and J. Rintala. Trace compounds of biogas from different biogas production plants. Energy, 32(8):1375–1380, 2007. doi: 10.1016/j.energy.2006.10.018.
[3] O. Jonsson, E. Polman, J.K. Jensen, R. Ekund, H. Schyl, and S. Ivarsson. Sustainable gas enters the European gas distribution system. In World Gas Conference, Tokyo, Japan, 2003.
[4] I.U. Khan, M.H.D. Othman, H. Hashim, T. Matsuura, A.F. Ismail, M. Rezaei-DashtArzhandi, and I.W. Azelee. Biogas as a renewable energy fuel – a review of biogas upgrading, utilization and storage. Energy Conversion and Management, 150:277–294, 2017. doi: 10.1016/j.enconman.2017.08.035.
[5] H.O.B. Nonaka and F.M. Pereira. Experimental and numerical study of CO ₂ content effects on the laminar burning velocity of biogas. Fuel, 182:382–390, 2016. doi: j.fuel.2016.05.098.
[6] M.S. Abdallah, M.S. Mansour, and N.K. Allam. Mapping the stability of free-jet biogas flames under partially premixed combustion. Energy, 220:119749, 2021. doi: 10.1016/j.energy.2020.119749.
[7] L. Zhang, X. Ren, R. Sun, andY.A. Levendis. A numerical and experimental study on the effects of CO ₂ on laminar diffusion methane/air flames. Journal of Energy Resources Technology, 142(8):82307, 2020. doi: 10.1115/1.4046228.
[8] T. Leung and I. Wierzba. The effect of hydrogen addition on biogas non-premixed jet flame stability in a co-flowing air stream. International Journal of Hydrogen Energy, 33(14):3856–3862, 2008. doi: 10.1016/j.ijhydene.2008.04.030.
[9] S. Verma, K. Kumar, L.M. Das, and S.C. Kaushik. Effects of hydrogen enrichment strategy on performance and emission features of biodiesel-biogas dual fuel engine using simulation and experimental analyses. Journal of Energy Resources Technology, 143(9):092301, 2021. doi: 10.1115/1.4049179.
[10] H.S. Zhen, C.W. Leung, and C.S. Cheung. Effects of hydrogen addition on the characteristics of a biogas diffusion flame. International Journal of Hydrogen Energy, 38(16):6874–6881, 2013. doi: 10.1016/j.ijhydene.2013.02.046.
[11] H.S. Zhen, C.W. Leung, and C.S. Cheung. A comparison of the heat transfer behaviors of biogas–H ₂ diffusion and premixed flames. International Journal of Hydrogen Energy, 39(2):1137–1144, 2014. doi: 10.1016/j.ijhydene.2013.10.100.
[12] H.S. Zhen, Z.L. Wei, Z.B. Chen, M.W. Xiao, L.R. Fu, and Z.H. Huang. An experimental comparative study of the stabilization mechanism of biogas-hydrogen diffusion flame. International Journal of Hydrogen Energy, 44(3):1988–1997, 2019. doi: 10.1016/j.ijhydene.2018.11.171.
[13] M.R.J. Charest, Ö.L. Gülder, and C.P.T. Groth. Numerical and experimental study of soot formation in laminar diffusion flames burning simulated biogas fuels at elevated pressures. Combustion and Flame, 161(10):2678–2691, 2014. doi: 10.1016/j.combustflame.2014.04.012.
[14] Z.L.Wei, C.W. Leung, C.S. Cheung, and Z.H. Huang. Effects of H ₂ andCO ₂ addition on the heat transfer characteristics of laminar premixed biogas-hydrogen Bunsen flame. International Journal of Heat Mass Transfer, 98:359–366, 2016. doi: 10.1016/j.ijheatmasstransfer.2016.02.064.
[15] A. Mameri and F. Tabet. Numerical investigation of counter-flow diffusion flame of biogas-hydrogen blends: Effects of biogas composition, hydrogen enrichment and scalar dissipation rate on flame structure and emissions. International Journal of Hydrogen Energy, 41 (3):2011–2022, 2016. doi: 10.1016/j.ijhydene.2015.11.035.
[16] X. Li, S. Xie, J. Zhang, T. Li, and X. Wang. Combustion characteristics of non-premixed CH ₄/CO ₂ jet flames in coflow air at normal and elevated temperatures. Energy, 214:118981, 2021. doi: 10.1016/j.energy.2020.118981.
[17] A.V. Prabhu, A. Avinash, K. Brindhadevi, and A. Pugazhendhi. Performance and emission evaluation of dual fuel CI engine using preheated biogas-air mixture. Science of The Total Environment, 754:142389, 2021. doi: 10.1016/j.scitotenv.2020.142389.
[18] M.H. Moghadasi, R. Riazi, S. Tabejamaat, and A. Mardani. Effects of preheating and CO ₂ dilution on Oxy-MILD combustion of natural gas. Journal of Energy Resources Technology, 141(12):12200, 2019. doi: 10.1115/1.4043823.
[19] A. Harish, H.R. Rakesh Ranga, A. Babu, and V. Raghavan. Experimental study of the flame characteristics and stability regimes of biogas – air cross flow non-premixed flames. Fuel, 223:334–343, 2018. doi: 10.1016/j.fuel.2018.03.055.
[20] G. Tsatsaronis, T. Morosuk, D. Koch, and M. Sorgenfrei. Understanding the thermodynamic inefficiencies in combustion processes. Energy, 62:3–11, 2013. doi: 10.1016/j.energy.2013.04.075.
[21] A. Datta. Entropy generation in a confined laminar diffusion flame. Combustion Science and Technology, 159(1):39–56, 2000. doi: 10.1080/00102200008935776.
[22] K.M. Saqr and M.A. Wahid. Entropy generation in turbulent swirl-stabilized flame: Effect of hydrogen enrichment. Applied Mechanics and Materials, 388:280–284, 2013. doi: 10.4028/www.scientific.net/AMM.388.280.
[23] H.R. Arjmandi and E. Amani. A numerical investigation of the entropy generation in and thermodynamic optimization of a combustion chamber. Energy, 81:706–718, 2015. doi: 10.1016/j.energy.2014.12.077.
[24] A.M. Briones, A. Mukhopadhyay, and S.K. Aggarwal. Analysis of entropy generation in hydrogen-enriched methane–air propagating triple flames. International Journal of Hydrogen Energy, 34(2):1074–1083, 2009. doi: 10.1016/j.ijhydene.2008.09.103.
[25] K. Nishida, T. Takagi, and S. Kinoshita. Analysis of entropy generation and exergy loss during combustion. Proceedings of the Combustion Institute, 29(1):869–874, 2002. doi: 10.1016/S1540-7489 (02)80111-0.
[26] W. Wang, Z. Zuo, J. Liu, and W. Yang. Entropy generation analysis of fuel premixed CH ₄/H ₂/air flames using multistep kinetics. International Journal of Hydrogen Energy, 41(45):20744–20752, 2016. doi: 10.1016/j.ijhydene.2016.08.103.
[27] R.S. Barlow, N.S.A. Smith, J.Y. Chen, and R.W. Bilger. Nitric oxide formation in dilute hydrogen jet flames: isolation of the effects of radiation and turbulence–chemistry sub models. Combustion and Flame, 117(1-2):4–31, 1999. doi: 10.1016/S0010-2180(98)00071-6.
[28] J.O. Hirschfelder, C.F. Curtiss, and R.B. Bird. Molecular Theory of Gases and Liquids. Wiley, New York, 1954.
[29] K.K.Y. Kuo. Principles of Combustion. Wiley, New York, 1986.
[30] C.T. Bowman, R.K. Hanson, D.F. Davidson, W.C. Gardiner, Jr., V. Lissianski, G.P. Smith, D.M. Golden, M. Frenklach, and M. Goldenberg. GRI_Mech 2.11. Available: http://combustion.berkeley.edu/gri-mech/new21/version21/text21.html.
[31] D.N. Pope, V. Raghavan, and G. Gogos. Gas-phase entropy generation during transient methanol droplet combustion. International Journal of Thermal Sciences, 49(7):1288–1302, 2010. doi: 10.1016/j.ijthermalsci.2010.02.012.
[32] A.V. Mokhov, B.A.V Bennett, H.B. Levinsky, and M.D. Smooke. Experimental and computational study of C ₂H ₂ and CO in a laminar axisymmetric methane-air diffusion flame. Proceedings of the Combustion Institute, 31(1):997–1004, 2007. doi: 10.1016/j.proci.2006.08.094.
[33] J. Lim, J. Gore, and R. Viskanta. A study of the effects of air preheat on the structure of methane/air counterflow diffusion flames. Combustion and Flame, 121(1-2):262–274, 2000. doi: 10.1016/S0010-2180(99)00137-6.
[34] H.S. Zhen, J. Miao, C.W. Leung, C.S. Cheung, and Z.H. Huang. A study on the effects of air preheat on the combustion and heat transfer characteristics of Bunsen flames. Fuel, 184:50–58, 2016. doi: 10.1016/j.fuel.2016.07.007.
[35] C.J. Sung, J.B. Liu, and C.K. Law. Structural response of counterflow diffusion flames to strain rate variations. Combustion and Flame, 102(4):481–492, 1995. doi: 10.1016/0010-2180(95)00041-4.

[1] J. Bear. Dynamics of fluids in porous media. Courier Corporation, 2013.
[2] H.C. Brinkman. A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Flow, Turbulence and Combustion, 1(1):27–34, 1949. doi: 10.1007/bf02120313.
[3] R.H. Davis and H.A. Stone. Flow through beds of porous particles. Chemical Engineering Science, 48(23):3993–4005, 1993. doi: 10.1016/0009-2509(93)80378-4.
[4] B. Barman. Flow of a Newtonian fluid past an impervious sphere embedded in a porous medium. Indian Journal of Pure and Applied Mathematics, 27:1249–1256, 1996.
[5] I. Pop and D.B. Ingham. Flow past a sphere embedded in a porous medium based on the Brinkman model. International Communications in Heat and Mass Transfer, 23(6):865–874, 1996. doi: 10.1016/0735-1933(96)00069-3.
[6] D. Srinivasacharya and J.V. Ramana Murthy. Flow past an axisymmetric body embedded in a saturated porous medium. Comptes Rendus Mécanique, 330(6):417–423, 2002. doi: 10.1016/s1631-0721(02)01478-x.
[7] T. Grosan, A. Postelnicu, and I. Pop. Brinkman flowof a viscous fluid through a spherical porous medium embedded in another porous medium. Transport in Porous Media, 81(1):89–103, 2010. doi: 10.1007/s11242-009-9389-y.
[8] S. Deo and B.R. Gupta. Drag on a porous sphere embedded in another porous medium. Journal of Porous Media, 13(11):1009–1016, 2010. doi: 10.1615/JPorMedia.v13.i11.70.
[9] N.E. Leontev. Flow past a cylinder and a sphere in a porous medium within the framework of the Brinkman equation with the Navier boundary condition. Fluid Dynamics, 49(2):232–237, 2014. doi: 10.1134/S0015462814020112.
[10] S. El-Sapa. Effect of permeability of Brinkman flow on thermophoresis of a particle in a spherical cavity. European Journal of Mechanics-B/Fluids, 79:315–323, 2020. doi: 10.1016/j.euromechflu.2019.09.017.
[11] M.S. Faltas, H.H. Sherief, A.A. Allam, and B.A. Ahmed. Mobilities of a spherical particle straddling the interface of a semi-infinite Brinkman flow. Journal of Fluids Engineering, 143(7):071402, 2021. doi: 10.1115/1.4049931.
[12] M. Krishna Prasad and D. Srinivasacharya. Micropolar fluid flow through a cylinder and a sphere embedded in a porous medium. International Journal of Fluid Mechanics Research, 44(3):229–240, 2017. doi: 10.1615/InterJFluidMechRes.2017015283.
[13] B.R. Jaiswal. A non-Newtonian liquid sphere embedded in a polar fluid saturated porous medium: Stokes flow. Applied Mathematics and Computation, 316:488–503, 2018. doi: 10.1016/j.amc.2017.08.009.
[14] K. Ramalakshmi and P. Shukla. Drag on a fluid sphere embedded in a porous medium with solid core. International Journal of Fluid Mechanics Research, 46(3):219–228, 2019. doi: 10.1615/InterJFluidMechRes.2018025197.
[15] K.P. Madasu and T. Bucha. Influence of mhd on micropolar fluid flow past a sphere implanted in porous media. Indian Journal of Physics, 95(6):1175–1183, 2021. doi: 10.1007/s12648-020-01759-7.
[16] V.K. Stokes. Couple stresses in fluids. In Theories of Fluids with Microstructure, pages 34–80. Springer, 1966. doi: 10.1007/978-3-642-82351-0_4.
[17] V.K. Stokes. Theories of Fluids with Microstructure: An Introduction. Springer Science & Business Media, 2012. doi: 10.1007/978-3-642-82351-0.
[18] D. Pal, N. Rudraiah, and R. Devanathan. A couple stress model of blood flow in the microcirculation. Bulletin of Mathematical Biology, 50(4):329–344, 1988. doi: 10.1007/BF02459703.
[19] N.A. Khan, A. Mahmood, and A. Ara. Approximate solution of couple stress fluid with expanding or contracting porous channel. Engineering Computations, 30(3):399–408, 2013. doi: 10.1108/02644401311314358.
[20] D. Srinivasacharya and K. Kaladhar. Mixed convection flowof couple stress fluid in a non-Darcy porous medium with Soret and Dufour effects. Journal of Applied Science and Engineering, 15(4):415–422, 2012.
[21] M. Devakar, D. Sreenivasu, and B. Shankar. Analytical solutions of couple stress fluid flows with slip boundary conditions. Alexandria Engineering Journal, 53(3):723–730, 2014. doi: 10.1016/j.aej.2014.06.005.
[22] D. Srinivasacharya, N. Srinivasacharyulu, and O. Odelu. Flow of couple stress fluid between two parallel porous plates. International Journal of Applied Mathematics, 41(2).
[23] E.A. Ashmawy. Drag on a slip spherical particle moving in a couple stress fluid. Alexandria Engineering Journal, 55(2):1159–1164, 2016. doi: 10.1016/j.aej.2016.03.032.
[24] P. Aparna, P. Padmaja, N. Pothanna, and J.V. Ramana Murthy. Couple stress fluid flow due to slow steady oscillations of a permeable sphere. Nonlinear Engineering, 9(1):352–360, 2020. doi: 10.1515/nleng-2020-0021.
[25] S.O. Adesanya, S.O. Kareem, J.A. Falade, and S.A. Arekete. Entropy generation analysis for a reactive couple stress fluid flow through a channel saturated with porous material. Energy, 93:1239–1245, 2015. doi: 10.1016/j.energy.2015.09.115.
[26] A.R. Hassan. The entropy generation analysis of a reactive hydromagnetic couple stress fluid flow through a saturated porous channel. Applied Mathematics and Computation, 369:124843, 2020. doi: 10.1016/j.amc.2019.124843.
[27] S.I.Abdelsalam, J.X.Velasco-Hernández, and A.Z. Zaher. Electro-magnetically modulated selfpropulsion of swimming sperms via cervical canal. Biomechanics and Modeling in Mechanobiology, 20(3):861–878, 2021. doi: 10.1007/s10237-020-01407-3.
[28] M.M. Bhatti, S.Z. Alamri, R. Ellahi, and S.I. Abdelsalam. Intra-uterine particle–fluid motion through a compliant asymmetric tapered channel with heat transfer. Journal of Thermal Analysis and Calorimetry, 144(6):2259–2267, 2021. doi: 10.1007/s10973-020-10233-9.
[29] A.R. Hadjesfandiari and G.F. Dargush. Polar continuum mechanics. arXiv preprint arXiv:1009.3252, 2010.
[30] A.R. Hadjesfandiari and G.F. Dargush. Couple stress theory for solids. International Journal of Solids and Structures, 48(18):2496–2510, 2011. doi: 10.1016/j.ijsolstr.2011.05.002.
[31] A.R. Hadjesfandiari, G.F. Dargush, and A. Hajesfandiari. Consistent skew-symmetric couple stress theory for size-dependent creeping flow. Journal of Non-Newtonian Fluid Mechanics, 196:83–94, 2013. doi: 10.1016/j.jnnfm.2012.12.012.
[32] A.R. Hadjesfandiari, A. Hajesfandiari, and G.F. Dargush. Skew-symmetric couple-stress fluid mechanics. Acta Mechanica, 226(3):871–895, 2015. doi: 10.1007/s00707-014-1223-0.
[33] C.L.M.H. Navier. Mémoires de l’Académie Royale des Sciences de l’Institut de France. Royale des Sciences de l’Institut de France, 1823.
[34] I.M. Eldesoky, S.I. Abdelsalam, W.A. El-Askary, A.M. El-Refaey, and M.M. Ahmed. Joint effect of magnetic field and heat transfer on particulate fluid suspension in a catheterized wavy tube. BioNanoScience, 9(3):723–739, 2019. doi: >10.1007/s12668-019-00651-x.
[35] M.M. Bhatti and S.I. Abdelsalam. Thermodynamic entropy of a magnetized ree-eyring particle-fluid motion with irreversibility process: A mathematical paradigm. Journal of Applied Mathmatics nd Mechanics/Zeitschrift fur Angewandte Mathematik und Mechanik, 101(6):e202000186, 2021. doi: 10.1002/zamm.202000186.
[36] S. El-Sapa and N.S. Alsudais. Effect of magnetic field on the motion of two rigid spheres embedded in porous media with slip surfaces. The European Physical Journal E, 44(5):1–11, 2021. doi: 10.1140/epje/s10189-021-00073-2.
[37] K.P. Madasu, M. Kaur, and T. Bucha. Slow motion past a spheroid implanted in a Brinkman medium: Slip condition. International Journal of Applied and Computational Mathematics, 7(4):1–15, 2021. doi: 10.1007/s40819-021-01104-4.
[38] J. Happel and H. Brenner. Low Reynolds Number Hydrodynamics: with Special Applications to Particulate Media. Springer Science & Business Media, 2012.
[39] S. El-Sapa, E.I. Saad, and M.S. Faltas. Axisymmetric motion of two spherical particles in a brinkman medium with slip surfaces. European Journal of Mechanics-B/Fluids, 67:306–313, 2018. doi: 10.1016/j.euromechflu.2017.10.003.
[40] V.K. Stokes. Effects of couple stresses in fluids on the creeping flow past a sphere. The Physics of Fluids, 14(7):1580–1582, 1971. doi: 10.1063/1.1693645.

[1] R.M. Arunachalam, M.A. Mannan, and A.C. Spowage. Surface integrity when machining age hardened Inconel 718 with coated carbide cutting tools. International Journal of Machine Tools and Manufacture, 44(14):1481–1491, 2004. doi: 10.1016/j.ijmachtools.2004.05.005.
[2] L. Li, N. He, M.Wang, and Z.G.Wang. High-speed cutting of Inconel 718 with coated carbide and ceramic inserts. Journal of Materials Processing Technology, 129(1–3):127–130, 2002. doi: 10.1016/S0924-0136(02)00590-3.
[3] E.O. Ezugwu. Key improvements in the machining of difficult-to-cut aerospace superalloys. International Journal of Machine Tools and Manufacture, 45(12–13):1353–1367, 2005. doi: 10.1016/j.ijmachtools.2005.02.003.
[4] T. Kitagawa, A. Kubo, and K. Maekawa. Temperature and wear of cutting tools in high-speed machining of Inconel and Ti–6Al–6V–2Sn. Wear, 202(2):142–148, 1997. doi: 10.1016/S0043-1648(96)07255-9.
[5] S. Chinchanikar, S.S. Kore, and P. Hujare. A review on nanofluids in minimum quantity lubrication machining. Journal of Manufacturing Processes, 68(A):56–70, 2021. doi: 10.1016/j.jmapro.2021.05.028.
[6] A.C. Okafor and T.O. Nwoguh. Comparative evaluation of soybean oil–based MQL flow rates and emulsion flood cooling strategy in high-speed face milling of Inconel 718. The International Journal of Advanced Manufacturing Technology, 107(9–10):3779–3793, 2020. doi: 10.1007/s00170-020-05248-3.
[7] J. Kaminski and B. Alvelid. Temperature reduction in the cutting zone in water-jet assisted turning. Journal of Materials Processing Technology, 106(1–3):68–73, 2000. doi: 10.1016/S0924-0136(00)00640-3.
[8] A. Marques, M. Paipa Suarez, W. Falco Sales, and Á. Rocha Machado. Turning of Inconel 718 with whisker-reinforced ceramic tools applying vegetable-based cutting fluid mixed with solid lubricants by MQL. Journal of Materials Processing Technology, 266:530–543, 2019. doi: 10.1016/j.jmatprotec.2018.11.032.
[9] A. Suárez, L.N. López de Lacalle, R. Polvorosa, F. Veiga, and A. Wretland. Effects of highpressure cooling on the wear patterns on turning inserts used on alloy IN718. Materials and Manufacturing Processes, 32(6):678–686, 2017. doi: 10.1080/10426914.2016.1244838.
[10] R. Polvorosa, A. Suárez, L.N. López de Lacalle, I. Cerrillo, A. Wretland, and F. Veiga: Tool wear on nickel alloys with different coolant pressures: Comparison of Alloy 718 andWaspaloy. Journal of Manufacturing Processes, 26:44–56, 2017. doi: 10.1016/j.jmapro.2017.01.012.
[11] A.R.C. Sharman, J.I. Hughes, and K. Ridgway. Surface integrity and tool life when turning Inconel 718 using ultra-high pressure 786 and flood coolant systems. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 222(6):653–664, 2008. doi: 10.1243/09544054JEM936.
[12] W.H. Pereira and S. Delijaicov. Surface integrity of Inconel 718 turned under cryogenic conditions at high cutting speeds. The International Journal of Advanced Manufacturing Technology, 104:2163–2177, 2019. doi: 10.1007/s00170-019-03946-1.
[13] H. González, O. Pereira, L.N. López de Lacalle, A. Calleja, I. Ayesta, and J. Muñoa. Flankmilling of integral blade rotors made in Ti6Al4V using cryo CO2 and minimum quantity lubrication. ASME. Journal of Manufacturing Science and Engineering, 143(9):091011, 2021. doi: 10.1115/1.4050548.
[14] A. Devillez, F. Schneider, S. Dominiak, D. Dudzinski, and D. Larrouquere. Cutting forces and wear in dry machining of Inconel 718 with coated carbide tools. Wear, 262(7–8):931–942, 2007. doi: 10.1016/j.wear.2006.10.009.
[15] N.R. Dhar, M.W. Islam, S. Islam, and M.A.H. Mithu. The influence of minimum quantity of lubrication (MQL) on cutting temperature, chip and dimensional accuracy in turning AISI- 1040 steel. Journal of Materials Processing Technology, 171(1):93–99, 2006. doi: 10.1016/j.jmatprotec.2005.06.047.
[16] D. Dudzinski, A. Devillez, A. Moufki, D. Larrouquère,V. Zerrouki, and J. Vigneau. A review of developments towards dry and high speed machining of Inconel 718 alloy. International Journal of Machine Tools and Manufacture, 44(4):439–456, 2004. doi: 10.1016/S0890-6955(03)00159-7.
[17] I.A. Choudhury and M.A. El-Baradie. Machining nickel base super alloys: Inconel 718. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture. 212(3):195–206, 1998. doi: 10.1243/0954405981515617.
[18] S.K. Thandra and S.K. Choudhury. Effect of cutting parameters on cutting force, surface finish and tool wear in hot machining. International Journal of Machining and Machinability of Materials, 7(3-4):260–273, 2010. doi: 10.1504/IJMMM.2010.033070.
[19] L.N. Lopez de Lacalle, J.A. Sanchez, A. Lamikiz, and A. Celaya. Plasma assisted milling of heatresistant superalloys. ASME Journal of Manufacturing Science and Engineering, 126(2):274– 285, 2016. doi: 10.1115/1.1644548.
[20] M.C. Shaw. Metal Cutting Principles. Clarendon, Oxford, 1984.
[21] E.O. Ezugwu, J. Bonney, and Y. Yamane. An overview of the machinability of aeroengine alloys. Journal of Materials Processing Technology, 134(2):233–253, 2003. doi: 10.1016/S0924-0136(02)01042-7.
[22] A. Jawaid, S. Koksal, and S. Sharif. Wear behavior of PVD and CVD coated carbide tools when face milling Inconel 718. Tribology Transactions, 43(2):325–331, 2000. doi: 10.1080/10402000008982347.
[23] T. Sugihara, H. Tanaka, and T. Enomoto. Development of novel CBN cutting tool for high speed machining of Inconel 718 focusing on coolant behaviors. Procedia Manufacturing, 10:436–442, 2017. doi: 10.1016/j.promfg.2017.07.021.
[24] G.A. Ibrahim, C.H.C. Haron, J.A. Ghani, A.Y.M. Said, and M.Z.A. Yazid. Performance of PVD-coated carbide tools when turning Inconel 718 in dry machining. Advances in Mechanical Engineering, 3:790975, 2011. doi: 10.1155/2011/790975.
[25] Z.P. Hao, Y.H. Fan, J.Q. Lin, and Z.X Yu. Wear characteristics and wear control method of PVD-coated carbide tool in turning Inconel 718. The International Journal of Advanced Manufacturing Technology, 78(5–8):1329–1336, 2015. doi: 10.1007/s00170-014-6752-0.
[26] B. Zhang, M.J. Njora, and Y. Sato. High-speed turning of Inconel 718 by using TiAlN- and (Al, Ti) N-coated carbide tools. The International Journal of Advanced Manufacturing Technology, 96(5–8):2141–2147, 2018. doi: 10.1007/s00170-018-1765-8.
[27] F. Zemzemi, J. Rech, W.B. Salem, A. Dogui, and P. Kapsa. Identification of friction and heat partition model at the tool-chip-workpiece interfaces in dry cutting of an Inconel 718 alloy with CBN and coated carbide tools. Advances in Manufacturing Science and Technology, 38(1):5-22, 2014. doi: 10.2478/amst-2014-0001.
[28] W. Grzesik, J. Małecka, Z. Zalisz, K. Zak, and P. Niesłony. Investigation of friction and wear mechanisms of TiAlV coated carbide against Ti6Al4V Titanium alloy using pin-on-disc tribometer. Archive of Mechanical Engineering, 63(1):114-127, 2016. doi: 10.1515/meceng-2016-0006.
[29] V. Bushlya, F. Lenrick, A. Bjerke, H. Aboulfadl, M. Thuvander; J.-E. Ståhl, and R. M’Saoubi: Tool wear mechanisms of PcBN in machining Inconel 718: Analysis across multiple length scale. CIRP Annals, 70(1):73–78, 2021. doi: 10.1016/j.cirp.2021.04.008.
[30] A.R.F. Oliveira, L.R.R. da Silva, V. Baldin, M.P.C. Fonseca, R.B. Silva, and A.R. Machado: Effect of tool wear on the surface integrity of Inconel 718 in face milling with cemented carbide tools. Wear, 476:203752, 2021. doi: 10.1016/j.wear.2021.203752.
[31] A.K.M.N. Amin, S.A. Sulaiman, and M.D. Arif. Development of mathematical model for chip serration frequency in turning of stainless steel 304 using RSM. Advanced Materials and Process Technology, 217-219:2206–2209, 2012. doi: .
[32] J. Hua, and R. Shivpuri. Prediction of chip morphology and segmentation during the machining of titanium alloys. Journal of Materials Processing Technology, 150(1-2):124–133, 2004. doi: 10.1016/j.jmatprotec.2004.01.028.
[33] K. Lin, W. Wang, R. Jiang and Y. Xiong. Effect of tool nose radius and tool wear on residual stresses distribution while turning in situ TiB2/7050Al metal matrix composites. The International Journal of Advanced Manufacturing Technology, 100:143–151, 2019. doi: 10.1007/s00170-018-2742-y.
[34] K. Mahesh, J.T. Philip, S.N. Joshi and B. Kuriachen. Machinability of Inconel 718: A critical review on the impact of cutting temperatures. Materials and Manufacturing Processes, 36(7):753–791, 2021. doi: 10.1080/10426914.2020.1843671.
[35] V. Sivalingam Y. Zhao, R. Thulasiram, J. Sun, G. Kai, and T. Nagamalai. Machining behaviour, surface integrity and tool wear analysis in environment friendly turning of Inconel 718 alloy. Measurement,174:109028, 2021. doi: 10.1016/j.measurement.2021.109028.
[36] Z. Peng, X. Zhang, and D. Zhang. Performance evaluation of high-speed ultrasonic vibration cutting for improving machinability of Inconel 718 with coated carbide tools. Tribology International, 155:106766, 2021. doi: 10.1016/j.triboint.2020.106766.
[37] D.G. Flom, R. Komanduri, and M. Lee. High-speed machining of metals. Annual Review of Material Science, 14:231–278, 1984. doi: 10.1146/annurev.ms.14.080184.001311.
[38] N.L. Bhirud and R.R. Gawande. Optimization of process parameters during end milling and prediction of work piece temperature rise. Archive of Mechanical Engineering, 64(3):327–346, 2017. doi: 10.1515/meceng-2017-0020.
[39] R.S. Pawade, S.S. Joshi, P.K. Brahmankar, and M. Rahman. An investigation of cutting forces and surface damage in high-speed turning of Inconel 718. J ournal of Materials Processing Technology, 192-193:139–146, 2007. doi: 10.1016/j.jmatprotec.2007.04.049.
[40] A. Shokrani, V. Dhokia, and S.T. Newman. Environmentally conscious machining of difficultto- machine materials with regard to cutting fluids. International Journal of Machine Tools and Manufacture, 57:83–101, 2012. doi: 10.1016/j.ijmachtools.2012.02.002.
[41] Y.S. Liao, H.M. Lin, and J.H. Wang. Behaviors of end milling Inconel 718 superalloy by cemented carbide tools. Journal of Materials Processing Technology, 201(1–3):460–465, 2008. doi: 10.1016/j.jmatprotec.2007.11.176.
[42] R. Komanduri and T.A. Schroeder. On shear instability in machining a nickel-iron base superalloy. Journal of Engineering for Industry, 108(2):93–100. 1986. doi: 10.1115/1.3187056.
[43] R. Rakesh and S. Datta. Machining of Inconel 718 using coated wc tool: effects of cutting speed on chip morphology and mechanisms of tool wear. Arabian Journal for Science and Engineering, 45:797–816, 2020. doi: 10.1007/s13369-019-04171-4.
[44] S. Belhadi, T. Mabrouki, J.F. Rigal, and L. Boulanouar. Experimental and numerical study of chip formation during straight turning of hardened AISI 4340 steel. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 219(7):515– 524, 2005. doi: 10.1243/095440505X32445.
[45] A. Thakur and S. Gangopadhyay. Evaluation of micro-features of chips of Inconel 825 during dry turning with uncoated and chemical vapour deposition multilayer coated tools. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 232(6):979–994, 2018. doi: 10.1177/0954405416661584.
[46] M. Rahman,W.K.H. Seah, and T.T. Teo. The machinability of Inconel 718. Journal of Materials Processing Technology, 63(1–3):199–204, 1997. doi: 10.1016/S0924-0136(96)02624-6.
[47] S.P. Sahoo and S. Datta. Dry machining performance of AA7075-T6 alloy using uncoated carbide and MT-CVD TiCN-Al2O3 coated carbide Inserts. Arabian Journal of Science and Engineering,45:9777–9791, 2020. doi: 10.1007/s13369-020-04947-z.
[48] H.Z. Li, H. Zeng, and X.Q. Chen. An experimental study of tool wear and cutting force variation in the end milling of Inconel 718 with coated carbide inserts. Journal of Materials Processing Technology, 180(1–3):296–304, 2006. doi: 10.1016/j.jmatprotec.2006.07.009.

[1] X. Cao, Y. Ye, Q. Tang, E. Chen, Z. Jiang, J. Pan, and T. Guo. Numerical analysis of droplets from multinozzle inkjet printing. The Journal of Physical Chemistry Letters, 11(19):8442–8450, 2020. doi: 10.1021/acs.jpclett.0c02250.
[2] H. Wijshoff. Drop dynamics in the inkjet printing process. Current Opinion in Colloid & Interface Science, 36:20–27, 2018. doi: 10.1016/j.cocis.2017.11.004.
[3] W. Zhou, D. Loney, A.G. Fedorov, F.L. Degertekin, and D.W. Rosen. Shape evolution of droplet impingement dynamics in ink-jet manufacturing. Proceedings for the 2011 International Solid Freeform Fabrication Symposium, pages 309–325, Austin, USA, 2011. doi: 10.26153/tsw/15297.
[4] L. Mouzai and M. Bouhadef. Water drop erosivity: Effects on soil splash. Journal of Hydraulic Research, 41(1):61–68, 2003. doi: 10.1080/00221680309499929.
[5] M. Hajigholizadeh, A.M. Melesse, and H.R. Fuentes. Raindrop-induced erosion and sediment transport modelling in shallow waters: A review. Journal of Soil and Water Science, 1(1):15–25, 2018. doi: 10.36959/624/427.
[6] P.C. Ekern. Raindrop impact as the force initiating soil erosion. Soil Science Society of America Journal, 15(C):7–10, 1951. doi: 10.2136/sssaj1951.036159950015000C0002x.
[7] R. Andrade, O. Skurtys, and F. Osorio. Drop impact behavior on food using spray coating: Fundamentals and applications. Food Research International, 54(1):397–405, 2013. doi: 10.1016/j.foodres.2013.07.042.
[8] M. Toivakka. Numerical investigation of droplet impact spreading in spray coating of paper. Proceedings of the 2003 Spring Advanced Coating Fundamentals Symposium, Atlanta, USA, 2003.
[9] A. Prasad and H. Henein. Droplet cooling in atomization sprays. Journal of Materials Science, 43(17):5930–5941, 2008. doi: 10.1007/s10853-008-2860-2.
[10] W. Jia and H.-H. Qiu. Experimental investigation of droplet dynamics and heat transfer in spray cooling. Experimental Thermal and Fluid Science, 27(7):829–838, 2003. doi: 10.1016/S0894-1777(03)00015-3.
[11] G. Duursma, K. Sefiane, and A. Kennedy. Experimental studies of nanofluid droplets in spray cooling. Heat Transfer Engineering, 30(13):1108–1120, 2009. doi: 10.1080/01457630902922467.
[12] W.-C. Qin, B.-J. Qiu, X.-Y. Xue, C. Chen, Z.-F. Xu, and Q.-Q. Zhou. Droplet deposition and control effect of insecticides sprayed with an unmanned aerial vehicle against plant hoppers. Crop Protection, 85:79–88, 2016. doi: 10.1016/j.cropro.2016.03.018.
[13] S. Chen, Y. Lan, Z. Zhou, F. Ouyang, G. Wang, X. Huang, X. Deng, and S. Cheng. Effect of droplet size parameters on droplet deposition and drift of aerial spraying by using plant protection UAV. Agronomy, 10(2):195, 2020. doi: 10.3390/agronomy10020195.
[14] D.T. Sheppard. Spray Characteristics of Fire Sprinklers. Ph.D. Thesis, Northwestern University, Evanston, USA, June 2002.
[15] H. Liu, C.Wang, I.M. De Cachinho Cordeiro, A.C.Y. Yuen, Q. Chen, Q.N. Chan, S. Kook, and G.H. Yeoh. Critical assessment on operating water droplet sizes for fire sprinkler and water mist systems. Journal of Building Engineering, 28:100999, 2020. doi: 10.1016/j.jobe.2019.100999.
[16] D.C. Blanchard. The behavior of water drops at terminal velocity in air. Eos, Transactions American Geophysical Union, 31(6):836–842, 1950. doi: 10.1029/TR031i006p00836.
[17] H.R. Pruppacher and K.V. Beard. A wind tunnel investigation of the internal circulation and shape of water drops falling at terminal velocity in air. Quarterly Journal of the Royal Meteorological Society, 96(408):247–256, 1970. doi: 10.1002/qj.49709640807.
[18] H.R. Pruppacher and R.L. Pitter. A semi-empirical determination of the shape of cloud and rain drops. Journal of the Atmospheric Sciences, 28(1):86–94, 1971. doi: 10.1175/1520-0469(1971)0280086:ASEDOT>2.0.CO;2.
[19] K.V. Beard and C. Chuang. A new model for the equilibrium shape of raindrops. Journal of the Atmospheric Sciences, 44(11):1509–1524, Jun. 1987. doi: 10.1175/1520-0469(1987)0441509:ANMFTE>2.0.CO;2.
[20] É.Reyssat, F. Chevy, A.L. Biance, L. Petitjean, and D. Quéré. Shape and instability of free-falling liquid globules. Europhysics Letters, 80(3):34005, 2007. doi: 10.1209/0295-5075/80/34005.
[21] R. Clift, J.R. Grace, and M.E. Weber. Bubbles, Drops and Particles. Academic Press, 1978.
[22] S.-C. Yao and V.E. Schrock. Heat and mass transfer from freely falling drops. Journal of Heat Transfer, 98(1):120–126, 1976. doi: 10.1115/1.3450453.
[23] T.J. Horton, T.R. Fritsch, and R.C. Kintner. Experimental determination of circulation velocities inside drops. The Canadian Journal of Chemical Engineering, 43(3):143–146, 1965. doi: 10.1002/cjce.5450430309.
[24] R.H. Magarvey and B.W. Taylor. Free fall breakup of large drops. Journal of Applied Physics, 27(10):1129–1135, 1956. doi: 10.1063/1.1722216.
[25] M.N. Chowdhury, F.Y. Testik, M.C. Hornack, and A.A. Khan. Free fall of water drops in laboratory rainfall simulations. Atmospheric Research, 168:158–168, 2016. doi: 10.1016/j.atmosres.2015.08.024.
[26] M. Abdelouahab and R. Gatignol. Study of falling water drop in stagnant air. European Journal of Mechanics - B/Fluids, 60:82–89, 2016. doi: 10.1016/j.euromechflu.2016.07.007.
[27] J.H. van Boxel. Numerical model for the fall speed of raindrops in a rainfall simulator. I.C.E Special Report, 1998/1, 77–85,
[28] A.K. Kamra and D.V Ahire. Wind-tunnel studies of the shape of charged and uncharged water drops in the absence or presence of an electric field. Atmospheric Research, 23(2):117–134, 1989. doi: 10.1016/0169-8095(89)90003-3.
[29] M. Thurai and V.N. Bringi. Drop axis ratios from a 2D video disdrometer. Journal of Atmospheric and Oceanic Technology, 22(7):966–978, 2005. doi: 10.1175/JTECH1767.1.
[30] C. Josserand and S.T. Thoroddsen. Drop impact on a solid surface. Annual Review of Fluid Mechanics, 48:365–391, 2016. doi: 10.1146/annurev-fluid-122414-034401.
[31] J. Eggers, M.A. Fontelos, C. Josserand, and S. Zaleski. Drop dynamics after impact on a solid wall: Theory and simulations. Physics of Fluids, 22(6):062101, 2010. doi: 10.1063/1.3432498.
[32] S. Chandra and C.T. Avedisian. On the collision of a droplet with a solid surface. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 432(1884):13–41, 1991. doi: 10.1098/rspa.1991.0002.
[33] O.G. Engel. Waterdrop collisions with solid surfaces. Journal of Research of the National Bureau of Standards, 54(5):281–298, 1955. doi: 10.6028/jres.054.033.
[34] I.V. Roisman, R. Rioboo, and C. Tropea. Normal impact of a liquid drop on a dry surface: model for spreading and receding. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 458(2022):1411–1430, 2002. doi: 10.1098/rspa.2001.0923.
[35] Y. Renardy, S. Popinet, L. Duchemin, M. Renardy, S. Zaleski, C. Josserand, M.A. Drumright-Carke, D. Richard, C. Clanet, and D. Quéré. Pyramidal and toroidal water drops after impact on a solid surface. Journal of Fluid Mechanics, 484:69–83, 2003. doi: 10.1017/S0022112003004142.
[36] D. Bartolo, F. Bouamrirene, É. Verneuil, A. Buguin, P. Silberzan, and S. Moulinet. Bouncing or sticky droplets: Impalement transitions on superhydrophobic micropatterned surfaces. Europhysics Letters, 74(2):299–305, 2006. doi: 10.1209/epl/i2005-10522-3.
[37] D. Bartolo, C. Josserand, and D. Bonn. Singular jets and bubbles in drop impact. Physical Review Letters, 96:124501, 2006. doi: 10.1103/PhysRevLett.96.124501.
[38] C. Clanet, C. Béguin, D. Richard, and D. Quéré. Maximal deformation of an impacting drop. Journal of Fluid Mechanics, 517:199–208, 2004. doi: 10.1017/S0022112004000904.
[39] L.H.J. Wachters, L. Smulders, J.R. Vermeulen, and H.C. Kleiweg. The heat transfer from a hot wall to impinging mist droplets in the spheroidal state. Chemical Engineering Science, 21(12):1047–1056, 1966. doi: 10.1016/0009-2509(66)85042-X.
[40] C.O. Pedersen. An experimental study of the dynamic behavior and heat transfer characteristics of water droplets impinging upon a heated surface. International Journal of Heat and Mass Transfer, 13(2):369–381, 1970. doi: 10.1016/0017-9310(70)90113-4.
[41] M.A. Styricovich, Y.V. Baryshev, G.V. Tsiklauri and M E. Grigorieva. The mechanism of heat and mass transfer between a water drop and a heated surface. Proceedings of the Sixth International Heat Transfer Conference, Vol. 1, pages 239-243, Toronto, Canada, August 7-11, 1978.
[42] P. Savic and G.T. Boult. The fluid flow associated with the impact of liquid drops with solid surfaces. Proceedings of Heat Transfer Fluid Mechanics Institution, 43-84, 1957.
[43] S.E. Hinkle. Water drop kinetic energy and momentum measurement considerations. Applied Engineering in Agriculture, 5(3):386–391, 1989. doi: 10.13031/2013.26532.
[44] C.D. Stow and R.D. Stainer. The physical products of a splashing water drop. Journal of Meteorological Society of Japan, 55(5):518–532, 1977.
[45] Z. Levin and P.V. Hobbs. Splashing of water drops on solid and wetted surfaces, Hydrodynamics and charge separation. Philosophical Transactions of the Royal Society A Mathematical, Physical and Engineering Sciences, 269(1200):555–585, 1971. doi: 10.1098/rsta.1971.0052.
[46] C.D. Stow, M.G. Hadfield. An experimental investigation of fluid flow resulting from the impact of a water drop with an unyielding dry surface. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 37(1755):419–441, 1981. doi: 10.1098/rspa.1981.0002.
[47] C. Mundo, M. Sommerfeld, and C. Tropea. Droplet-wall collisions: Experimental studies of the deformation and breakup process. I nternational Journal of Multiphase Flow, 21(2):151–173, 1995. doi: 10.1016/0301-9322(94)00069-V.
[48] M. Bussmann, S. Chandra, and J. Mostaghimi. Modeling the splash of a droplet impacting a solid surface. Physics of Fluids, 12(12):3121–3132, 2000. doi: 10.1063/1.1321258.
[49] L. Xu, W.W. Zhang, and S.R. Nagel. Drop splashing on a dry smooth surface. Physical Review Letters, 94(18):184505, 2005. doi: 10.1103/PhysRevLett.94.184505.
[50] B.T. Helenbrook and C.F. Edwards. Quasi-steady deformation and drag of uncontaminated liquid drops. International Journal of Multiphase Flow, 28(10):1631–1657, 2002. doi: 10.1016/S0301-9322(02)00073-3.
[51] J.Q. Feng. A deformable liquid drop falling through a quiescent gas at terminal velocity. Journal of Fluid Mechanics, 658:438–462, 2010. doi: 10.1017/S0022112010001825.
[52] J.Q. Feng and K.V. Beard. Raindrop shape determined by computing steady axisymmetric solutions for Navier-Stokes equations. Atmospheric Research, 101(1–2):480–491, 2011. doi: 10.1016/j.atmosres.2011.04.012.
[53] J. Han and G. Tryggvason. Secondary breakup of axisymmetric liquid drops. I. Acceleration by a constant body force. Physics of Fluids, 11(12):3650–3667, 1999. doi: 10.1063/1.870229.
[54] J. Han and G. Tryggvason. Secondary breakup of a axisymmetric liquid drops. II. Impulsive acceleration. Physics of Fluids, 13(6):1554–1565, 2001. doi: 10.1063/1.1370389.
[55] P. Khare and V. Yang. Breakup of non-Newtonian liquid droplets. 44th AIAA Fluid Dynamics Conference, Atlanta, USA, 16-20 June 2014. doi: 10.2514/6.2014-2919.
[56] M. Sussman and E.G. Puckett. A Coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows. Journal of Computational Physics, 162(2):301–337, 2000. doi: 10.1006/jcph.2000.6537.
[57] R. Scardovelli and S. Zaleski. Direct numerical simulation of free-surface and interfacial flow. Annual Review of Fluid Mechanics, 31:567–603, 1999. doi: 10.1146/annurev.fluid.31.1.567.
[58] S. Shin and D. Juric. Simulation of droplet impact on a solid surface using the level contour reconstruction method. Journal of Mechanical Science and Technology, 23:2434–2443, 2009. doi: 10.1007/s12206-009-0621-z.
[59] M. García Pérez and E. Vakkilainen. A comparison of turbulence models and two and three dimensional meshes for unsteady CFD ash deposition tools. Fuel, 237:806–811, 2019. doi: 10.1016/j.fuel.2018.10.066.
[60] M. Mezhericher, A. Levy, and I. Borde. Modeling of droplet drying in spray chambers using 2D and 3D computational fluid dynamics. Drying Technology, 27(3):359–370, 2009. doi: 10.1080/07373930802682940.
[61] S. Afkhami and M. Bussmann. Height functions for applying contact angles to 2D VOF simulations. International Journal for Numerical Methods in Fluids, 57(4):453-472, 2008. doi: 10.1002/fld.1651.
[62] J. Zheng, J. Wang, Y. Yu, and T. Chen. Hydrodynamics of droplet impingement on a thin horizontal wire. Mathematical Problems in Engineering, 2018:9818494, 2018. doi: 10.1155/2018/9818494.
[63] J. Thalackottore Jose and J.F. Dunne. Numerical simulation of single-droplet dynamics, vaporization, and heat transfer from impingement onto static and vibrating surfaces. Fluids, 5(4):188, 2020. doi: 10.3390/fluids5040188.
[64] H. Liu. Science and Engineering of Droplets: Fundamentals and Applications. Noyes Publications, USA, 1999.

[1] L.F. Cabeza, A. Castell, C. Barreneche, A. de Gracia, and A. Fernández. Materials used as PCM in thermal energy storage in buildings: A review. Renewable and Sustainable Energy Reviews, 15(3):1675–1695, 2011. doi: 10.1016/j.rser.2010.11.018.
[2] K. Nedjem, M. Teggar, K.A.R. Ismail, and D. Nehari. Numerical investigation of charging and discharging processes of a shell and tube nano-enhanced latent thermal storage unit. Journal of Thermal Science and Engineering Applications, 12(2):021021, 2020. doi: 10.1115/1.4046062.
[3] K. Hosseinzadeh, M.A. Efrani Moghaddam, A. Asadi, A.R. Mogharrebi, and D.D. Ganji. Effect of internal fins along with hybrid nano-particles on solid process in star shape triplex latent heat thermal energy storage system by numerical simulation. Renewable Energy, 154:497–507, 2020. doi: 10.1016/j.renene.2020.03.054.
[4] M.M. Joybari, S. Seddegh, X. Wang, and F. Haghighat. Experimental investigation of multiple tube heat transfer enhancement in a vertical cylindrical latent heat thermal energy storage system. Renewable Energy,} 140:234–244, 2019. doi: 10.1016/j.renene.2019.03.037.
[5] A.A. Al-Abidi, S. Mat, K. Sopian, M.Y. Sulaiman, and A.T. Mohammad. Internal and external fin heat transfer enhancement technique for latent heat thermal energy storage in triplex tube heat exchangers. Applied Thermal Engineering, 53(1):147–156, 2013. doi: 10.1016/j.applthermaleng.2013.01.011.
[6] X. Yang, Z. Lu, Q. Bai, Q. Zhang, L. Jin, and J. Yan. Thermal performance of a shell-and-tube latent heat thermal energy storage unit: Role of annular fins. Applied Energy, 202:558–570, 2017. doi: 10.1016/j.apenergy.2017.05.007.
[7] C. Zhao, M. Opolot, M. Liu, F. Bruno, S. Mancin, and K. Hooman. Numerical study of melting performance enhancement for PCM in an annular enclosure with internal-external fins and metal foams. International Journal of Heat and Mass Transfer, 150:119348, 2020. doi: 10.1016/j.ijheatmasstransfer.2020.119348.
[8] M. Longeon, A. Soupart, J.-F. Fourmigué, A. Bruch, and P. Marty. Experimental and numerical study of annular PCM storage in the presence of natural convection. Applied Energy, 112:175–184, 2013. doi: 10.1016/j.apenergy.2013.06.007.
[9] S. Seddegh, S.S.M. Tehrani, X. Wang, F. Cao, and R.A. Taylor. Comparison of heat transfer between cylindrical and conical vertical shell-and-tube latent heat thermal energy storage systems. Applied Thermal Engineering, 130:1349–1362, 2018. doi: 10.1016/j.applthermaleng.2017.11.130.
[10] I. Al Siyabi, S. Khanna, T. Mallick, and S. Sundaram. An experimental and numerical study on the effect of inclination angle of phase change materials thermal energy storage system. Journal of Energy Storage, 23:57–68, 2019. doi: 10.1016/j.est.2019.03.010.
[11] S. Sebti, S. Khalilarya, I. Mirzaee, S. Hosseinizadeh, S. Kashani, and M. Abdollahzadeh. A numerical investigation of solidification in horizontal concentric annuli filled with nano-enhanced phase change material (NEPCM). World Applied Sciences Journal, 13(1):9–15, 2011.
[12] N. Dhaidan, J. Khodadadi, T.A. Al-Hattab, and S. Al-Mashat. Experimental and numerical investigation of melting of NePCM inside an annular container under a constant heat flux including the effect of eccentricity. International Journal of Heat and Mass Transfer, 67:455–468, 2013. doi: 10.1016/j.ijheatmasstransfer.2013.08.002.
[13] Q. Ren, F. Meng, and P. Guo. A comparative study of PCM melting process in a heat pipe-assisted LHTES unit enhanced with nanoparticles and metal foams by immersed boundary-lattice Boltzmann method at pore-scale. International Journal of Heat and Mass Transfer, 121:1214–1228, 2018. doi: 10.1016/j.ijheatmasstransfer.2018.01.046.
[14] C. Nie, J. Liu, and S. Deng. Effect of geometric parameter and nanoparticles on PCM melting in a vertical shell-tube system. Applied Thermal Engineering, 184:116290, 2020. doi: 10.1016/j.applthermaleng.2020.116290.
[15] M. Gorzin, M.J. Hosseini, M. Rahimi, and R. Bahrampoury. Nano-enhancement of phase change material in a shell and multi-PCM-tube heat exchanger. Journal of Energy Storage, 22:88–97, 2019. doi: 10.1016/j.est.2018.12.023.
[16] M. Khatibi, R. Nemati-Farouji, A. Taheri, A. Kazemian, T. Ma, and H. Niazmand. Optimization and performance investigation of the solidification behavior of nano-enhanced phase change materials in triplex-tube and shell-and-tube energy storage units. Journal of Energy Storage, 33:102055, 2020. doi: 10.1016/j.est.2020.102055.
[17] P. Manoj Kumar, K. Mylsamy, and P.T. Saravanakumar. Experimental investigations on thermal properties of nano-SiO ₂/paraffin phase change material (PCM) for solar thermal energy storage applications. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 42(19):2420–2433, 2020. doi: 10.1080/15567036.2019.1607942.
[18] P. Manoj Kumar, K. Mylsamy, K. Alagar, and K. Sudhakar. Investigations on an evacuated tube solar water heater using hybrid-nano based organic phase change material. International Journal of Green Energy, 17(13):872–883, 2020. doi: 10.1080/15435075.2020.1809426.
[19] S. Ebadi, S.H. Tasnim, A.A. Aliabadi, and S. Mahmud. Melting of nano-PCM inside a cylindrical thermal energy storage system: Numerical study with experimental verification. Energy Conversion and Management, 166:241–259, 2018. doi: 10.1016/j.enconman.2018.04.016.
[20] J.M. Mahdi and E.C. Nsofor. Solidification enhancement of PCM in a triplex-tube thermal energy storage system with nanoparticles and fins. Applied Energy, 211:975–986, 2018. doi: 10.1016/j.apenergy.2017.11.082.
[21] M.J. Hosseini, A.A. Ranjbar, K. Sedighi, and M. Rahimi. A combined experimental and computational study on the melting behavior of a medium temperature phase change storage material inside shell and tube heat exchanger. International Communications in Heat and Mass Transfer, 39(9):1416–1424, 2012. doi: 10.1016/j.icheatmasstransfer.2012.07.028.
[22] S. Harikrishnan, K. Deepak, and S. Kalaiselvam. Thermal energy storage behavior of composite using hybrid nanomaterials as PCM for solar heating systems. Journal of Thermal Analysis and Calorimetry, 115:1563–1571, 2014. doi: 10.1007/s10973-013-3472-x.
[23] ANSYS. Fluent. (2017), Copyright 2017 SAS IP, Inc.
[24] Z. Khan, Z.A. Khan, and P. Sewell. Heat transfer evaluation of metal oxides based nano-PCMs for latent heat storage system application. International Journal of Heat and Mass Transfer, 144:118619, 2019. doi: 10.1016/j.ijheatmasstransfer.2019.118619.
[25] J.C. Maxwell. Electricity and Magnetism. Clarendon Press, Oxford, 1873.
[26] S. Ghadikolaei, K. Hosseinzadeh, and D.D. Ganji. Investigation on three dimensional squeezing flow of mixture base fluid (ethylene glycol-water) suspended by hybrid nanoparticle (Fe ₃O ₄-Ag) dependent on shape factor. Journal of Molecular Liquids, 262:376–388, 2018. doi: 10.1016/j.molliq.2018.04.094.
[27] S.S. Ghadikolaei, M. Yassari, H. Sadeghi, K. Hosseinzadeh, and D.D. Ganji. Investigation on thermophysical properties of TiO ₂–Cu/H ₂O hybrid nanofluid transport dependent on shape factor in MHD stagnation point flow. Powder Technology, 322:428–438, 2017. doi: 10.1016/j.powtec.2017.09.006.
[28] A.D. Brent, V.R. Voller, and K. Reid. Enthalpy-porosity technique for modeling convection-diffusion phase change: application to the melting of a pure metal. Numerical Heat Transfer, 13(3):297–318, 1988. doi: 10.1080/10407788808913615.
[29] S.V. Patankar. Numerical Heat Transfer and Fluid Flow. CRC Press, 1980.
[30] M.L. Benlekkam, D. Nehari, and N. Cheriet. Numerical investigation of latent heat thermal energy storage system. Recueil de Mécanique, 3:229-235, 2018. doi: 10.5281/zenodo.1490505.
[31] M.A. Kibria, M.R. Anisur, M.H. Mahfuz, R. Saidur, and I.H.S.C. Metselaar. Numerical and experimental investigation of heat transfer in a shell and tube thermal energy storage system. International Communications in Heat and Mass Transfer, 53:71–78, 2014. doi: 10.1016/j.icheatmasstransfer.2014.02.023.
[32] M.J. Hosseini, M. Rahimi, and R. Bahrampoury. Experimental and computational evolution of a shell and tube heat exchanger as a PCM thermal storage system. International Communications in Heat and Mass Transfer, 50:128–136, 2014. doi: 10.1016/j.icheatmasstransfer.2013.11.008.

[1] S. Gross and E.W. Abel. A finite element analysis of hollow stemmed hip prostheses as a means of reducing stress shielding of the femur. Journal of Biomechanics, 34(8):995–1003, 2001. doi: 10.1016/s0021-9290(01)00072-0.
[2] D. Lin, Q. Li, W. Li, S. Zhou, and M.V. Swain. Design optimization of functionally graded dental implant for bone remodeling. Composites Part B: Engineering, 40(7):668–675, 2009. doi: 10.1016/j.compositesb.2009.04.015.
[3] G. Jin, M. Takeuchi, S. Honda, T. Nishikawa, and H. Awaji. Properties of multilayered mullite/Mo functionally graded materials fabricated by powder metallurgy processing. Materials Chemistry and Physics, 89(2-3):238–243, 2005. doi: 10.1016/j.matchemphys.2004.03.031.
[4] E. Yılmaz, A. Gökçe, F. Findik, H.O. Gulsoy, and O. İyibilgin. Mechanical properties and electrochemical behavior of porous Ti-Nb biomaterials. Journal of the Mechanical Behavior of Biomedical Materials, 87:59–67, 2018. doi: 10.1016/j.jmbbm.2018.07.018.
[5] A.T. Şensoy. M. Çolak, I. Kaymaz, and F. Findik. Optimal material selection for total hip implant: a finite element case study. Arabian Journal for Science and Engineering, 44:10293--10301, 2019. doi: 10.1007/s13369-019-04088-y.
[6] T.A. Enab and N.E. Bondok. Material selection in the design of the tibia tray component of cemented artificial knee using finite element method. Materials and Design, 44:454–460, 2013. doi: 10.1016/j.matdes.2012.08.017.
[7] H. Weinans, R.Huiskes, and H.J. Grootenboer. The behavior of adaptive bone-remodeling simulation models. Journal of Biomechanics, 25(12):1425–1441, 1992. doi: 10.1016/0021-9290(92)90056-7.
[8] J.A. Simões and A.T. Marques. Design of a composite hip femoral prosthesis. Materials & Design, 26(5):391–401, 2005. doi: 10.1016/j.matdes.2004.07.024.
[9] S. Tyagi and S.K. Panigrahi. Transient analysis of ball bearing fault simulation using finite element method. Journal of The Institution of Engineers (India): Series C, 95:309–318, 2014. doi: 10.1007/s40032-014-0129-x.
[10] I.S. Jalham. Computer-aided quality function deployment method for material selection. International Journal of Computer Applications in Technology, 26((4):190–196, 2006. doi: 10.1504/IJCAT.2006.010764.
[11] E. Karana, P. Hekkert, and P. Kandachar. Material considerations in product design: A survey on crucial material aspects used by product designers. Materials & Design, 29(6):1081–1089, 2008. doi: 10.1016/j.matdes.2007.06.002.
[12] M.F. Ashby. Materials Selection in Mechanical Design. Butterworth-Heinemann, Oxford, 1995.
[13] C. Vezzoli and E. Manzini. Environmental complexity and designing activity. In: Design for Environmental Sustainability, pages 215–217. Springer, London, 2008. doi: 10.1007/978-1-84800-163-3_11.
[14] M. Kutz. Handbook of Materials Selection. John Wiley & Sons, New York, 2002.
[15] R.V. Rao and B.K. Patel. A subjective and objective integrated multiple attribute decision making method for material selection. Materials & Design, 31(10):4738–4747, 2010. doi: 10.1016/j.matdes.2010.05.014.
[16] X.F. Zha. A web-based advisory system for process and material selection in concurrent product design for a manufacturing environment. The International Journal of Advanced Manufacturing Technology, 25:233–243, 2005. doi: 10.1007/s00170-003-1838-0.
[17] F. Giudice, G. La Rosa, and A. Risitano. Materials selection in the Life-Cycle Design process: a method to integrate mechanical and environmental performances in optimal choice. Materials & Design, 26(1):9–20, 2005. doi: 10.1016/j.matdes.2004.04.006.
[18] F. Findik and K. Turan. Materials selection for lighter wagon design with a weighted property index method. Materials & Design, 37:470–477, 2012. doi: 10.1016/j.matdes.2012.01.016.
[19] M. İpek, İ.H. Selvi, F. Findik, O. Torkul, and I.H. Cedimoğlu. An expert system based material selection approach to manufacturing. Materials & Design, 47:331–340, 2013. doi: 10.1016/j.matdes.2012.11.060.
[20] J.A. Basurto-Hurtado, G.I. Perez-Soto, R.A. Osornio-Rios, A. Dominguez-Gonzalez, and L.A. Morales-Hernandez. A new approach to modeling the ductile cast iron microstructure for a finite element analysis. Arabian Journal for Science and Engineering, 44:1221–1231, 2019. doi: 10.1007/s13369-018-3465-y.
[21] E. Yılmaz, F. Kabataş, A. Gökçe, and F. Fındık. Production and characterization of a bone-like porous Ti/Ti-hydroxyapatite functionally graded material. Journal of Materials Engineering and Performance, 29:6455--6467, 2020. doi: 10.1007/s11665-020-05165-2.
[22] E. Yılmaz, A. Gökçe, F. Findik, and H.Ö. Gulsoy. Assessment of Ti–16Nb– xZr alloys produced via PIM for implant applications. Journal of Thermal Analysis and Calorimetry, 134:7–14, 2018. doi: 10.1007/s10973-017-6808-0.
[23] H.F. El-Sheikh, B.J. MacDonald, and M.S.J. Hashmi. Material selection in the design of the femoral component of cemented total hip replacement. Journal of Materials Processing Technology, 122(2-3):309–317, 2002. doi: 10.1016/S0924-0136(01)01128-1.
[24] T.S. Rubak, S.W. Svendsen, K. Søballe, and P. Frost. Total hip replacement due to primary osteoarthritis in relation to cumulative occupational exposures and lifestyle factors: a nationwide nested case–control study. Arthritis Care & Research, 66(10):1496–1505. doi: 10.1002/acr.22326.
[25] İ. Çelik and H. Eroğlu. Selection application of material to be used in hip prosthesis production with analytic hierarchy process. Materials Science & Engineering Technology, 48(11):1125–1132, 2017. doi: 10.1002/mawe.201700046.
[26] A. Aherwar, A. Patnaik, M. Bahraminasab, and A. Singh. Preliminary evaluations on development of new materials for hip joint femoral head. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 233(5):885–899, 2019. doi: 10.1177/1464420717714495.
[27] A. Hafezalkotob and A. Hafezalkotob. Comprehensive MULTIMOORA method with target-based attributes and integrated significant coefficients for materials selection in biomedical applications. Materials & Design, 87:949–959, 2015. doi: 10.1016/j.matdes.2015.08.087.
[28] G. Bergmann, G. Deuretzbacher, M. Heller, F. Graichen, A. Rohlmann, J. Strauss, anf G.N. Duda. Hip contact forces and gait patterns from routine activities. Journal of Biomechanics, 34(7):859–871, 2001. doi: 10.1016/s0021-9290(01)00040-9.
[29] A.Z. Şenalp, O. Kayabasi, and H. Kurtaran. Static, dynamic and fatigue behavior of newly designed stem shapes for hip prosthesis using finite element analysis. Materials and Design, 28(5):1577–1583, 2007. doi: 10.1016/j.matdes.2006.02.015.

[1] M. Abshirini, N. Soltani, and P. Marashizadeh. On the mode I fracture analysis of cracked Brazilian disc using a digital image correlation method. Optics and Lasers in Engineering, 78:99–105, 2016. doi: 10.1016/j.optlaseng.2015.10.006.
[2] M. Sahlabadi and N. Soltani. Experimental and numerical investigations of mixed-mode ductile fracture in high-density polyethylene. Archive of Applied Mechanics, 88(6):933–942, 2018. doi: 10.1007/s00419-018-1350-5.
[3] M.R.Y. Dehnavi, I. Eshraghi, and N. Soltani. Investigation of fracture parameters of edge Vnotches in a polymer material using digital image correlation. Polymer Testing, 32(4):778–784, 2013. doi: 10.1016/j.polymertesting.2013.03.012.
[4] N.S. Ha, V.T. Le, and S.G. Goo. Investigation of fracture properties of a piezoelectric stack actuator using the digital image correlation technique. International Journal of Fatigue, 101(1):106–111, 2017. doi: 10.1016/j.ijfatigue.2017.02.020.
[5] B. Pan. Digital image correlation for surface deformation measurement: historical developments, recent advances and future goals. Measurement Science and Technology, 29(8):082001, 2018. doi: 10.1088/1361-6501/aac55b.
[6] Y.L. Dong and B. Pan. A review of speckle pattern fabrication and assessment for digital image correlation. Experimental Mechanics, 57(8):1161–1181, 2017. doi: 10.1007/s11340-017-0283-1.
[7] N.S. Ha, T.L. Jin, N.S. Goo, and H.C. Park. Anisotropy and non-homogeneity of an Allomyrina Dichotoma beetle hind wing membrane. Bioinspiration and Biomimetics, 6(4):046003, 2011. doi: 10.1088/1748-3182/6/4/046003.
[8] T. Jin,N.S. Ha,V.T. Le,N.S. Goo, and H.C. Jeon. Thermal buckling measurement of a laminated composite plate under a uniform temperature distribution using the digital image correlation method. Composite Structures, 123:420–429, 2015. doi: 10.1016/j.compstruct.2014.12.025.
[9] T.L. Jin,N.S. Ha, andN.S. Goo.Astudy of the thermal buckling behavior of a circular aluminum plate using the digital image correlation technique and finite element analysis. Thin-Walled Structures, 77:187–197, 2014. doi: 10.1016/j.tws.2013.10.012.
[10] N.S. Ha, V.T. Le, and N.S. Goo. Thermal strain measurement of austin stainless steel (SS304) during a heating-cooling process. International Journal of Aeronautical and Space Sciences, 18(2):206-214, 2017. doi: 10.5139/ijass.2017.18.2.206.
[11] N.S. Ha, H.M. Vang, andN.S. Goo. Modal analysis using digital image correlation technique: an application to artificial wing mimicking beetle’s hind wing. Experimental Mechanics, 55:989– 998, 2015. doi: 10.1007/s11340-015-9987-2.
[12] T. Sadowski and M. Knec. Application of DIC techniques for monitoring of deformation process of spr hybrid joints. Archives of Metallurgy and Materials, 58(1):119–125, 2013. doi: 10.2478/v10172-012-0161-x.
[13] W.H. Peters and W.F. Ranson. Digital imaging techniques in experimental stress analysis. Optical Engineering, 21(3):427–431, 1982. doi: 10.1117/12.7972925.
[14] W.H. Peters, W.F. Ranson, M.A. Sutton, T.C. Chu, and J. Anderson. Application of digital correlation methods to rigid body mechanics. Optical Engineering, 22(6):738–742, 1983. doi: 10.1117/12.7973231.
[15] M.A. Sutton, W.J. Wolters, W.H. Peters, W.F. Ranson, and S.R. McNeill. Determination of displacements using an improved digital correlation method. Image and Vision Computing, 1(3)133–139, 1983. doi: 10.1016/0262-8856(83)90064-1.
[16] T.C. Chu, W.F. Ranson, and M.A. Sutton. Applications of digital-image-correlation techniques to experimental mechanics. Experimental Mechanics, 25(3):232–244, 1985. doi: 10.1007/BF02325092.
[17] J.S. Lyons, J. Liu, and M.A. Sutton. High-temperature deformation measurements using digitalimage correlation. Experimental Mechanics, 36(1):64–70, 1996. doi: 10.1007/BF02328699.
[18] T.A. Berfield, J.K. Patel, R.G. Shimmin, P.V. Braun, J. Lambros, and N.R. Sottos. Micro- and nanoscale deformation measurement of surface and internal planes via digital image correlation. Experimental Mechanics, 47(1):51–62, 2007. doi: 10.1007/s11340-006-0531-2.
[19] Y. Dong, H. Kakisawa, and Y. Kagawa. Development of microscale pattern for digital image correlation up to 1400°C. Optics and Lasers in Engineering, 68:7–15, 2015. doi: 10.1016/j.optlaseng.2014.12.003.
[20] T. Niendorf, C. Burs, D. Canadinc, and H.J. Maier. Early detection of crack initiation sites in TiAl alloys during low-cycle fatigue at high temperatures utilizing digital image correlation. International Journal of Materials Research, 100(4):603–608, 2009. doi: 10.3139/146.110064.
[21] M.A. Sutton, X. Ke, S.M. Lessner, M. Goldbach, M. Yost, F. Zhao, and H.W. Schreier. Strain field measurements on mouse carotid arteries using microscopic three-dimensional digital image correlation. Journal of Biomedical Materials Research Part A, 84A(1):178–190, 2007. doi: 10.1002/jbm.a.31268.
[22] A.D. Kammers and S. Daly. Self-assembled nanoparticle surface patterning for improved digital image correlation in a scanning electron microscope. Experimental Mechanics, 53(8):1333–1341, 2013. doi: 10.1007/s11340-013-9734-5.
[23] K.N. Jonnalagadda, I. Chasiotis, S. Yagnamurthy, J. Lambros, J. Pulskamp, R. Polcawich, and M Dubey. Experimental investigation of strain rate dependence of nanocrystalline Pt films. Experimental Mechanics, 50(1):25–35, 2010. doi: 10.1007/s11340-008-9212-7.
[24] W.A. Scrivens, Y. Luo, M.A. Sutton, S.A. Collette, M.L. Myrick, P. Miney, P.E. Colavita, A.P. Reynolds, and X. Li. Development of patterns for digital image correlation measurements at reduced length scales. Experimental Mechanics, 47(1):63–77, 2007. doi: 10.1007/s11340-006-5869-y.
[25] N. Li, M.A. Sutton, X. Li, and H.W. Schreier. Full-field thermal deformation measurements in a scanning electron microscope by 2D digital image correlation. Experimental Mechanics, 48(5):635–646, 2008. doi: 10.1007/s11340-007-9107-z.
[26] F. Di Gioacchino and J.Q. da Fonseca. Plastic strain mapping with sub-micron resolution using digital image correlation. Experimental Mechanics, 53(5):743–754, 2013. doi: 10.1007/s11340-012-9685-2.
[27] P. Reu. All about speckles: contrast. Experimental Techniques, 39(1):1–2, 2015. doi: 10.1111/ext.12126.
[28] P. Reu. All about speckles: speckle density. Experimental Techniques, 39(3):1–2, 2015. doi: 10.1111/ext.12161.
[29] P. Reu. All about speckles: aliasing. Experimental Techniques, 38(5):1–3, 2014. doi: 10.1111/ext.12111.
[30] P. Reu. All about speckles: speckle size measurement. Experimental Techniques, 38(6):1–2, 2014. doi: 10.1111/ext.12110.
[31] B. Pan, H. Xie, Z. Wang, K. Qian, and Z. Wang. Study on subset size selection in digital image correlation for speckle patterns. Optics Express, 16(10):7037–7048, 2008. doi:
10.1364/OE.16.007037.
[32] B.Wang and B. Pan. Random errors in digital image correlation due to matched or overmatched shape functions. Experimental Mechanics, 55(9):1717–1727, 2015. doi: 10.1007/s11340-015- 0080-7.
[33] B. Pan, K. Qian, H. Xie, and A. Asundi. Two-dimensional digital image correlation for inplane displacement and strain measurement: a review. Measurement Science and Technology, 20(6):062001, 2009. doi: 10.1088/0957-0233/20/6/062001.
[34] H. Haddadi and S. Belhabib. Use of rigid-body motion for the investigation and estimation of the measurement errors related to digital image correlation technique. Optics and Lasers in Engineering, 46(2):185–196, 2007. doi: 10.1016/j.optlaseng.2007.05.008.

[1] J.A. Matts and D.H. McCoy. A graphical firing table model and a comparison of the accuracy of three utilization schemes. Report No. BRL-MR-2035, Army Ballistic Research Lab., Aberdeen Proving Ground, MD, U.S., April 1970.
[2] H.L. Reed Jr. Firing table computations on the ENIAC. In Proceeding of the 1952 ACM national meeting (Pittsburgh), pages 103-106, Pennsylvania, USA, 2 May, 1952. doi: 10.1145/609784.609796.
[3] E.R. Dickinson. The production of firing tables for cannon artillery. Report No. BRL-R-1371, Army Ballistic Research Lab., Aberdeen Proving Ground, MD, U.S., November 1967.
[4] S. Gorn and N.L. Juncosa. On the computational procedures for firing and bombing tables. Report No. BRL-R-889, Army Ballistic Research Lab., Aberdeen Proving Ground, MD, U.S., November 1954.
[5] C. Niekerk, and W. Rossouw. A proposed format for firing tables of a series of carrier projectiles possessing ballistic similarity with a HE projectile. In Proceeding of the 20th International Symposium on Ballistics, pages 187–194, Orlando, USA, 23–27 September, 2002.
[6] S.A. Ortac, U. Durak, U. Kutluay, K. Kucuk, and M.C. Candan. NABK based next generation ballistic table toolkit. In Proceeding of the 23rd International Symposium on Ballistics, pages 765–774, Tarragona, Spain, 16–20 April, 2007.
[7] A.J. Sowa. NATO shareable software developing into true suite supporting national operational fire control systems. In Proceeding of the 24th International Symposium on Ballistics, pages 126–133, Louisiana, USA, 22–26 September, 2008.
[8] Z. Leciejewski, T. Zawada, P. Kowalczuk, J. Szymonik, and P. Czyronis. Selected ballistic aspects of fire control system designed to anti-aircraft gun. In Proceeding of the 28th International Symposium on Ballistics, pages 655–665, Atlanta, USA, 22–26 September, 2014.
[9] NATO. The Modified Point Mass and five Degrees of Freedom Trajectory Models. Standard No. STANAG-4355, NATO Standardization Agency, Belgium, April 2009.
[10] M. Khalil, X. Rui, Q. Zha, H. Yu, and H. Hendy. Projectile impact point prediction based on self-propelled artillery dynamics and doppler radar measurements. Advances in Mechanical Engineering, 2013:53913, 2013. doi: 10.1155/2013/153913.
[11] L. Baranowski. Feasibility analysis of the modified point mass trajectory model for the need of ground artillery fire control systems. Journal of Theoretical and Applied Mechanics, 51(3):511–522, 2013.
[12] M. Khalil, X. Rui, and H. Hendy. Discrete time transfer matrix method for projectile trajectory prediction. Journal of Aerospace Engineering, 28(2):04014057, 2015. doi: 10.1061/(ASCE)AS.1943- 5525.0000381.
[13] L. Baranowski. Effect of the mathematical model and integration step on the accuracy of the results of computation of artillery projectile flight parameters. Bulletin of the Polish Academy of Sciences: Technical Sciences, 61(2):475–484, 2013. doi: 10.2478/bpasts-2013-0047.
[14] A. Szklarski, R. Głębocki, and M. Jacewicz. Impact point prediction guidance parametric study for 155 mm rocket assisted artillery projectile with lateral thrusters. Archive of Mechanical Engineering, 67(1):31–56, 2020. doi: 10.24425/ame.2020.131682.
[15] M. Aldoegre. Comparison Between Trajectory Models for Firing Table Application. MSc. Thesis, North-West University, Potchefstroom, South Africa, 2019.
[16] C. Donneaud, R. Cayzac and P. Champigny. Recent developments on aeroballistics of yawing and spinning projectiles: Part II: free flight tests. In Proceeding of the 20th International Symposium on Ballistics, pages 655–665, Orlando, USA, 23–27 September, 2002.
[17] A. Dupuis, C. Berner, and V. Fleck. Aerodynamic characteristics of a long-range spinning artillery shell: Part 1: from aeroballistic range free-flight tests. In Proceeding of the 21st International Symposium on Ballistics, Adelaide, Australia, 19–23 April, 2004.
[18] T. Brown, T. Harkins, M. Don, R. Hall, J. Garner, and B. Davis. Development and demonstration of a new capability for aerodynamic characterization of medium caliber projectiles. In Proceedings of the 28th International Symposium on Ballistics, pages 655–665, Atlanta, USA, 22–26 September, 2014.
[19] W. Zhou. An improved hybrid extended kalman filter based drag coefficient estimation for projectiles. In Proceedings of the 30th International Symposium on Ballistics, pages 80–91, California, USA, 11–15 September, 2017.
[20] M. Albisser, S. Dobre, C. Decrocq, F. Saada, B. Martinez, and P. Gnemmi. Aerodynamic characterization of a new concept of long range projectiles from free flight data. In Proceeding of the 30th International Symposium on Ballistics, pages 256–267, California, USA, 11–15 September, 2017.
[21] A. Ishchenko, V. Burkin, V. Faraponov, L. Korolkov, E. Maslov, A. Diachkovskiy, A. Chupashev, and A. Zykova. Determination of extra trajectory parameters of projectile layout motion. Journal of Physics: Conference Series, 919:012010, 2017, 1-5. doi: 10.1088/1742-6596/919/1/012010.
[22] G. Surdu, I. Vedinaş, G. Slămnoiu, and Ş. Pamfil. Projectile’s drag coefficient evaluation for small finite differences of his geometrical dimensions using analytical methods. In: International Conference of Scientific Paper (AFASES 2015), Brasov, Romania, 28–30 May, 2015.
[23] R.L. McCoy. Modern Exterior Ballistics: The Launch and Flight Dynamics of Symmetric Projectiles, 2nd ed., Schiffer Publishing, 2009.
[24] R. H. Whyte. SPIN-73 an Updated Version of the SPINNER Computer Program. Report No. TR-4588, Armament Systems Dept., VT, U.S., November 1973.
[25] W. Yingbin. The application of ballistic filtering theory in the production of firing tables. Journal of Ballistics, 7(1):65–70, 1995. (in Chinese)
[26] W. Liang, B. Jiang, and Y. Sa. The application of simple regression method in producing the curve of accommodation coefficient in test for firing table. Journal of of Shanxi Datong University (Natural Science Edition), 26(1):23–25, 2010. (in Chinese)
[27] C. Xinjun. A study of fitting method for making ground artillery firing tables. Journal of Ballistics, 9(2):76–79, 1997. (in Chinese)
[28] W.-Q. Huang. A series of base functions for global analytical approach to firing table. Applied Mathematics and Mechanics, 2(5):575–579, 1981. doi: 10.1007/bf01895460.
[29] N.P. Roberts. Ballistic analysis of firing table data for 155mm, M825 smoke projectile. Report No. BRL-MR-3865, Army Ballistic Research Lab., Aberdeen Proving Ground, MD, U.S., September 1990.
[30] S. Wu, Q. Kang, L. Fu, and X. Jinxiang. A study on comparing test and its application on the firing table design. Journal of Ballistics, 15(4):22–26, 2003. (in Chinese)
[31] S. Floroff and B. Salatino. 120-MM Ammunition Feasibility Assessment for Light Artillery. Report No. ARFSD TR 99002, U.S Army Armament Reseach, Development and Engineering Center, NJ, USA, March 2000.
[32] D.L. Johnson, B.C. Roberts, and W.W. Vaughan. Reference and standard atmosphere models. In Proceedings of the 10th Conference on Aviation, Range and Aerospace Meteorology, Boston, USA, 13–16 May, 2002.
[33] V. Cech and J. Jevicky. Improved theory of generalized meteo-ballistic weighting factor functions and their use. Defence Technology, 12(3):242–254, 2016. doi: 10.1016/j.dt.2016.01.009.
[34] V. Cech and J. Jevicky. Improved theory of projectile trajectory reference heights as characteristics of meteo-ballistic sensitivity functions. Defence Technology, 13(3):177–187, 2017. doi: 10.1016/j.dt.2017.04.001.
[35] G.E. Wood. Test Design Plan (TDP) for the Production Qualification Testing (PQT) of the 81mm M984/M983 High Explosive (HE) Cartridges. Report No. AD-A257 403, U.S Army Materiel Systems Analysis Activity, Aberdeen Proving Ground, MD, U.S., October 1992.
[36] W. Haifeng, W. Pengxin, W. Long, and D. Lijie. Discussion on the revision of artillery standard firing conditions of our army. Journal of Projectiles, Rockets, Missiles and Guidance, 37(4):153–156, 2017. (in Chinese)
[37] FT-122-2A18: Firing Tables for Cannon, 122mm Howitzer, 2A18. Former Soviet Union, 1968.
[38] S. Karel and B. Martin. Conversions of METB3 meteorological messages into the METEO11 format. In Proceedings of the 2017 International Conference on Military Technologies (ICMT), pages 278-284, Brno, Czech Republic, 31 May - 2 Jun, 2017. doi: 10.1109/MILTECHS.2017.7988770.
[39] FT-155-AM-2: Firing Tables for Cannon, 155mm Howitzer, M185. US Department of the Army, 1983.
[40] Manual of the ICAO Standard Atmosphere: Extended to 80 Kilometres. International Civil Aviation Organization, 1993.
[41] K. Šilinger, L. Potužák, and J. Šotnar. Conversion of the METCM into the METEO-11. In Proceedings of the 13th International Conference on Instrumentation, Measurement, Circuits And Systems (IMCAS '14), pages 212–218, Istanbul, Turkey, 15–17 December, 2014.
[42] Š. Karel, I. Jan, and P. Ladislav. Composition of the METEO11 meteorological message according to abstract of a measured meteorological data. In Proceedings of the 2017 International Conference on Military Technologies (ICMT), pages 194–199, Brno, Czech Republic, 31 May - 2 Jun, 2017. doi: 10.1109/MILTECHS.2017.7988755.
[43] NATO. Adoption of Standard Ballistic Meteorological Message. Standard No. STANAG 4061, NATO Standardization Agency, Belgium, October 2000.
[44] B. Karpov and L. Schmidt. The Aerodynamic Properties of the 155-mm Shell M101 from Free flight Range Tests of Full Scale and 1/12 Scale Models. Report No. BRL-MR-1582, Army Ballistic Research Lab., Aberdeen Proving Ground, MD, U.S., June 1964.
[45] M. Khalil, H. Abdalla, and O. Kamal. Dispersion analysis for spinning artillery projectile. In Proceeding of the 13th International Conference on Aerospace Sciences and Aviation Technology, pages 1-12, Cairo, Egypt, 26–28 May, 2009. doi: 10.21608/asat.2009.23740.

[1] S.V. Joshi, L.T. Drzal, A.K Mohanty, and S. Arora. Are natural fiber composites environmentally superior to glass fiber reinforced composites? Composites Part A: Applied Science and Manufacturing, 35(3):371–376, 2004. doi: 10.1016/j.compositesa.2003.09.016.
[2] P. Wambua, J. Ivens .and I.Verpoest. Natural fibers: can they replace glass in fiber reinforced plastics? Composites Science and Technology, 63(9):1259–1264, 2003. doi: 10.1016/S0266-3538(03)00096-4.
[3] D.B. Dittenber and H.V.S. GangaRao. Critical review of recent publications on use of natural composites in infrastructure. Composites Part A: Applied Science and Manufacturing, 43(8):1419–1429, 2012. doi: 10.1016/j.compositesa.2011.11.019.
[4] A. Stamboulis, C.A. Baillie, and T. Peijs. Effects of environmental conditions on mechanical and physical properties of flax fibers. Composites Part A: Applied Science and Manufacturing, 32(8):1105–1115, 2001. doi: 10.1016/S1359-835X(01)00032-X.
[5] L. Pil, F. Bensadoun, J. Pariset, and I. Verpoest. Why are designers fascinated by flax and hemp fiber composites? Composites Part A: Applied Science and Manufacturing, 83:193–205, 2016. doi: 10.1016/j.compositesa.2015.11.004.
[6] H.Y. Cheung, M.P. Ho, K.T. Lau, F. Cardona, And D. Hui. Natural fiber-reinforced composites for bioengineering and environmental engineering applications. Composites Part B: Engineering, 40(7):655–663, 2009. doi: 10.1016/j.compositesb.2009.04.014.
[7] M.I. Misnon, Md M. Islam, J.A. Epaarachchi, and K.T. Lau. Potentiality of utilising natural textile materials for engineering composites applications. Materials & Design, 59:359–368, 2014. doi: 10.1016/j.matdes.2014.03.022.
[8] T. Gurunathan, S. Mohanty, and S.K. Nayak. A review of the recent developments in biocomposites based on natural fibers and their application perspectives. Composites Part A: Applied Science and Manufacturing, 77:1–25, 2015. doi: 10.1016/j.compositesa.2015.06.007.
[9] H.L. Bos, M.J.A. Van Den Oever, and O.C.J.J. Peters. Tensile and compressive properties of flax fibers for natural fiber reinforced composites. Journal of Materials Science, 37:1683–1692, 2002. doi: 10.1023/A:1014925621252.
[10] C. Baley. Analysis of the flax fibers tensile behavior and analysis of the tensile stiffness increase. Composites Part A: Applied Science and Manufacturing, 33(7):939–948, 2002. doi: 10.1016/S1359-835X(02)00040-4.
[11] C. Baley, M. Gomina, J. Breard, A. Bourmaud, and P. Davies. Variability of mechanical properties of flax fibers for composite reinforcement. A review. Industrial Crops and Products, 145:111984, 2020. doi: 10.1016/j.indcrop.2019.111984.
[12] I. El Sawi, H. Bougherara, R. Zitoune, and Z. Fawaz. Influence of the manufacturing process on the mechanical properties of flax/epoxy composites. J ournal of Biobased Materials and Bioenergy, 8(1):69–76, 2014. doi: 10.1166/jbmb.2014.1410.
[13] K. Strohrmann and M. Hajek. Bilinear approach to tensile properties of flax composites in finite element analyses. Journal of Materials Science, 54:1409–1421, 2019. doi: 10.1007/s10853-018-2912-1.
[14] Z. Mahboob, Y. Chemisky, F. Meraghni, and H. Bougherara. Mesoscale modelling of tensile response and damage evolution in natural fiber reinforced laminates. Composites Part B: Engineering, 119:168–183, 2017. doi: 10.1016/j.compositesb.2017.03.018.
[15] Z. Mahboob, I. El Sawi, R. Zdera, Z. Fawaz, and H. Bougherara. Tensile and compressive damaged response in Flax fiber reinforced epoxy composites. Composites Part A: Applied Science and Manufacturing, 92:118–133, 2017. doi: 10.1016/j.compositesa.2016.11.007.
[16] C. Nicolinco, Z. Mahboob, Y. Chemisky, F. Meraghni, D. Oguamanam, and H. Bougherara. Prediction of the compressive damage response of flax-reinforced laminates using a mesoscale framework. Composites Part A: Applied Science and Manufacturing, 140:106153, 2021. doi: 10.1016/j.compositesa.2020.106153.
[17] R.T. Durai Prabhakaran, H. Teftegaard, C.M. Markussen, and B. Madsen. Experimental and theoretical assessment of flexural properties of hybrid natural fiber composites. Acta Mechanica, 225:2775–2782, 2014. doi: 10.1007/s00707-014-1210-5.
[18] M. Fehri, A. Vivet, F. Dammak, M. Haddar, and C. Keller. A characterization of the damage process under buckling load in composite reinforced by flax fibers. Journal of Composites Science, 4(3):85, 2020. doi: 10.3390/jcs4030085.
[19] V. Gopalan, V. Suthenthiraveerappa, J.S. David, J. Subramanian,A.R. Annamalai, and C.P. Jen. Experimental and numerical analyses on the buckling characteristics of woven flax/epoxy laminated composite plate under axial compression. Polymers, 13(7):995, 2021. doi: 10.3390/polym13070995.
[20] J. Gawryluk and A. Teter. Experimental-numerical studies on the first-ply failure analysis of real, thin-walled laminated angle columns subjected to uniform shortening. Composite Structures, 269:114046, 2021. doi: 10.1016/j.compstruct.2021.114046.
[21] J. Gawryluk. Impact of boundary conditions on the behavior of thin-walled laminated angle column under uniform shortening. Materials, 14(11):2732, 2021. doi: 10.3390/ma14112732.
[22] J. Gawryluk. Post-buckling and limit states of a thin-walled laminated angle column under uniform shortening. Engineering Failure Analysis, 139:106485, 2022. doi: 10.1016/j.engfailanal.2022.106485.
[23] ABAQUS 2020 HTML Documentation, DassaultSystemes.
[24] T. Kubiak and L. Kaczmarek, Estimation of load-carrying capacity for thin-walled composite beams. Composite Structures, 119:749–756, 2015. doi: 10.1016/j.compstruct.2014.09.059.
[25] T. Kubiak, S. Samborski, and A. Teter. Experimental investigation of failure process in compressed channel-section GFRP laminate columns assisted with the acoustic emission method. Composite Structures, 133:921–929, 2015. doi: 10.1016/j.compstruct.2015.08.023.
[26] M. Urbaniak, A. Teter, and T. Kubiak. Influence of boundary conditions on the critical and failure load in the GFPR channel cross-section columns subjected to compression. Composite Structures, 134:199–208, 2015. doi: 10.1016/j.compstruct.2015.08.076.
[27] A. Teter and Z. Kolakowski. On using load-axial shortening plots to determine the approximate buckling load of short, real angle columns under compression. Composite Structures, 212:175–183, 2019. doi: 10.1016/j.compstruct.2019.01.009.
[28] A. Teter, Z. Kolakowski, and J. Jankowski. How to determine a value of the bifurcation shortening of real thin-walled laminated columns subjected to uniform compression? Composite Structures, 247, 12430, 2020 doi: 10.1016/j.compstruct.2020.112430.

[1] B. Dziegielewski and D. Baumann. Tapping alternatives: The benefits of managing urban water demands. Environment: Science and Policy for Sustainable Development, 34(9):6–41, 2010. doi: 10.1080/00139157.1992.9930929.
[2] D. Marmer. Water conservation equals energy conservation. Energy Engineering, 115(5):48–63, 2018. doi: 10.1080/01998595.2018.12027708.
[3] J.M. Burns, D.C. Burns, and J.S. Burns. Retrofitting cooling towers: estimates required to achieve the next level of CWA 316(b) compliance. In Proceedings of the ASME Power Conference, pages 25–33, 2004. doi: 10.1115/POWER2004-52051.
[4] A. Loew, P. Jaramillo, and H. Zhai. Marginal costs of water savings from cooling system retrofits: a case study for Texas power plants. Environmental Research Letters, 11(10):104004, 2016. doi: 10.1088/1748-9326/11/10/104004.
[5] A.E. Conradie and D.G. Kröger. Performance evaluation of dry-cooling systems for power plant applications. Applied Thermal Engineering, 16(3):219–232, 1996. doi: 10.1016/1359-4311(95)00068-2.
[6] A.E. Conradie, J.D. Buys, and D.G. Kröger. Performance optimization of dry-cooling systems for power plants through SQP methods. Applied Thermal Engineering, 18(1-2):25–45, 1998. doi: 10.1016/S1359-4311(97)00020-3.
[7] J.D. Buys and D.G. Kröger. Dimensioning heat exchangers for existing dry cooling towers. Energy Conversion and Management, 29(1):63–71, 1989. doi: 10.1016/0196-8904(89)90014-9.
[8] Z. Zou, Z. Guan, H. Gurgenci, and Y. Lu. Solar enhanced natural draft dry cooling tower for geothermal power applications. Solar Energy, 86(9):2686–2694, 2012. doi: 10.1016/j.solener.2012.06.003.
[9] S. Bagheri and M. Nikkhoo. Investigation of the optimum location for adding two extra Heller-type cooling towers in Shazand power plant. Proceedings of the 17th IAHR International Conference on Cooling Tower and Heat, pages. 74–83, Australia, 2015.
[10] W. Peng and O.K. Sadaghiani. Presentation of an integrated cooling system for enhancement of cooling capability in Heller cooling tower with thermodynamic analyses and optimization. International Journal of Refrigeration, 131:786–802, 2021. doi: 10.1016/j.ijrefrig.2021.07.016.
[11] M.A. Ardekani, F. Farhani, and M. Mazidi. Effects of cross wind conditions on efficiency of Heller dry cooling tower. Experimental Heat Transfer, 28(4):344–353, 2015. doi: 10.1080/08916152.2014.883449.
[12] A. Jahangiri, A. Borzooee, and E. Armoudli. Thermal performance improvement of the three aligned natural draft dry cooling towers by wind breaking walls and flue gas injection under different crosswind conditions. International Journal of Thermal Sciences, 137:288–298, 2019. doi: 10.1016/j.ijthermalsci.2018.11.028.
[13] A.R. Seifi, O.A. Akbari, A.A. Alrashed, F. Afshari, G.A.S. Shabani, R. Seifi, M. Goodarzi, and F. Pourfattah. Effects of external wind breakers of Heller dry cooling system in power plants. Applied Thermal Engineering, 129: 1124–1134, 2018. doi: 10.1016/j.applthermaleng.2017.10.118.
[14] R.A. Kheneslu, A. Jahangiri, and M. Ameri. Interaction effects of natural draft dry cooling tower (NDDCT) performance and 4E (energy, exergy, economic and environmental) analysis of steam power plant under different climatic conditions. Sustainable Energy Technologies and Assessments, 37:100599, 2020. doi: 10.1016/j.seta.2019.100599.
[15] A. Jahangiri and F. Rahmani. Power production limitations due to the environmental effects on the thermal effectiveness of NDDCT in an operating powerplant. Applied Thermal Engineering, 141:444–455, 2018. doi: 10.1016/j.applthermaleng.2018.05.108.
[16] A.D. Samani. Combined cycle power plant with indirect dry cooling tower forecasting using artificial neural network. Decision Science Letters, 7:131–142, 2018. doi: 10.5267/j.dsl.2017.6.004.
[17] T.L. Bergman, F.P. Incropera, D.P. DeWitt, and A.S. Lavine. Fundamentals of Heat and Mass Transfer. John Wiley & Sons, 2011.
[18] Archive of Isfahan Mohammad Montazeri Power Station. Isfahan, Iran, 1984.
[19] H. Ahmadikia and G. Iravani. Numerical and analytical study of natural dry cooling tower in a steam power plant. Journal of Advanced Materials in Engineering (Esteghlal), 26(1):183–195, 2007. (in Persian).
[20] H.G. Zavaragh, M.A. Ceviz, and M.T.S. Tabar. Analysis of windbreaker combinations on steam power plant natural draft dry cooling towers. Applied Thermal Engineering, 99:550–559, 2016. doi: 10.1016/j.applthermaleng.2016.01.103.
[21] K.F. Reinschmidt and R. Narayanan. The optimum shape of cooling towers. Computers & Structures, 5(5-6):321–325, 1975. doi: 10.1016/0045-7949(75)90039-5.
[22] Isfahan Thermal Power Plant documents, No. C.583 and C.749, Islam Abad Power Plant, Isfahan, Iran, 1988.
[23] I.H. Shames. Mechanics of Fluids. 4th ed. McGraw-Hill, New York, 2003.
[24] C.R.F. Azevedo and A. Sinátora. Erosion-fatigue of steam turbine blades. Engineering Failure Analysis, 16(2):2290–2303, 2009. doi: 10.1016/j.engfailanal.2009.03.007.
[25] H. Kim. Crack evaluation of the fourth stage blade in a low-pressure steam turbine. Engineering Failure Analysis, 18(3):907–913, 2011. doi: 10.1016/j.engfailanal.2010.11.004.
[26] L.K. Bhagi, P. Gupta, and V. Rastogi. Fractographic investigations of the failure of L-1 pressure steam turbine blade. Case Studies in Engineering Failure Analysis, 1(2):72–78, 2013. doi: 10.1016/j.csefa.2013.04.007.

[1] L.F.M. da Silva, P.J.C. das Neves, R.D. Adams, and J.K. Spelt. Analytical models of adhesively bonded joints. Part I: Literature survey. International Journal of Adhesion and Adhesives, 29(3):319–330, 2009. doi: 10.1016/j.ijadhadh.2008.06.005.
[2] E.H. Wong and J. Liu. Interface and interconnection stresses in electronic assemblies – A critical review of analytical solutions. Microelectronics Reliability, 79:206–220, 2017. doi: 10.1016/j.microrel.2017.03.010.
[3] S. Budhe, M.D. Banea, S. de Barros, and L.F.M. da Silva. An updated review of adhesively bonded joints in composite materials. International Journal of Adhesion and Adhesives, 72:30–42, 2017. doi: 10.1016/j.ijadhadh.2016.10.010.
[4] K.P. Barakhov and I.M. Taranenko. Influence of joint edge shape on stress distribution in adhesive film. In: M. Nechyporuk, V. Pavlikov, D. Kritskiy (eds) Integrated Computer Technologies in Mechanical Engineering – 2021. ICTM 2021. Lecture Notes in Networks and Systems, 367:123–132, Springer, Cham, 2022. doi: 10.1007/978-3-030-94259-5_12.
[5] H. Lee, S. Seon, S. Park, R. Walallawita, and K. Lee. Effect of the geometric shapes of repair patches on bonding strength. The Journal of Adhesion, 97(3):1–18, 2019. doi: 10.1080/00218464.2019.1649660.
[6] F. Ramezani, M.R. Ayatollahi, A. Akhavan-Safar, and L.F.M. da Silva. A comprehensive experimental study on bi-adhesive single lap joints using DIC technique. International Journal of Adhesion and Adhesives, 102:102674, 2020. doi: 10.1016/j.ijadhadh.2020.102674.
[7] Ya.S. Karpov. Jointing of high-loaded composite structural components. Part 2. Modeling of stress-strain state. Strength of Materials, 38(5):481–491, 2006. doi: 10.1007/s11223-006-0067-9.
[8] J. Kupski and S. Teixeira de Freitas. Design of adhesively bonded lap joints with laminated CFRP adherends: Review, challenges and new opportunities for aerospace structures. Composite Structures, 268:113923, 2021. doi: 10.1016/j.compstruct.2021.113923.
[9] S. Amidi and J. Wang. An analytical model for interfacial stresses in double-lap bonded joints. The Journal of Adhesion, 95(11):1031–1055, 2018. doi: 10.1080/00218464.2018.1464917.
[10] H. Kumazawa and T. Kasahara. Analytical investigation of thermal and mechanical load effects on stress distribution in adhesive layer of double-lap metal-composite bonded joints. Advanced Composite Materials, 28(4):425–444, 2019. doi: 10.1080/09243046.2019.1575028.
[11] S. Kurennov and N. Smetankina. Stress-strain state of a double lap joint of circular form. Axisymmetric model. In: M. Nechyporuk, V. Pavlikov D. Kritskiy (eds) Integrated Computer Technologies in Mechanical Engineering – 2021. ICTM 2021. Lecture Notes in Networks and Systems, 367:36–46, Springer, Cham, 2022. doi: 10.1007/978-3-030-94259-5_4.
[12] S. E. Stapleton, B. Stier, S. Jones, A. Bergan, I. Kaleel, M. Petrolo, E. Carrera, and B.A. Bednarcyk. A critical assessment of design tools for stress analysis of adhesively bonded double lap joints. Mechanics of Advanced Materials and Structures, 28(8):791–811, 2019. doi: 10.1080/15376494.2019.1600768.
[13] R.H. Kaye and M. Heller. Through-thickness shape optimisation of bonded repairs and lap-joints. I nternational Journal of Adhesion and Adhesives, 22(1):7–21, 2002. doi: 10.1016/s0143-7496(01)00029-x.
[14] S. Kurennov, K. Barakhov, I. Taranenko, and V. Stepanenko. A genetic algorithm of optimal design of beam at restricted sagging. Radioelectronic and Computer Systems, 1:83–91, 2022. doi: 10.32620/reks.2022.1.06.
[15] V.S. Symonov, I.S. Karpov, and J. Juračka. Optimization of a panelled smooth composite shell with a closed cross-sectional contour by using a genetic algorithm. Mechanics of Composite Materials, 49(5):563–570, 2013. doi: 10.1007/s11029-013-9372-0.
[16] N.S. Kulkarni, V.K. Tripathi. Variable thickness approach for finding minimum laminate thickness and investigating effect of different design variables on its performance. Archive of Mechanical Engineering, 65(4):527–551, 2018. doi: 10.24425/ame.2018.125441.
[17] H. Ejaz, A. Mubashar, I.A. Ashcroft, E. Uddin, and M. Khan. Topology optimisation of adhesive joints using non-parametric methods. International Journal of Adhesion and Adhesives, 81:1–10, 2018. doi: 10.1016/j.ijadhadh.2017.11.003.
[18] H.L. Groth and P. Nordlund. Shape optimization of bonded joints. International Journal of Adhesion and Adhesives, 11(4):204–212, 1991. doi: 10.1016/0143-7496(91)90002-y.
[19] R.Q. Rodríguez, R. Picelli, P. Sollero, and R. Pavanello. Structural shape optimization of bonded joints using the ESO method and a honeycomb-like mesh. J ournal of Adhesion Science and Technology, 28(14-15):1451–1466, 2014. doi: 10.1080/01694243.2012.698112.
[20] E.G. Arhore, M. Yasaee, and I. Dayyani. Comparison of GA and topology optimization of adherend for adhesively bonded metal composite joints. International Journal of Solids and Structures, 226-227:111078, 2021. doi: 10.1016/j.ijsolstr.2021.111078.
[21] S. Kumar, and de A. de Tejada Alvarez. Modeling of geometrically graded multi-material single-lap joints. 56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. doi: 10.2514/6.2015-1885.
[22] S.S. Kurennov: Refined mathematical model of the stress state of adhesive lap joint: experimental determination of the adhesive layer strength criterion. Strength of Materials, 52:779–789, 2020. doi: 10.1007/s11223-020-00231-5.
[23] P. Zou, J. Bricker, and W. Uijttewaal. Optimization of submerged floating tunnel cross section based on parametric Bézier curves and hybrid backpropagation – genetic algorithm. Marine Structures, 74:102807, 2020. doi: 10.1016/j.marstruc.2020.102807.
[24] O. Coskun and H.S.Turkmen. Multi-objective optimization of variable stiffness laminated plates modeled using Bézier curves. Composite Structures, 279:114814, 2022. doi: 10.1016/j.compstruct.2021.114814.
[25] S. Kumar and P.C. Pandey. Behaviour of bi-adhesive joints. Journal of Adhesion Science and Technology, 24(7):1251–1281, 2010. doi: 10.1163/016942409x12561252291982.
[26] Ö. Öz and H. Özer. On the von Mises elastic stress evaluations in the bi-adhesive single-lap joint: a numerical and analytical study. Journal of Adhesion Science and Technology, 28(21):2133–2153, 2014. doi: 10.1080/01694243.2014.948110.
[27] E. Selahi. Elasticity solution of adhesive tubular joints in laminated composites with axial symmetry. Archive of Mechanical Engineering, 65(3):441–456, 2018. doi: 10.24425/124491.
[28] K. Barakhov, D. Dvoretska, and O. Poliakov. One-dimensional axisymmetric model of the stress state of the adhesive joint. In: M. Nechyporuk, V. Pavlikov, D. Kritskiy (eds) I ntegrated Computer Technologies in Mechanical Engineering – 2020. ICTM 2020. Lecture Notes in Networks and Systems, 188:310–319, Springer, Cham, 2021. doi: 10.1007/978-3-030-66717-7_26.
[29] S. Kurennov, N. Smetankina, V. Pavlikov, D. Dvoretskaya, V. Radchenko. Mathematical model of the stress state of the antenna radome joint with the load-bearing edging of the skin cutout. In: D.D. Cioboată, (ed.) International Conference on Reliable Systems Engineering (ICoRSE) – 2021. ICoRSE 2021. Lecture Notes in Networks and Systems, 305:287–295, Springer, Cham, 2022. doi: 10.1007/978-3-030-83368-8_28.

[1] M.I. Sarigecili and I.D. Akcali. Design of a uniform ice cutting device. In Proceeding of the 2nd Cilicia International Symposium on Engineering and Technology (CISET 2019), pages 311–317, Mersin, Turkey, 10-12 October, 2019.
[2] İ.D. Akçalı and M.A. Arıoğlu. Geometric design of slider-crank mechanisms for desirable slider positions and velocities. Forschung im Ingenieurwesen, 75:61–71, 2011. doi: 10.1007/s10010-011-0134-7.
[3] M.I. Sarigecili and I.D. Akcali. Development of constant output-input force ratio in slider-crank mechanisms. Inverse Problems in Science and Engineering, 27(5):565–588, 2019. doi: 10.1080/17415977.2018.1470625.
[4] F. Ahmad, A.L. Hitam, K. Hudha, and H. Jamaluddin. Position tracking of slider crank mechanism using PID controller optimized by Ziegler Nichol’s method. Journal of Mechanical Engineering and Technology, 3(2):27–41, 2011.
[5] C.D. Lee, C.W. Chuang, and C.C. Kao. Apply fuzzy PID rule to PDA based control of position control of slider crank mechanisms. In Proceeding of the IEEE Conference on Cybernetics and Intelligent Systems, pages 508–513, Singapore, 1-3 December, 2004. doi: 10.1109/ICCIS.2004.1460467.
[6] P.A. Simionescu. Optimum synthesis of oscillating slide actuators for mechatronic applications. Journal of Computational Design and Engineering, 5(2):215–231, 2018. doi: 10.1016/j.jcde.2017.09.002.
[7] R.R. Bulatović and S.R. Djordjević. Optimal synthesis of a four-bar linkage by method of controlled deviation. Theoretical and Applied Mechanics, 31(3-4):265–280, 2004. doi: 10.2298/TAM0404265B.
[8] A. Arshad, P. Cong, A.A.E. Elmenshawy, and I. Blumbergs. Design optimization for the weight reduction of 2-cylinder reciprocating compressor crankshaft. Archive of Mechanical Engineering, 68(4):449–471, 2021. doi: 10.24425/ame.2021.139311.
[9] J. Beckers, T. Verstraten, B. Verrelst, F. Contino, and J.V. Mierlo. Analysis of the dynamics of a slider-crank mechanism locally actuated with an act-and-wait controller. Mechanism and Machine Theory, 159:104253, 2021. doi: 10.1016/j.mechmachtheory.2021.104253.
[10] A. Antoniou and W-S. Lu. Practical Optimization. Algorithms and Engineering Applications. Springer, New York, 2007. doi: 10.1007/978-0-387-71107-2.
[11] S. Wu, J. Akroyd, S. Mosbach, G. Brownbridge, O. Parry, V. Page, W. Yang, and M. Kraft. Efficient simulation and auto-calibration of soot particle processes in Diesel engines. Applied Energy, 262:114484, 2020. doi: 10.1016/j.apenergy.2019.114484.
[12] L. Mazouz, S.A. Zidi, A. Hafaifa, S. Hadjeri, and T. Benaissa. Optimal regulators conception for wind turbine PMSG generator using Hooke Jeeves method. Periodica Polytechnica Electrical Engineering and Computer Science, 63(3):151–158, 2019. doi: 10.3311/PPee.13548.
[13] L. Benasla, A. Belmadani, and M. Rahli. Hooke-Jeeves’ method applied to a new economic dispatch problem formulation. Journal of Information Science and Engineering, 24(3):907–917, 2008.
[14] C. Li and A. Rahman. Three-phase induction motor design optimization using the modified Hooke-Jeeves method. Electric Machines & Power Systems, 18(1):1–12, 1990. doi: 10.1080/07313569008909446.
[15] L. Litvinas. A hybrid of Bayesian-based global search with Hooke–Jeeves local refinement for multi-objective optimization problems. Nonlinear Analysis: Modelling and Control, 27(3):534–555, 2022. doi: 10.15388/namc.2022.27.26558.
[16] T.M. Alkhamis and M.A. Ahmed. A modified Hooke and Jeeves algorithm with likelihood ratio performance extrapolation for simulation optimization. European Journal of Operational Research, 174(3):1802–1815, 2006. doi: 10.1016/j.ejor.2005.04.032.
[17] M.F. Tabassum, M. Saeed, N.A. Chaudhry, J. Ali, M. Farman, and S. Akram. Evolutionary simplex adaptive Hooke-Jeeves algorithm for economic load dispatch problem considering valve point loading effects. Ain Shams Engineering Journal, 12(1):1001–1015, 2021. doi: 10.1016/j.asej.2020.04.006.
[18] S.C. Chapra and R. Canale. Numerical Methods for Engineers. Sixth ed. McGraw-Hill, New York, 2010.
[19] C. Zhang, S. Hu, Y. Liu and Q. Wang. Optimal design of borehole heat exchangers based on hourly load simulation. Energy, 116(1):1180–1190, 2016. doi: 10.1016/j.energy.2016. 10.045.
[20] M.H. Heydari, Z. Avazzadeh, C. Cattani. Taylor’s series expansion method for nonlinear variable-order fractional 2D optimal control problems. Alexandria Engineering Journal, 59(6):4737–4743, 2020. doi: 10.1016/j.aej.2020.08.035.

[1] W. Muzykiewicz, Validation tests for the 6082-grade sheet in the "0" state with an account of its application for deep drawing processes. Rudy i Metale Nieżelazne, 51(7):422–427, 2006. (in Polish).
[2] A.C.S. Reddy, S. Rajesham, P.R. Reddy, and A.C. Umamaheswar. Formability: A review on different sheet metal tests for formability. AIP Conference Proceedings, 2269:030026, 2020. doi: 10.1063/5.0019536.
[3] Y. Dewang, V. Sharma, and Y. Batham. influence of punch velocity on deformation behavior in deep drawing of aluminum alloy. Journal of Failure Analysis and Prevention, 21(2):472–487, 2021. doi: 10.1007/s11668-020-01084-5.
[4] S. Bansal. Study of Deep Drawing Process and its Parameters Using Finite Element Analysis. Master Thesis, Delhi Technological University, India, 2022.
[5] E. Nghishiyeleke, M. Mashingaidze, and A. Ogunmokun, Formability characterization of aluminium AA6082-O sheet metal by uniaxial tension and Erichsen cupping tests. International Journal of Engineering and Technology, 7(4):6768–6777, 2018.
[6] J. Adamus, M. Motyka, and K. Kubiak. Investigation of sheet-titanium drawability. In: 12th World Conference on Titanium (Ti-2011), Beijing, China, 19-24 June 2011.
[7] R.R. Goud, K.E. Prasad, and S.K. Singh. formability limit diagrams of extra-deep-drawing steel at elevated temperatures. Procedia Materials Science, 6:123–128, 2014. doi: 10.1016/j.mspro.2014.07.014.
[8] R. Norz, F.R. Valencia, S. Gerke, M. Brünig, and W. Volk. Experiments on forming behaviour of the aluminium alloy AA6016. IOP Conference Series: Materials Science and Engineering, 1238(1):012023, 2022. doi: 10.1088/1757-899X/1238/1/012023.
[9] W.S. Miller, L. Zhuang, J. Bottema, A.J. Wittebrood, P. De Smet, A. Haszler, and A. Vieregge. Recent development in aluminium alloys for the automotive industry. Materials Science and Engineering: A, 280(1):37–49, 2000. doi: 10.1016/S0921-5093(99)00653-X.
[10] J.C. Benedyk. Aluminum alloys for lightweight automotive structures. In P.K. Mallick (ed.): Materials, Design and Manufacturing for Lightweight Vehicles. Woodhead Publishing, pages 79–113, 2010. doi: 10.1533/9781845697822.1.79.
[11] M. Bloeck. Aluminium sheet for automotive applications. In J. Rowe (ed.): Advanced Materials in Automotive Engineering. Woodhead Publishing Limited, pages 85–108, 2012. doi: 10.1533/9780857095466.85.
[12] N.I. Kolobnev, L.B. Ber, L.B. Khokhlatova, and D.K. Ryabov. Structure, properties and application of alloys of the Al – Mg – Si – (Cu) system. Metal Science and Heat Treatment, 53(9-10):440–444, 2012. doi: 10.1007/s11041-012-9412-8.
[13] P. Lackova, M. Bursak, O. Milkovic, M. Vojtko, and L. Dragosek, Influence of heat treatment on properties of EN AW 6082 aluminium alloy. Acta Metallurgica Slovaca, 21(1):25–34, 2015. doi: 10.12776/ams.v21i1.553.
[14] R. Prillhofer, G. Rank, J. Berneder, H. Antrekowitsch, P. Uggowitzer, and S. Pogatscher. Property criteria for automotive Al-Mg-Si sheet alloys. Materials, 7(7):5047–5068, 2014. doi: 10.3390/ma7075047.
[15] N.C.W. Kuijpers, W.H. Kool, P.T.G. Koenis, K.E. Nilsen, I. Todd, and S. van der Zwaag. Assessment of different techniques for quantification of α-Al(FeMn)Si and β-AlFeSi intermetallics in AA 6xxx alloys. Materials Characterization, 49(5):409–420, 2002. doi: 10.1016/S1044-5803(03)00036-6.
[16] G. Mrówka-Nowotnik. Influence of chemical composition variation and heat treatment on microstructure and mechanical properties of 6xxx alloys. Archives of Materials Science and Engineering, 46(2):98–107, 2010.
[17] G. Mrówka-Nowotnik, J. Sieniawski, and A. Nowotnik. Tensile properties and fracture toughness of heat treated 6082 alloy. Journal of Achievements of Materials and Manufacturing Engineering, 12(1-2):105–108, 2006.
[18] G. Mrówka-Nowotnik, J. Sieniawski, and A. Nowotnik. Effect of heat treatment on tensile and fracture toughness properties of 6082 alloy. Journal of Achievements of Materials and Manufacturing Engineering, 32(2):162–170, 2009.
[19] X. He, Q. Pan, H. Li, Z. Huang, S. Liu, K. Li, and X. Li. Effect of artificial aging, delayed aging, and pre-aging on microstructure and properties of 6082 aluminum alloy. Metals, 9(2):173, 2019. doi: 10.3390/met9020173.
[20] Z. Li, L. Chen, J. Tang, G. Zhao, and C. Zhang. Response of mechanical properties and corrosion behavior of Al–Zn–Mg alloy treated by aging and annealing: A comparative study. Journal of Alloys and Compounds, 848:156561, 2020. doi: 10.1016/j.jallcom.2020.156561.
[21] J.R. Hirsch. Automotive trends in aluminium - the European perspective. Materials Forum, 28(1):15–23, 2004.
[22] W. Moćko and Z.L. Kowalewski. Dynamic properties of aluminium alloys used in automotive industry. Journal of KONES Powertrain and Transport, 19(2):345–351, 2012.
[23] N. Kumar, S. Goel, R. Jayaganthan, and H.-G. Brokmeier. Effect of solution treatment on mechanical and corrosion behaviors of 6082-T6 Al alloy. Metallography, Microstructure, and Analysis, 4(5):411–422, 2015. doi: 10.1007/s13632-015-0219-z.
[24] M. Fujda, T. Kvackaj, and K. Nagyová. Improvement of mechanical properties for EN AW 6082 aluminium alloy using equal-channel angular pressing (ECAP) and post-ECAP aging. Journal of Metals, Materials and Minerals, 18(1):81–87, 2008.
[25] I. Torca, A. Aginagalde, J.A. Esnaola, L. Galdos, Z. Azpilgain, and C. Garcia. Tensile behaviour of 6082 aluminium alloy sheet under different conditions of heat treatment, temperature and strain rate. Key Engineering Materials, 423:105–112, 2009. doi: 10.4028/www.scientific.net/KEM.423.105.
[26] O. Çavuşoğlu, H.İ. Sürücü, S. Toros, and M. Alkan, Thickness dependent yielding behavior and formability of AA6082-T6 alloy: experimental observation and modeling. The International Journal of Advanced Manufacturing Technology, 106:4083–4091, 2020. doi: 10.1007/s00170-019-04878-6.
[27] J. Slota, I. Gajdos, T. Jachowicz, M. Siser, and V. Krasinskyi. FEM simulation of deep drawing process of aluminium alloys. Applied Computer Science, 11(4):7–19, 2015.
[28] Ö. Özdilli. An investigation of the effects of a sheet material type and thickness selection on formability in the production of the engine oil pan with the deep drawing method. International Journal of Automotive Science And Technology, 4(4):198–205, 2020. doi: 10.30939/ijastech..773926.
[29] W.T. Lankford, S.C. Snyder, and J.A. Bauscher. New criteria for predicting the press performance of deep drawing sheets. ASM Transactions Quarterly, 42:1197–1232, 1950.
[30] A.C. Sekhara Reddy, S. Rajesham, and P. Ravinder Reddy. Evaluation of limiting drawing ratio (LDR) in deep drawing by rapid determination method. International Journal of Current Engineering and Technology, 4(2):757–762, 2014.
[31] R.U. Kumar. Analysis of Fukui’s conical cup test. International Journal of Innovative Technology and Exploring Engineering, 2(2):30–31, 2013.
[32] Ł. Kuczek, W. Muzykiewicz, M. Mroczkowski, and J. Wiktorowicz. Influence of perforation of the inner layer on the properties of three-layer welded materials. Archives of Metallurgy and Materials, 64(3):991–996, 2019. doi: 10.24425/AMM.2019.129485.
[33] O. Engler and J. Hirsch. Polycrystal-plasticity simulation of six and eight ears in deep-drawn aluminum cups. Materials Science and Engineering: A, 452–453:640–651, 2007. doi: 10.1016/j.msea.2006.10.108.
[34] M. Koç, J. Culp, and T. Altan. Prediction of residual stresses in quenched aluminum blocks and their reduction through cold working processes. Journal of Materials Processing Technology, 174(1-3):342–354, 2006. doi: 10.1016/j.jmatprotec.2006.02.007.
[35] C.S.T. Chang, I. Wieler, N. Wanderka, and J. Banhart. Positive effect of natural pre-ageing on precipitation hardening in Al–0.44 at% Mg–0.38 at% Si alloy. Ultramicroscopy, 109(5):585–592, 2009. doi: 10.1016/j.ultramic.2008.12.002.
[36] S. Jin, T. Ngai, G. Zhang, T. Zhai, S. Jia, and L. Li. Precipitation strengthening mechanisms during natural ageing and subsequent artificial aging in an Al-Mg-Si-Cu alloy. Materials Science and Engineering: A, 724:53–59, 2018. doi: 10.1016/j.msea.2018.03.006.
[37] E. Ishimaru, A. Takahashi, and N. Ono. Effect of material properties and forming conditions on formability of high-purity ferritic stainless steel. Nippon Steel Technical Report. Nippon Steel & Sumikin Stainless Steel Corporation, 2010.
[38] E.H. Atzema. Formability of auto components. In R. Rana and S.B. Singh (eds.): Automotive Steels. Design, Metallurgy, Processing and Applications. Woodhead Publishing, pages 47–93, 2017. doi: 10.1016/B978-0-08-100638-2.00003-1.

[1] M. Zhang and R. Schmidt. Sensitivity analysis of an auto-correlation-function-based damage index and its application in structural damage detection. Journal of Sound and Vibration, 333(26):7352–7363, 2014. doi: 10.1016/j.jsv.2014.08.020.
[2] T.W. Kim and J.H. Kim. Eigensensitivity based optima distribution of a viscoelastic damping layer for a flexible beam. Journal of Sound and Vibration, 273(1-2):201–218, 2004. doi: 0.1016/S0022-460X(03)00479-6.
[3] F. van Keulen, R.T. Haftka, and N.H. Kim. Review of options for structural design sensitivity analysis. Part 1: Linear systems. Computer Methods in Applied Mechanics and Engineering, 194(30-33):3213–3243, 2005. doi: 0.1016/j.cma.2005.02.002.
[4] D.A. Tortorelli and P. Michaleris. Design sensitivity analysis: Overview and review. Inverse Problems in Engineering, 1(1):71–105, 1994, doi: 10.1080/174159794088027573.
[5] R.L. Fox and M.P. Kapoor. Rates of change of eigenvalues and eigenvectors. AIAA Journal, 6(12):2426–2429, 1968. doi: 10.2514/3.5008.
[6] S. Adhikari and M.I. Friswell. Eigenderivative analysis of asymmetric non-conservative systems. International Journal for Numerical Methods in Engineering, 51(6):709–733, 2001. doi: 10.1002/NME.186.
[7] R.B. Nelson. Simplified calculation of eigenvector derivatives. AIAA Journal, 14(9):1201–1205, 1976. doi: 10.2514/3.7211.
[8] M.I. Friswell and S. Adhikari. Derivatives of complex eigenvectors using Nelson’s method. AIAA Journal, 38(12):2355–2357, 2000. doi: 10.2514/2.907.
[9] S. Adhikari and M.I. Friswell. Calculation of eigenrelation derivatives for nonviscously damped systems using Nelson’s method. AIAA Journal, 44(8):1799–1806, 2006. doi: 10.2514/1.20049.
[10] L. Li, Y. Hu, X. Wang, and L. Ling. Eigensensitivity analysis of damped systems with distinct and repeated eigenvalues. Finite Elements in Analysis and Design, 72:21–34, 2013. doi: 10.1016/j.finel.2013.04.006.
[11] L. Li, Y. Hu, and X. Wang. A study on design sensitivity analysis for general nonlinear eigenproblems. Mechanical Systems and Signal Processing, 34(1-2):88–105, 2013. doi: 10.1016/j.ymssp.2012.08.011.
[12] T.H. Lee. An adjoint variable method for structural design sensitivity analysis of a distinct eigenvalue problem. KSME International Journal, 13(6):470–476, 1999. doi: 10.1007/BF02947716.
[13] T.H. Lee. Adjoint method for design sensitivity analysis of multiple eigenvalues and associated eigenvectors. AIAA Journal, 45(8):1998–2004, 2007. doi: 10.2514/1.25347.
[14] S. He, Y. Shi, E. Jonsson, and J.R.R.A. Martins. Eigenvalue problem derivatives computation for a complex matrix using the adjoint method. Mechanical Systems and Signal Processing, 185:109717, 2023. doi: 10.1016/j.ymssp.2022.109717.
[15] R. Lewandowski and M. Łasecka-Plura. Design sensitivity analysis of structures with viscoelastic dampers. Computers and Structures, 164:95–107, 2016. doi: 10.1016/j.compstruc.2015.11.011.
[16] Z. Ding, L. Li, G. Zou, and J. Kong. Design sensitivity analysis for transient response of non-viscously damped systems based on direct differentiate method. Mechanical Systems and Signal Processing, 121:322–342, 2019. doi: 10.1016/j.ymssp.2018.11.031.
[17] Z. Ding, J. Shi, Q. Gao, Q. Huang, and W.H. Liao. Design sensitivity analysis for transient responses of viscoelastically damped systems using model order reduction techniques. Structural and Multidisciplinary Optimization, 64:1501–1526, 2021. doi: 10.1007/s00158-021-02937-9.
[18] R. Haftka. Second-order sensitivity derivatives in structural analysis. AIAA Journal, 20(12):1765–1766, 1982. doi: 10.2514/3.8020.
[19] M.S. Jankovic. Exact nth derivatives of eigenvalues and eigenvectors. Journal of Guidance, Control, and Dynamics, 17(1):136–144, 1994. doi: 10.2514/3.21170.
[20] J.Y. Ding, Z.K. Pan, and L.Q. Chen. Second-order sensitivity analysis of multibody systems described by differential/algebraic equations: adjoint variable approach. International Journal of Computer Mathematics, 85(6):899–913, 2008. doi: 10.1080/00207160701519020.
[21] M. Martinez-Agirre and M.J. Elejabarrieta. Higher order eigensensitivities-based numerical method for the harmonic analysis of viscoelastically damped structures. International Journal for Numerical Methods in Engineering, 88(12):1280–1296, 2011. doi: 10.1002/nme.3222.
[22] H. Kim and M. Cho. Study on the design sensitivity analysis based on complex variable in eigenvalue problem. Finite Elements in Analysis and Design, 45:892–900, 2009. doi: 10.1016/j.finel.2009.07.002.
[23] A. Bilbao, R. Aviles, J. Aguirrebeitia, and I.F. Bustos. Eigensensitivity-based optimal damper location in variable geometry trusses. AIAA Journal, 47(3):576–591, 2009. doi: 10.2514/1.37353.
[24] R.M. Lin, J.E. Mottershead, and T.Y. Ng. A state-of-the-art review on theory and engineering applications of eigenvalue and eigenvector derivatives. Mechanical Systems and Signal Processing, 138:106536, 2020. doi: 10.1016/j.ymssp.2019.106536.
[25] R. Lewandowski, A. Bartkowiak, and H. Maciejewski. Dynamic analysis of frames with viscoelastic dampers: a comparison of dampers models. Structural Engineering and Mechanics, 41(1):113–137, 2012. doi: 10.12989/sem.2012.41.1.113.
[26] S.W. Park. Analytical modeling of viscoelastic dampers for structural and vibration control. International Journal of Solids and Structures, 38(44-45):8065–8092, 2001. doi: 10.1016/S0020-7683(01)00026-9.
[27] R. Lewandowski. Sensitivity analysis of structures with viscoelastic dampers using the adjoint variable method. Civil-Comp Proceedings, 106, 2014.
[28] J.S. Arora and J.B. Cardoso. Variational principle for shape design sensitivity analysis. AIAA Journal, 30(2):538–547, 1992. doi: 10.2514/3.10949.
[29] Z. Pawlak and R. Lewandowski. The continuation method for the eigenvalue problem of structures with viscoelastic dampers. Computers and Structures, 125:53–61, 2013. doi: 10.1016/j.compstruc.2013.04.021.
[30] R. Lewandowski and M. Baum. Dynamic characteristics of multilayered beams with viscoelastic layers described by the fractional Zener model. Archive of Applied Mechanics, 85(12):1793–1814, 2015. doi: 10.1007/s00419-015-1019-2.
[31] R. Lewandowski, P. Litewka and P. Wielentejczyk. Free vibrations of laminate plates with viscoelastic layers using the refined zig-zag theory – Part 1: Theoretical background. Composite Structures, 278:114547, 2021. doi: 10.1016/j.compstruct.2021.114547.
[32] M. Kamiński, A. Lenartowicz, M. Guminiak, and M. Przychodzki. Selected problems of random free vibrations of rectangular thin plates with viscoelastic dampers. Materials, 15(19): 6811, 2022. doi: 10.3390/ma15196811.

[1] D. Ulutan and T. Ozel. Machining induced surface integrity in titanium and nickel alloys: A review. International Journal of Machine Tools and Manufacture, 51(3):250–280, 2011. doi: 10.1016/j.ijmachtools.2010.11.003.
[2] J.P. Davim (ed.). Machining of Titanium Alloys. Springer-Verlag, Berlin, 2014. doi: 10.1007/978-3-662-43902-9.
[3] M. Motyka, W. Zaja, and J. Sieniawski. Titanium Alloys – Novel Aspects of Their Manufacturing and Processing. IntechOpen, 2019.
[4] J.P. Davim (ed.). Surface Integrity in Machining. Springer, London, 2010. doi: 10.1007/978-1-84882-874-2.
[5] K. Cheng (ed.). Machining Dynamics. Fundamentals, Applications and Practices. Springer, London, 2009. doi: 10.1007/978-1-84628-368-0.
[6] T.L. Schmitz and K.S. Smith. Machining Dynamics. Frequency Response to Improved Productivity. Springer, New York, 2009. doi: 10.1007/978-0-387-09645-2.
[7] W. Cheng and J.C. Outeiro. Modelling orthogonal cutting of Ti-6Al-4 V titanium alloy using a constitutive model considering the state of stress. The International Journal of Advanced Manufacturing Technology, 119:4329–4347, 2022. doi: 10.1007/s00170-021-08446-9.
[8] M. Sima, and T. Özel. Modified material constitutive models for serrated chip formation simulations and experimental validation in machining of titanium alloy Ti–6Al–4V. I nternational Journal of Machine Tools and Manufacture, 50(11):943–960, 2010. doi: 10.1016/j.ijmachtools.2010.08.004.
[9] V. Stupnytskyy and I. Hrytsay. Comprehensive analysis of the product’s operational properties formation considering machining technology. Archive of Mechanical Engineering, 67(2):149–167, 2020. doi: 10.24425/ame.2020.131688.
[10] V. Stupnytskyy, I. Hrytsay, and Xianning She. Finite element analysis of thermal and stress-strain state during titanium alloys machining. In: Advanced Manufacturing Processes II. Lecture Notes in Mechanical Engineering, 629–639, Springer, 2021. doi: 10.1007/978-3-030-68014-5_61.
[11] M.K. Gupta, M.E. Korkmaz, M. Sarıkaya, G.M. Krolczyk, M. Günay and S. Wojciechowski. Cutting forces and temperature measurements in cryogenic assisted turning of AA2024-T351 alloy: An experimentally validated simulation approach. Measurement, 188:110594, 2022. doi: 10.1016/j.measurement.2021.110594.
[12] Y.-P. Liu and Y. Altintas. Predicting the position-dependent dynamics of machine tools using progressive network. Precision Engineering, 73: 409–422, 2022. doi: 10.1016/j.precisioneng.2021.10.010.
[13] A. Pramanik and G. Littlefair. Machining of titanium alloy (Ti-6Al-4V)—theory to application. Machining Science and Technology, 19(1):1–49, 2015. doi: 10.1080/10910344.2014.991031.
[14] W. Cheng, J. Outeiro, J.-P. Costes, R. M’Saoubi, H. Karaouni, L. Denguir, V. Astakhov, and F. Auzenat. Constitutive model incorporating the strain-rate and state of stress effects for machining simulation of titanium alloy Ti6Al4V. Procedia CIRP, 77:344–347, 2018. doi: 10.1016/j.procir.2018.09.031.
[15] S. Wojciechowski, P. Twardowski, and M. Pelic. Cutting forces and vibrations during ball end milling of inclined surfaces. P rocedia CIRP, 14:113–118, 2014. doi: 10.1016/j.procir.2014.03.102.
[16] D. Chen, J. Chen, and H. Zhou. The finite element analysis of machining characteristics of titanium alloy in ultrasonic vibration assisted machining. Journal of Mechanical Science and Technology, 35:3601–3618, 2021. doi: 10.1007/s12206-021-0731-9.
[17] Q. Yang, Z. Liu, Z. Shi, and B. Wang. Analytical modeling of adiabatic shear band spacing for serrated chip in high-speed machining. The International Journal of Advanced Manufacturing Technology. 71:1901–1908, 2014. doi: 10.1007/s00170-014-5633-x.
[18] A.Í.S. Antonialli, A.E. Diniz, and R. Pederiva. Vibration analysis of cutting force in titanium alloy milling. International Journal of Machine Tools and Manufacture. 50(1):65–74, 2010. doi: 10.1016/j.ijmachtools.2009.09.006.
[19] G. Korendyasev. An approach to modeling self-oscillations during metal machining based on a finite-element model with small amount of computing resources. Vibroengineering PROCEDIA, 32:6–12, 2020. doi: 10.21595/vp.2020.21437.
[20] J. Klingelnberg. Dynamics of machine tools. In: Klingelnberg, J. (ed.): Bevel Gear, pages 311–320, Springer Vieweg, 2016. doi: 10.1007/978-3-662-43893-0_8.
[21] Y. Petrakov, M. Danylchenko, and A. Petryshyn. Prediction of chatter stability in turning. Eastern-European Journal of Enterprise Technologies, 5(1):58–64, 2019. doi: 10.15587/1729-4061.2019.177291.
[22] S.K. Choudhury, N.N. Goudimenko, and V.A. Kudinov. On-line control of machine tool vibration in turning. International Journal of Machine Tools and Manufacture. 37(6):801–811, 1997. doi: 10.1016/S0890-6955(96)00031-4.
[23] A. Liljerehn. Machine Tool Dynamics. A constrained state-space substructuring approach. Ph.D. Thesis, Göteborg, Sweden, 2016.
[24] G.R. Johnson and W.N. Cook. A constitutive model and data for metals subjected to large strains. High rates and high temperatures. In 7th International Symposium on Ballistics, pages 541–547, Hague, Netherlands, 19–21 April 1983.
[25] Y. Zhang, J.C. Outeiro, and T. Mabrouki. On the selection of Johnson-Cook constitutive model parameters for Ti-6Al-4V using three types of numerical models of orthogonal cutting. Procedia CIRP, 31:112–117, 2015. doi: 10.1016/j.procir.2015.03.052.
[26] D. Yan, T. Wu, Y. Liu, and Y. Gao. An efficient sparse-dense matrix multiplication on a multicore system. In 17th International Conference on Communication Technology (ICCT), pages 1880–1883, Chengdu, China, 27-30 October 2017. doi: 10.1109/ICCT.2017.8359956.
[27] M. Binder, F. Klocke, and D. Lung. Tool wear simulation of complex shaped coated cutting tools. Wear, 330–331:600–607, 2015. doi: 10.1016/j.wear.2015.01.015.
[28] D. Alleyne and P. Cawley. A two-dimensional Fourier transform method for the measurement of propagating multimode signals. The Journal of the Acoustical Society of America, 89(3):1159–1168, 1991. doi: 10.1121/1.400530.
[29] C.M. Harris and A.G. Piersol. Harris' Shock and Vibration Handbook. McGraw-Hill, 2002.
[30] S.A. Sina, H.M. Navazi, and H. Haddadpour. An analytical method for free vibration analysis of functionally graded beams. Materials and Design, 30(3):741–747, 2009. doi: 10.1016/j.matdes.2008.05.015.

[1] Z. He and L. Zhao. A simple attitude control of quadrotor helicopter based on Ziegler-Nichols rules for tuning PD parameters. The Scientific World Journal, 2014: 280180, 2014. doi: 10.1155/2014/280180.
[2] P. Jimenez, P. Lichota, D. Agudelo, and K. Rogowski. Experimental validation of total energy control system for UAVs. Energies, 13(1):14, 2020. doi: 10.3390/en13010014.
[3] C. Aoun, N. Daher, and E. Shammas. An energy optimal path-planning scheme for quadcopters in forests. 2019 IEEE 58th Conference on Decision and Control (CDC), pages 8323–8328, Nice, France, 11–13 December 2019. doi: 10.1109/CDC40024.2019.9029345.
[4] T.A. Rodrigues, J. Patrikar, A. Choudhry, J. Feldgoise, V. Arcot, A. Gahlaut, S. Lau, B. Moon, B. Wagner, H. S. Matthews, S. Scherer, and C. Samaras. In-flight positional and energy use data set of a DJI Matrice 100 quadcopter for small package delivery. Scientific Data, 8:155, 2021. doi: 10.1038/s41597-021-00930-x.
[5] F. Yacef, N. Rizoug, and L. Degaa. Energy-efficiency path planning for quadrotor UAV under wind conditions. 2020 7th International Conference on Control, Decision and Information Technologies (CoDIT), pages 1133–1138, Prague, Czech Republic, 29 June–2 July 2020. doi: 10.1109/CoDIT49905.2020.9263968.
[6] F. Yacef, O. Bouhali, M. Hamerlain, and N. Rizoug. Observer-based adaptive fuzzy backstepping tracking control of quadrotor unmanned aerial vehicle powered by Li-ion battery. Journal of Intelligent and Robotic Systems, 84(1–4):179–197, 2016. doi: 10.1007/s10846-016-0345-0.
[7] F. Yacef, N. Rizoug, O. Bouhali, and M. Hamerlain. Optimization of energy consumption for quadrotor UAV. International Micro Air Vehicle Conference and Flight Competition (IMAV) 2017, Toulouse, France, 18-21 September 2017.
[8] F. Yacef, N. Rizoug, L. Degaa, O. Bouhali, and M. Hamerlain. Trajectory optimisation for a quadrotor helicopter considering energy consumption. 2017 4th International Conference on Control, Decision and Information Technologies (CoDIT), pages 1030–1035, Barcelona, Spain, 5–7 April 2017. doi: 10.1109/CoDIT.2017.8102734.
[9] G. Jia, S. Gong, R. Guo, and M. Li. Energy consumption model of BLDC quadrotor UAVs for mobile communication trajectory planning. TechRxiv. doi: 10.36227/techrxiv.19181228.v1.
[10] F. Morbidi, R. Cano, and D. Lara. Minimum-energy path generation for a quadrotor UAV. 2016 Ieee International Conference on Robotics and Automation (ICRA), pages 1492–1498, Stockholm, Sweden, 16–21 May 2016. doi: 10.1109/ICRA.2016.7487285.
[11] S. Jee and H. Cho. Comparing energy consumption following flight pattern for quadrotor. Journal of IKEEE, 22(3):747–753, 2018. doi: 10.7471/ikeee.2018.22.3.747.
[12] C.W. Chan and T.Y. Kam. A procedure for power consumption estimation of multi-rotor unmanned aerial vehicle. Journal of Physics: Conference Series, 1509:012015, 2020. doi: 10.1088/1742-6596/1509/1/012015.
[13] Y. Wang, Y. Wang, and B. Ren. Energy saving quadrotor control for field inspection. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 52(3):1768–1777, 2020. doi: 10.1109/TSMC.2020.3037071.
[14] H. Lu, K. Chen, X.B. Zhai, B. Chen, and Y. Zhao. Tradeoff between duration and energy optimization for speed control of quadrotor unmanned aerial vehicle. 2018 IEEE Symposium on Product Compliance Engineering - Asia (ISPCE-CN), pages 1–5, Shenzhen, China, 5–7 December 2018. doi: 10.1109/ISPCE-CN.2018.8805801.
[15] N. Bezzo, K. Mohta, C. Nowzari, I. Lee, V. Kumar, and G. Pappas. Online planning for energy-efficient and disturbance-aware UAV operations. 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 5027–5033, Daejeon, Korea, 9–14 October 2016. doi: 10.1109/IROS.2016.7759738.
[16] V. Agarwal and R.R. Tewari. Improving energy efficiency in UAV attitude control using deep reinforcement learning. Journal of Scientific Research, 65(3):209–219, 2021.
[17] A. Korneyev, M. Gorobetz, I. Alps, and L. Ribickis. Adaptive traction drive control algorithm for electrical energy consumption minimisation of autonomous unmanned aerial vehicle. Electrical, Control and Communication Engineering, 15(2):62–70, 2019. doi: 10.2478/ecce-2019-0009.
[18] J.F. Roberts, J.-C. Zufferey, and D. Floreano. Energy management for indoor hovering robots. 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 1242–1247, Nice, France, 22–26 September 2008. doi: 10.1109/IROS.2008.4650856.
[19] A.S. Prasetia, R.-J. Wai, Y.-L. Wen, and Y.-K. Wang. Mission-based energy consumption prediction of multirotor UAV. IEEE Access, 7:33055–33063, 2019. doi: 10.1109/ACCESS.2019.2903644.
[20] X. Wu, J. Zeng, A. Tagliabue, and M. W. Mueller. Model-free online motion adaptation for energy-efficient flight of multicopters. Arxiv. doi: 10.48550/arXiv.2108.03807.
[21] C. Di Franco and G. Buttazzo. Energy-aware coverage path planning of UAVs. 2015 IEEE International Conference on Autonomous Robot Systems and Competitions, pages 111–117, Vila Real, Portugal, 08–10 April 2015. doi: 10.1109/ICARSC.2015.17.
[22] T. Dietrich, S. Krug, and A. Zimmermann. An empirical study on generic multicopter energy consumption profiles. 2017 Annual IEEE International Systems Conference (SysCon), pages 1–6, Montreal, QC, Canada, 24–27 April 2017. doi: 10.1109/SYSCON.2017.7934762.
[23] H.V. Abeywickrama, B.A. Jayawickrama, Y. He, and E. Dutkiewicz. Empirical power consumption model for UAVs. 2018 IEEE 88th Vehicular Technology Conference (VTC-Fall), pages 1-5, Chicago, IL, USA, 27–30 August 2018. doi: 10.1109/VTCFall.2018.8690666.
[24] R. Shivgan and Z. Dong. Energy-efficient drone coverage path planning using genetic algorithm. 2020 IEEE 21st International Conference on High Performance Switching and Routing (HPSR), pages 1–6, Newark, NJ, USA, 11–14 May 2020. doi: 10.1109/HPSR48589.2020.9098989.
[25] C. Di Franco and G. Buttazzo. Coverage path planning for UAVs photogrammetry with energy and resolution constraints. Journal of Intelligent & Robotic Systems, 83:445–462, 2016. doi: 10.1007/s10846-016-0348-x.
[26] N. Gao, Y. Zeng, J. Wang, D. Wu, C. Zhang, Q. Song, J. Qian and S. Jin. Energy model for UAV communications: Experimental validation and model generalization. China Communications, 18(7):253–264, 2021. doi: 10.23919/JCC.2021.07.020.
[27] N. Kreciglowa, K. Karydis, and V. Kumar, Energy efficiency of trajectory generation methods for stop-and-go aerial robot navigation. 2017 International Conference on Unmanned Aircraft Systems (ICUAS), pages 656–662, Miami, USA, 13–16 June 2017. doi: 10.1109/ICUAS.2017.7991496.
[28] P. Pradeep, S.G. Park, and P. Wei. Trajectory optimization of multirotor agricultural. 2018 IEEE Aerospace Conference, pages 1–7, Big Sky, USA, 3–10 March 2018. doi: 10.1109/AERO.2018.8396617.
[29] M-h. Hwang, H-R. Cha and S.Y. Jung. Practical endurance estimation for minimizing energy consumption of multirotor unmanned aerial vehicles. Energies, 11(9):2221, 2018. doi: 10.3390/en11092221.
[30] A. Abdilla, A. Richards, and S. Burrow. Power and endurance modelling of battery-powered rotorcraft. 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 675–680, Hamburg, Germany, 28 September–2 October 2015. doi: 10.1109/IROS.2015.7353445.
[31] J. Apeland, D. Pavlou, and T. Hemmingsen. Suitability Analysis of implementing a fuel cell on a multirotor drone. Journal of Aerospace Technology and Management, 12:e3220, 2020. doi: 10.5028/jatm.v12.1172.
[32] Z. Liu, R. Sengupta and A. Kurzhanskiy. A power consumption model for multi-rotor small unmanned aircraft systems. 2017 International Conference on Unmanned Aircraft Systems (ICUAS), pages 310–315, Miami, FL, USA, 13–16 June 2017. doi: 10.1109/ICUAS.2017.7991310.
[33] L. Zhang, A. Celik, S. Dang, and B. Shihada. Energy-efficient trajectory optimization for UAV-assisted IoT networks. IEEE Transactions on Mobile Computing, 21(12):4323–4337, 2022. doi: 10.1109/TMC.2021.3075083.
[34] Y. Chen, D. Baek, A. Bocca, A. Macii, E. Macii, and M. Poncino. A case for a battery-aware model of drone energy consumption. 2018 IEEE International Telecommunications Energy Conference (INTELEC), pages 1–8, Turino, Italy, 7–11 October 2018. doi: 10.1109/INTLEC.2018.8612333.
[35] [Online]. https://www.dji.com/pl/mavic-2/info, [Accessed on: 13 July 2021].
[36] National Aeronautics and Space Administration, U.S. Standard Atmosphere, 1976, Washington, D.C., 1976.
[37] P.H. Zipfel. Modeling and Simulation of Aerospace Vehicle Dynamics. American Institute of Aeronautics and Astronautics. Reston, USA, 2000.
[38] D. Allerton. Principles of Flight Simulation. John Wiley and Sons, 2009.
[39] B.L. Stevens, F.L. Lewis, and E.N. Johnson. Aircraft Control and Simulation. Dynamics, Controls Design, and Autonomous Systems. John Wiley and Sons, 2015.
[40] M. Dreier. Introduction to Helicopter and Tiltrotor Simulation. American Institute of Aeronautics and Astronautics. Reston, USA, 2007.
[41] P. Lichota, F. Dul, and A. Karbowski. System identification and LQR controller design with incomplete state observation for aircraft trajectory tracking. Energies, 13(20):5354, 2020. doi: 10.3390/en13205354.
[42] M. Abzug. Computational Flight Dynamics. American Institute of Aeronautics and Astronautics. Reston, USA, 1998.
[43] S.K. Phang, C. Cai, B.M. Chen, and T.H. Lee. Design and Mathematical Modeling of a 4-Standard-Propeller (4SP) Quadrotor. In: Proceedings of the 10th World Congress on Intelligent Control and Automation, pages 3270–3275, Beijing, China, 6–8 July 2012. doi: 10.1109/WCICA.2012.6358437.
[44] J. Sanketi, R. Kasliwal, S. Raghavan, and S. Awan. Modelling and simulation of a multi-quadcopter concept. International Journal of Engineering Research & Technology (IJERT), 5(10):566–571, 2016.
[45] N.M. Salma and K. Osman. Modelling and PID control system integration for quadcopter DJIF450 attitude stabilization. Indonesian Journal of Electrical Engineering and Computer Science, 19(3):1235–1244. doi: 10.11591/ijeecs.v19.i3.pp1235-1244.
[46] P. Pounds, R. Mahony, and P. Corke. Modelling and control of a large quadrotor robot. Control Engineering Practice, 18(7):691–699, 2010. doi: 10.1016/j.conengprac.2010.02.008.
[47] Z. Benić, P. Piljek, and D. Kotarski. Mathematical modelling of unmanned aerial vehicles with four rotors. Interdisciplinary Description of Complex Systems, 14(1):88–100, 2016. doi: 10.7906/indecs.14.1.9.
[48] I.M. Salameh, E.M. Ammar, and T.A. Tutunji. Identification of quadcopter hovering using experimental data. 2015 IEEE Jordan Conference on Applied Electrical Engineering and Computing Technologies (AEECT), pages 1–6, Amman, Jordan, 3–5 November 2015. doi: 10.1109/AEECT.2015.7360559.
[49] [Online]. Available: https://airdata.com [Accessed on: 27 January 2022].
[50] W. Jaafar and H. Yanikomeroglu. Dynamics of quadrotor UAVs for aerial networks: An energy perspective. Arxiv, 2019. doi: 10.48550/arXiv.1905.06703.
[51] P. Pradeep and P. Wei. Energy efficient arrival with rta constraint for multirotor eVTOL in urban air mobility. Journal of Aerospace Information Systems, 16(7):1–15, 2019. doi: 10.2514/1.I010710.
[52] F. Morbidi and D. Pisarski. Practical and accurate generation of energy-optimal trajectories for a planar quadrotor. 2021 IEEE International Conference on Robotics and Automation (ICRA), pages 355–361, Xi'an, China, 30 May–5 June 2021. doi: 10.1109/ICRA48506.2021.9561395.
[53] T. Mesbahi, N. Rizoug, P. Bartholomeus, and P. Le Moigne. Li-ion battery emulator for electric vehicle applications. 2013 IEEE Vehicle Power and Propulsion Conference (VPPC), pages 1–8, Beijing, China, 15–18 October 2013. doi: 10.1109/VPPC.2013.6671688.
[54] F. Li, W.-P. Song, B.-F. Song, and H. Zhang, Dynamic modeling, simulation, and parameter study of electric quadrotor system of Quad-Plane UAV in wind disturbance environment. International Journal of Micro Air Vehicles, 13:1–23, 2021. doi: 10.1177/17568293211022211.
[55] O. Tremblay and L-A. Dessaint. Experimental validation of a battery dynamic model for ev applications. World Electric Vehicle Journal, 3(2):289–298, 2009. doi: 10.3390/wevj3020289.
[56] S.M. Mousavi and M. Nikdel. Various battery models for various simulation studies and applications. Renewable and Sustainable Energy Reviews, 32:477–485, 2014. doi: 10.1016/j.rser.2014.01.048.
[57] S.M. Azam. Battery Identification, Prediction and Modelling. Master Thesis, Colorado State University, Fort Collins, Colorado, USA, 2018.
[58] E. Raszmann, K. Baker, Y. Shi, and D. Christensen. Modeling stationary lithium-ion batteries for optimization and predictive control. 2017 IEEE Power and Energy Conference at Illinois (PECI), pages 1–7, Champaign, IL, USA, 23–24 February 2017. doi: 10.1109/PECI.2017.7935755.
[59] H. Hemi, N.K. M’Sirdi, and A. Naamane. A new proposed shepherd model of a li-ion open circuit battery based on data fitting. IMAACA 2019, Lisbon, Portugal, 2019.
[60] [Online]: https://www.mathworks.com/help/physmod/sps/powersys/ref/battery.html. [Accessed on: 9 October 2021].
[61] H. Hinz. Comparison of lithium-ion battery models for simulating storage systems in distributed power generation. Inventions, 4(3):41, 2019. doi: 10.3390/inventions4030041.
[62] L.E. Romero, D.F. Pozo, and J.A. Rosales. Quadcopter stabilization by using PID controllers. Maskana, 5:175–186, 2016.
[63] A. Rodić and G. Mester. The modeling and simulation of an autonomous quad-rotor microcopter in a virtual outdoor scenario. A cta Polytechnica Hungarica, 8(4):107–122, 2011.
[64] A.L. Salih, M. Moghavvemi, H.A.F. Mohamed, and K.S. Gaeid. Flight PID controller design for a UAV quadrotor. Scientific Research and Essays, 5(23):3660–3667, 2010.
[65] V. Brito, A. Brito, L.B. Palma, and P. Gil. Quadcopter control approaches and performance analysis. In Proceedings of the 15th International Conference on Informatics in Control, Automation and–Robotics - Volume 1: ICINCO, pages 86–93, Porto, Portugal, 29–31 July, 2018. doi: 10.5220/0006902600960103.
[66] [Online]. Available: https://www.dji.com/pl/downloads/products/mavic-2. [Accessed on: 7 August 2021].
[67] M. Jacewicz, M. Żugaj, R. Głębocki, and P. Bibik. Quadrotor model for energy consumption analysis. Energies, 15(19):7136, 2022. doi: 10.3390/en15197136.
[68] M. Jacewicz, P. Lichota, D. Miedziński, and R. Głębocki. Study of model uncertainties influence on the impact point dispersion for a gasodynamicaly controlled projectile. Sensors, 22(9):3257, 2022. doi: 10.3390/s22093257.
[69] M. Jacewicz, R. Głębocki, and R. Ożóg. Monte-Carlo based lateral thruster parameters optimization for 122 mm rocket. In: R. Szewczyk, C. Zieliński, M. Kaliczyńska (eds) Automation 2020: Towards Industry of the Future. AUTOMATION 2020. Advances in Intelligent Systems and Computing, volume 1140, pages 125–134, Springer, 2020. doi: 10.1007/978-3-030-40971-5_12.
[70] C. Coulombe, J.-F. Gamache, A. Mohebbi, C. Abolfazl, U. Chouinard and S. Achiche, Applying robust design methodology to a quadrotor drone. In Proceedings of the 21st International Conference on Engineering Design (ICED17), Vol 4: Design Methods and Tools, Vancouver, Canada, 21–25 August 2017.