Search results

Filters

  • Journals
  • Authors
  • Keywords
  • Date
  • Type

Search results

Number of results: 6
items per page: 25 50 75
Sort by:
Download PDF Download RIS Download Bibtex

Abstract

Discontinuous coefficients in the Poisson equation lead to the weak discontinuity in the solution, e.g. the gradient in the field quantity exhibits a rapid change across an interface. In the real world, discontinuities are frequently found (cracks, material interfaces, voids, phase-change phenomena) and their mathematical model can be represented by Poisson type equation. In this study, the extended finite element method (XFEM) is used to solve the formulated discontinuous problem. The XFEM solution introduce the discontinuity through nodal enrichment function, and controls it by additional degrees of freedom. This allows one to make the finite element mesh independent of discontinuity location. The quality of the solution depends mainly on the assumed enrichment basis functions. In the paper, a new set of enrichments are proposed in the solution of the Poisson equation with discontinuous coefficients. The global and local error estimates are used in order to assess the quality of the solution. The stability of the solution is investigated using the condition number of the stiffness matrix. The solutions obtained with standard and new enrichment functions are compared and discussed.

Go to article

Bibliography

[1] T.P. Fries and H.G. Matthies. Classification and overview of meshfree methods. Informatikbericht Nr.: 2003-3. Technical University Braunschweig, Brunswick, Germany, 2004.
[2] M.A. Schweitzer. Meshfree and generalized finite element methods. Postdoctoral dissertation. Mathematisch–Naturwissenschaftlichen Fakultat der Rheinischen Friedrich-Wilhelms-Universitat, Bonn, Germany, 2008.
[3] Vinh Phu Nguyen, C. Anitescu, S. Bordas, and T. Rabczuk. Isogeometric analysis: An overview and computer implementation aspects. Mathematics and Computers in Simulation, 117:89–116, 2015. doi: 10.1016/j.matcom.2015.05.008.
[4] T. Belytschko and T. Black. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 45(5):601–620, 1999.
[5] R. Merle and J. Dolbow. Solving thermal and phase change problems with the eXtended finite element method. Computational Mechanics, 28(5):339–350, 2002. doi: 10.1007/s00466-002-0298-y.
[6] J. Chessa, P. Smolinski, and T. Belytschko. The extended finite element method (XFEM) for solidification problems. International Journal for Numerical Methods in Engineering, 53(8):1959–1977, 2002. doi: 10.1002/nme.386.
[7] P. Stapór. The XFEM for nonlinear thermal and phase change problems. International Journal of Numerical Methods for Heat & Fluid Flow, 25(2):400–421, 2015. doi: 10.1108/HFF-02-2014-0052.
[8] J.Y. Wu and F.B. Li. An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks. Computer Methods in Applied Mechanics and Engineering, 295:77–107, 2015. doi: 10.1016/j.cma.2015.06.018.
[9] P. Hansbo, M.G. Larson, and S. Zahedi. A cut finite element method for a stokes interface problem. Applied Numerical Mathematics, 85:90–114, 2014. doi: 10.1016/j.apnum.2014.06.009.
[10] E. Wadbro, S. Zahedi, G. Kreiss, and M. Berggren. A uniformly well-conditioned, unfitted Nitsche method for interface problems. BIT Numerical Mathematics, 53(3):791–820, 2013. doi: 10.1007/s10543-012-0417-x.
[11] I. Babuška and U. Banerjee. Stable generalized finite element method (SGFEM). Computer Methods in Applied Mechanics and Engineering, 201:91–111, 2012. doi: 10.1016/j.cma.2011.09.012.
[12] K. Kergrene, I. Babuška, and U. Banerjee. Stable generalized finite element method and associated iterative schemes; application to interface problems. Computer Methods in Applied Mechanics and Engineering, 305:1–36, 2016. doi: 10.1016/j.cma.2016.02.030.
[13] G. Zi and T. Belytschko. New crack-tip elements for XFEM and applications to cohesive cracks. International Journal for Numerical Methods in Engineering, 57(15):2221–2240, 2003. doi: 10.1002/nme.849.
[14] G. Ventura, E. Budyn, and T. Belytschko. Vector level sets for description of propagating cracks in finite elements. International Journal for Numerical Methods in Engineering, 58(10):1571–1592, 2003. doi: 10.1002/nme.829.
[15] J.E. Tarancón, A.Vercher, E. Giner, and F.J. Fuenmayor. Enhanced blending elements for XFEM applied to linear elastic fracture mechanics. International Journal for Numerical Methods in Engineering, 77(1):126–148, 2009. doi: 10.1002/nme.2402.
[16] T.P. Fries. A corrected XFEM approximation without problems in blending elements. International Journal for Numerical Methods in Engineering, 75(5):503–532, 2008. doi: 10.1002/nme.2259.
[17] P. Stąpór. Application of XFEM with shifted-basis approximation to computation of stress intensity factors. Archive of Mechanical Engineering, 58(4):447–483, 2011. doi: 10.2478/v10180-011-0028-0.
[18] N. Moës, M. Cloirec, P. Cartraud, and J.-F. Remacle. A computational approach to handle complex microstructure geometries. Computer Methods in Applied Mechanics and Engineering, 192(28):3163–3177, 2003. doi: 10.1016/S0045-7825(03)00346-3.
[19] J. Dolbow, N. Moës, and T. Belytschko. Discontinuous enrichment in finite elements with a partition of unity method. Finite Elements in Analysis and Design, 36(3):235–260, 2000. doi: 10.1016/S0168-874X(00)00035-4.
[20] B.A. Saxby. High-order XFEM with applications to two-phase flows. PhD thesis, The University of Manchester, Manchester, UK, 2014. www.escholar.manchester.ac.uk/uk-ac-manscw:234445.
Go to article

Authors and Affiliations

Paweł Stąpór
1

  1. Faculty of Management and Computer Modelling, Kielce University of Technology, Poland
Download PDF Download RIS Download Bibtex

Abstract

In the paper, the extended finite element method (XFEM) is combined with a recovery procedure in the analysis of the discontinuous Poisson problem. The model considers the weak as well as the strong discontinuity. Computationally efficient low-order finite elements provided good convergence are used. The combination of the XFEM with a recovery procedure allows for optimal convergence rates in the gradient i.e. as the same order as the primary solution. The discontinuity is modelled independently of the finite element mesh using a step-enrichment and level set approach. The results show improved gradient prediction locally for the interface element and globally for the entire domain.

Go to article

Bibliography

[1] P. Stąpór. An improved XFEM for the Poisson equation with discontinuous coefficients. Archive of Mechanical Engineering, 64(1):123–144, 2017. doi: 10.1515/meceng-2017-0008.
[2] T. Grätsch and K.-J. Bathe. A posteriori error estimation techniques in practical finite element analysis. Computers & Structures, 83(4-5):235–265, 2005. doi: 10.1016/j.compstruc.2004.08.011.
[3] M. Ainsworth and J.T. Oden. A posteriori error estimation in finite element analysis. Computer Methods in Applied Mechanics and Engineering, 142(1-2):1–88, 1997. doi: 10.1016/S0045-7825(96)01107-3.
[4] P.J. Payen and K.-J. Bathe. A stress improvement procedure. Computers & Structures, 112-113:311–326, 2012. doi: 10.1016/j.compstruc.2012.07.006.
[5] T. Belytschko and T. Black. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 45(5):601–620, 1999. doi: 10.1002/(SICI)1097-0207(19990620)45:5601::AID-NME598>3.0.CO;2-S.
[6] P. Stąpór. Application of XFEM with shifted-basis approximation to computation of stress intensity factors. The Archive of Mechanical Engineering, 58(4):447–483, 2011. doi: 10.2478/v10180-011-0028-0.
[7] D. Belsley, R.E.Welsch, and E.Kuh. The Condition Number. Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. John Wiley & Sons, Inc., Hoboken, New Jersey, 1980.
[8] S. Hou and X.-D. Liu. A numerical method for solving variable coeffiecient elliptic equation with interfaces. Jurnal of Computational Physics, 202(2):411–445, 2005. doi: 10.1016/j.jcp.2004.07.016.
Go to article

Authors and Affiliations

Paweł Stąpór
1

  1. Faculty of Management and Computer Modelling, Kielce University of Technology, Kielce, Poland.
Download PDF Download RIS Download Bibtex

Abstract

Unconventional oil and gas reservoirs are characterised by low porosity, low permeability and low natural deliverability. At present, horizontal wells staged fracturing is an effective development method. However, in the case of staged hydraulic fracturing in horizontal wells, stress interference occurs between multiple fractures, leading to fracture deformation and even inhibiting the formation of fractures, thereby affecting reservoir production. In this paper, based on the extended finite element method (XFEM), considering the fluid flow in the fracture and fracturing fluid filtration, we analyse the effects of fracturing fluid pumping rate, fracture spacing and elastic modulus on horizontal in-situ stress, fracture parameters and fracture extension pattern during different fracturing initiation processes. The results show that the induced stress generated by the action of fracturing fluid changes the direction of horizontal in-situ stress in the elliptical region around the fracture. In the mode of simultaneous fracture initiation (TFIS), the extension of two symmetrical fractures is “repulsive”; in the mode of two fractures initiated at different times (TFIDT), the extension direction is “mutual attraction”. A large pumping rate and small elastic modulus are conducive to fracture propagation. In the TFIS mode, two fractures alternately expand, while in the TFIDT mode, the impact of rock mechanical properties and construction parameters on fracture propagation will be amplified. The extension of subsequent fractures will be restrained, especially when the fracture spacing is less than 10 m. The width of the previously created fracture will be severely affected, even causing a partial closure and becoming elongated fractures.
Go to article

Authors and Affiliations

Shuang Liang
1 2 3
ORCID: ORCID
Di Wang
1 2
ORCID: ORCID
Dan Liu
4
Yang Tian
3
ORCID: ORCID
Haibo Wang
1 2
ORCID: ORCID
Fengxia Li
1 2
ORCID: ORCID
Gang Dong
5
ORCID: ORCID
Chengfeng Yin
6
ORCID: ORCID
Yi Yang
7
ORCID: ORCID

  1. State Key Laboratory of Shale Oil and Gas Enrichment Mechanisms and Effective Development, Beijing, China
  2. State Energy Center for Shale Oil Research and Development, Beijing, China
  3. Department of Petroleum Engineering, Northeast Petroleum University, Daqing, China
  4. PipeChina Oil & Gas Pipeline Control Center, Beijing, 122000, China
  5. The Eighth Oil Production Plant of Daqing Oilfield Limited Company, Daqing, China
  6. The Fourth Oil Production Plant of Daqing Oilfield Limited Company, Daqing, China
  7. The Tenth Oil Production Plant of Daqing Oilfield Limited Company, Daqing, China
Download PDF Download RIS Download Bibtex

Abstract

The paper deals with the application of the eXtended Finite Element Method (XFEM) to simulations of discrete macro-cracks in plain concrete specimens under tension, bending and shear. Fundamental relationships and basic discrete constitutive laws were described. The most important aspects of the numerical implementation were discussed. Advantages and disadvantages of the method were outlined.

Go to article

Authors and Affiliations

J. Bobinski
J. Tejchman
Download PDF Download RIS Download Bibtex

Abstract

Nominal strength reduction in cross ply laminates of [0/90]2s is observed in tensile tests of glass fiber composite laminates having central open hole of diameters varying from 2 to 10 mm. This is well known as the size effect. The extended finite element method (XFEM) is implemented to simulate the fracture process and size effect (scale effect) in the glass fiber reinforced polymer laminates weakened by holes or notches. The analysis shows that XFEM results are in good agreement with the experimental results specifying nominal strength and in good agreement with the analytical results based on the cohesive zone model specifying crack opening displacement and the fracture process zone length.

Go to article

Bibliography

[1] A. Valera-Medina, A. Giles, D. Pugh, S. Morris, M. Pohl, and A. Ortwein. Investigation of combustion of emulated biogas in a gas turbine test rig. Journal of Thermal Science, 27:331–340, 2018. doi: 10.1007/s11630-018-1024-1.
[2] K. Tanaka and I. Ushiyama. Thermodynamic performance analysis of gas turbine power plants with intercooler: 1st report, Theory of intercooling and performance of intercooling type gas turbine. Bulletin of JSME, 13(64):1210–1231, 1970. doi: 10.1299/jsme1958.13.1210.
[3] H.M. Kwon, T.S. Kim, J.L. Sohn, and D.W. Kang. Performance improvement of gas turbine combined cycle power plant by dual cooling of the inlet air and turbine coolant using an absorption chiller. Energy, 163:1050–1061, 2018. doi: 10.1016/j.energy.2018.08.191.
[4] A.T. Baheta and S.I.-U.-H. Gilani. The effect of ambient temperature on a gas turbine performance in part load operation. AIP Conference Proceedings, 1440:889–893, 2012. doi: 10.1063/1.4704300.
[5] F.R. Pance Arrieta and E.E. Silva Lora. Influence of ambient temperature on combined-cycle power-plant performance. Applied Energy, 80(3):261–272, 2005. doi: 10.1016/j.apenergy.2004.04.007.
[6] M. Ameri and P. Ahmadi. The study of ambient temperature effects on exergy losses of a heat recovery steam generator. In: Cen, K., Chi, Y., Wang, F. (eds) Challenges of Power Engineering and Environment. Springer, Berlin, Heidelberg, 2007. doi: 10.1007/978-3-540-76694-0_9.
[7] M.A.A. Alfellag: Parametric investigation of a modified gas turbine power plant. Thermal Science and Engineering Progress, 3:141–149, 2017. doi: 10.1016/j.tsep.2017.07.004.
[8] J.H. Horlock and W.A. Woods. Determination of the optimum performance of gas turbines. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 214:243–255, 2000. doi: 10.1243/0954406001522930.
[9] L. Battisti, R. Fedrizzi, and G. Cerri. Novel technology for gas turbine blade effusion cooling. In: Proceedings of the ASME Turbo Expo 2006: Power for Land, Sea, and Air. Volume 3: Heat Transfer, Parts A and B. pages 491–501. Barcelona, Spain. May 8–11, 2006. doi: 10.1115/GT2006-90516.
[10] F.J. Wang and J.S. Chiou. Integration of steam injection and inlet air cooling for a gas turbine generation system. Energy Conversion and Management, 45(1):15–26, 2004. doi: 10.1016/S0196-8904 (03)00125-0.
[11] Z. Wang. 1.23 Energy and air pollution. In I. Dincer (ed.): Comprehensive Energy Systems, pp. 909–949. Elsevier, 2018. doi: 10.1016/B978-0-12-809597-3.00127-9.
[12] Z. Khorshidi, N.H. Florin, M.T. Ho, and D.E. Wiley. Techno-economic evaluation of co-firing biomass gas with natural gas in existing NGCC plants with and without CO$_2$ capture. International Journal of Greenhouse Gas Control, 49:343–363, 2016. doi: 10.1016/j.ijggc.2016.03.007.
[13] K. Mohammadi, M. Saghafifar, and J.G. McGowan. Thermo-economic evaluation of modifications to a gas power plant with an air bottoming combined cycle. Energy Conversion and Management, 172:619–644, 2018. doi: 10.1016/j.enconman.2018.07.038.
[14] S. Mohtaram, J. Lin, W. Chen, and M.A. Nikbakht. Evaluating the effect of ammonia-water dilution pressure and its density on thermodynamic performance of combined cycles by the energy-exergy analysis approach. Mechanika, 23(2):18110, 2017. doi: 10.5755/j01.mech.23.2.18110.
[15] M. Maheshwari and O. Singh. Comparative evaluation of different combined cycle configurations having simple gas turbine, steam turbine and ammonia water turbine. Energy, 168:1217–1236, 2019. doi: 10.1016/j.energy.2018.12.008.
[16] A. Khaliq and S.C. Kaushik. Second-law based thermodynamic analysis of Brayton/Rankine combined power cycle with reheat. Applied Energy, 78(2):179–197, 2004. doi: 10.1016/j.apenergy.2003.08.002.
[17] M. Aliyu, A.B. AlQudaihi, S.A.M. Said, and M.A. Habib. Energy, exergy and parametric analysis of a combined cycle power plant. Thermal Science and Engineering Progress. 15:100450, 2020. doi: 10.1016/j.tsep.2019.100450.
[18] M.N. Khan, T.A. Alkanhal, J. Majdoubi, and I. Tlili. Performance enhancement of regenerative gas turbine: air bottoming combined cycle using bypass valve and heat exchanger—energy and exergy analysis. Journal of Thermal Analysis and Calorimetry. 144:821–834, 2021. doi: 10.1007/s10973-020-09550-w.
[19] F. Rueda Martínez, A. Rueda Martínez, A. Toleda Velazquez, P. Quinto Diez, G. Tolentino Eslava, and J. Abugaber Francis. Evaluation of the gas turbine inlet temperature with relation to the excess air. Energy and Power Engineering, 3(4):517–524, 2011. doi: 10.4236/epe.2011.34063.
[20] A.K. Mohapatra and R. Sanjay. Exergetic evaluation of gas-turbine based combined cycle system with vapor absorption inlet cooling. Applied Thermal Engineering, 136:431–443, 2018. doi: 10.1016/j.applthermaleng.2018.03.023.
[21] A.A. Alsairafi. Effects of ambient conditions on the thermodynamic performance of hybrid nuclear-combined cycle power plant. International Journal of Energy Research, 37(3):211–227, 2013. doi: 10.1002/er.1901.
[22] A.K. Tiwari, M.M. Hasan, and M. Islam. Effect of ambient temperature on the performance of a combined cycle power plant. Transactions of the Canadian Society for Mechanical Engineering, 37(4):1177–1188, 2013. doi: 10.1139/tcsme-2013-0099.
[23] T.K. Ibrahim, M.M. Rahman, and A.N. Abdalla. Gas turbine configuration for improving the performance of combined cycle power plant. Procedia Engineering, 15:4216–4223, 2011. doi: 10.1016/j.proeng.2011.08.791.
[24] M.N. Khan and I. Tlili. New advancement of high performance for a combined cycle power plant: Thermodynamic analysis. Case Studies in Thermal Engineering. 12:166–175, 2018. doi: 10.1016/j.csite.2018.04.001.
[25] S.Y. Ebaid and Q.Z. Al-hamdan. Thermodynamic analysis of different configurations of combined cycle power plants. Mechanical Engineering Research. 5(2):89–113, 2015. doi: 10.5539/mer.v5n2p89.
[26] R. Teflissi and A. Ataei. Effect of temperature and gas flow on the efficiency of an air bottoming cycle. Journal of Renewable and Sustainable Energy, 5(2):021409, 2013. doi: 10.1063/1.4798486.
[27] A.A. Bazmi, G. Zahedi, and H. Hashim. Design of decentralized biopower generation and distribution system for developing countries. Journal of Cleaner Production, 86:209–220, 2015. doi: 10.1016/j.jclepro.2014.08.084.
[28] A.I. Chatzimouratidis and P.A. Pilavachi. Decision support systems for power plants impact on the living standard. Energy Conversion and Management, 64:182–198, 2012. doi: 10.1016/j.enconman.2012.05.006.
[29] T.K. Ibrahim, F. Basrawi, O.I. Awad, A.N. Abdullah, G. Najafi, R. Mamat, and F.Y. Hagos. Thermal performance of gas turbine power plant based on exergy analysis. Applied Thermal Engineering, 115:977–985, 2017. doi: 10.1016/j.applthermaleng.2017.01.032.
[30] M. Ghazikhani, I. Khazaee, and E. Abdekhodaie. Exergy analysis of gas turbine with air bottoming cycle. Energy, 72:599–607, 2014. doi: 10.1016/j.energy.2014.05.085.
[31] M.N. Khan, I. Tlili, and W.A. Khan. thermodynamic optimization of new combined gas/steam power cycles with HRSG and heat exchanger. Arabian Journal for Science and Engineering, 42:4547–4558, 2017. doi: 10.1007/s13369-017-2549-4.
[32] N. Abdelhafidi, İ.H. Yılmaz, and N.E.I. Bachari. An innovative dynamic model for an integrated solar combined cycle power plant under off-design conditions. Energy Conversion and Management, 220:113066, 2020. doi: 10.1016/j.enconman.2020.113066.
[33] T.K. Ibrahim, M.K. Mohammed, O.I. Awad, M.M. Rahman, G. Najafi, F. Basrawi, A.N. Abd Alla, and R. Mamat. The optimum performance of the combined cycle power plant: A comprehensive review. Renewable and Sustainable Energy Reviews, 79:459–474, 2017. doi: 10.1016/j.rser.2017.05.060.
[34] M.N. Khan. Energy and exergy analyses of regenerative gas turbine air-bottoming combined cycle: optimum performance. Arabian Journal for Science and Engineering, 45:5895–5905, 2020. doi: 10.1007/s13369-020-04600-9.
[35] A.M. Alklaibi, M.N. Khan, and W.A. Khan. Thermodynamic analysis of gas turbine with air bottoming cycle. Energy, 107:603–611, 2016. doi: 10.1016/j.energy.2016.04.055.
[36] M. Ghazikhani, M. Passandideh-Fard, and M. Mousavi. Two new high-performance cycles for gas turbine with air bottoming. Energy, 36(1):294–304, 2011. doi: 10.1016/j.energy.2010.10.040.
[37] M.N. Khan and I. Tlili. Innovative thermodynamic parametric investigation of gas and steam bottoming cycles with heat exchanger and heat recovery steam generator: Energy and exergy analysis. Energy Reports, 4:497–506, 2018. doi: 10.1016/j.egyr.2018.07.007.
[38] M.N. Khan and I. Tlili. Performance enhancement of a combined cycle using heat exchanger bypass control: A thermodynamic investigation. Journal of Cleaner Production, 192:443–452, 2018. doi: 10.1016/j.jclepro.2018.04.272.
[39] M. Korobitsyn. Industrial applications of the air bottoming cycle. Energy Conversion and Management, 43(9-12):1311–1322, 2002. doi: 10.1016/S0196-8904(02)00017-1.
[40] T.K. Ibrahim and M.M. Rahman. optimum performance improvements of the combined cycle based on an intercooler–reheated gas turbine. Journal of Energy Resources Technology, 137(6):061601, 2015. doi: 10.1115/1.4030447.
Go to article

Authors and Affiliations

Mohammed Y. Abdellah
Mohammad S. Alsoufi
Mohamed K. Hassan
Hamza A. Ghulman
Ahmed F. Mohamed

Download PDF Download RIS Download Bibtex

Abstract

The essential parameters for structure integrity assessment in Linear Elastic Fracture Mechanics (LEFM) are Stress Intensity Factors (SIFs). The estimation of SIFs can be done by analytical or numerical techniques. The analytical estimation of SIFs is limited to simple structures with non-complicated boundaries, loads and supports. An effective numerical technique for analyzing problems with singular fields, such as fracture mechanics problems, is the extended finite element method (XFEM). In the paper, XFEM is applied to compute an actual stress field in a two-dimensional cracked body. The XFEM is based on the idea of enriching the approximation in the vicinity of the discontinuity. As a result, the numerical model consists of three types of elements: non-enriched elements, fully enriched elements (the domain of whom is cut by a discontinuity), and partially enriched elements (the so-called blending elements). In a blending element, some but not all of the nodes are enriched, which adds to the approximation parasitic term. The error caused by the parasitic terms is partly responsible for the degradation of the convergence rate. It also limits the accuracy of the method. Eliminating blending elements from approximation space and replacing them with standard elements, together with applying shifted-basis enrichment, makes it possible to avoid the problem. The numerical examples show improvements in results when compared with the standard XFEM approach.

Go to article

Authors and Affiliations

Paweł Stąpór

This page uses 'cookies'. Learn more