Szczegóły

Tytuł artykułu

Nonlinear mechanics of a compliant beam system undergoing large curvature deformation

Tytuł czasopisma

Archive of Mechanical Engineering

Rocznik

2020

Wolumin

vol. 67

Numer

No 4

Afiliacje

Akano, Theddeus Tochukwu : University of Lagos, Lagos, Nigeria. ; Olayiwola, Patrick Shola : University of Lagos, Lagos, Nigeria.

Autorzy

Słowa kluczowe

compliant beam ; differential transformation method ; large deformation ; nonlinear equation ; mechanics

Wydział PAN

Nauki Techniczne

Zakres

471-489

Wydawca

Polish Academy of Sciences, Committee on Machine Building

Bibliografia

[1] L.L. Howell, S.P. Magleby, and B.M. Olsen. Handbook of Compliant Mechanisms. Wiley, 2013. doi: 10.1002/9781118516485.
[2] K.E. Bisshopp and D.C. Drucker. Large deflection of cantilever beams. Quarterly of Applied Mathematics, 3(3):272–275, 1945. doi: 10.1090/qam/13360.
[3] T.M. Wang. Nonlinear bending of beams with concentrated loads. Journal of the Franklin Institute, 285(5):386–390, 1968. doi: 10.1016/0016-0032(68)90486-9.
[4] T.M. Wang. Non-linear bending of beams with uniformly distributed loads. International Journal of Non-Linear Mechanics, 4(4):389–395, 1969. doi: 10.1016/0020-7462(69)90034-1.
[5] I.S. Sokolnikoff and R.D. Specht. Mathematical Theory of Elasticity. McGraw-Hill, New York, 1956.
[6] R. Frisch-Fay. Flexible bars. Butterworths, 1962.
[7] S.P. Timoshenko and J.M. Gere. Theory of Elastic Stability. Courier Corporation, 2009.
[8] L.L. Howell. Compliant Mechanisms. Wiley, New York, 2001.
[9] T. Beléndez, C. Neipp, and A. Beléndez. Large and small deflections of a cantilever beam. European Journal of Physics, 23(3):371–379, 2002. doi: 10.1088/0143-0807/23/3/317.
[10] T. Beléndez, M. Pérez-Polo, C. Neipp, and A. Beléndez. Numerical and experimental analysis of large deflections of cantilever beams under a combined load. Physica Scripta, 2005(T118):61–64. 2005. doi: 10.1238/Physica.Topical.118a00061.
[11] K. Mattiasson. Numerical results from large deflection beam and frame problems analysed by means of elliptic integrals. Interational Journal for Numerical Methods in Engineering, 17(1):145–153, 1981. doi: 10.1002/nme.1620170113.
[12] F. De Bona and S. Zelenika. A generalised elastica-type approach to the analysis of large displacements of spring-strips. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 211(7):509–517, 1997. doi: 10.1243/0954406971521890.
[13] H.-J. Su. A pseudorigid-body 3R model for determining large deflection of cantilever beams subject to tip loads. Journal of Mechanisms and Robotics, 1(2):021008, 2009. doi: 10.1115/1.3046148.
[14] H. Tari, G.L. Kinzel, and D.A. Mendelsohn. Cartesian and piecewise parametric large deflection solutions of tip point loaded Euler–Bernoulli cantilever beams. International Journal of Mechanical Sciences, 100:216–225, 2015. doi: 10.1016/j.ijmecsci.2015.06.024.
[15] Y.V. Zakharov and K.G. Okhotkin. Nonlinear bending of thin elastic rods. Journal of Applied Mechanics and Technical Physics, 43(5):739–744, 2002. doi: 10.1023/A:1019800205519.
[16] M. Batista. Analytical treatment of equilibrium configurations of cantilever under terminal loads using Jacobi elliptical functions. International Journal of Solids and Structures, 51(13):2308–2326, 2014, doi: 10.1016/j.ijsolstr.2014.02.036.
[17] R. Kumar, L.S. Ramachandra, and D. Roy. Techniques based on genetic algorithms for large deflection analysis of beams. Sadhana, 29(6):589–604, 2004.
[18] M. Dado and S. Al-Sadder. A new technique for large deflection analysis of non-prismatic cantilever beams. Mechanics Research Communications, 32(6):692–703, 2005. doi: 10.1016/j.mechrescom.2005.01.004.
[19] B.S. Shvartsman. Large deflections of a cantilever beam subjected to a follower force. Journal of Sound and Vibration, 304(3-5):969–973, 2007. doi: 10.1016/j.jsv.2007.03.010.
[20] M. Mutyalarao, D. Bharathi, and B.N. Rao. On the uniqueness of large deflections of a uniform cantilever beam under a tip-concentrated rotational load. International Journal of Non-Linear Mechanics, 45(4):433–441, 2010. doi: 10.1016/j.ijnonlinmec.2009.12.015.
[21] M.A. Rahman, M.T. Siddiqui, and M.A. Kowser. Design and non-linear analysis of a parabolic leaf spring. Journal of Mechanical Engineering, 37:47–51, 2007. doi: 10.3329/jme.v37i0.819.
[22] D.K. Roy and K.N. Saha. Nonlinear analysis of leaf springs of functionally graded materials. Procedia Engineering, 51:538–543, 2013. doi: 10.1016/j.proeng.2013.01.076.
[23] A. Banerjee, B. Bhattacharya, and A.K. Mallik. Large deflection of cantilever beams with geometric nonlinearity: Analytical and numerical approaches. International Journal of Non-Linear Mechanics, 43(5):366–376, Jun. 2008. doi: 10.1016/j.ijnonlinmec.2007.12.020.
[24] L. Chen. An integral approach for large deflection cantilever beams. International Journal of Non-Linear Mechanics, 45(3)301–305, 2010. doi: 10.1016/j.ijnonlinmec.2009.12.004.
[25] C.A. Almeida, J.C.R. Albino, I.F.M. Menezes, and G.H. Paulino. Geometric nonlinear analyses of functionally graded beams using a tailored Lagrangian formulation. Mechanics Research Communications, 38(8):553–559, 2011. doi: 10.1016/j.mechrescom.2011.07.006.
[26] M. Sitar, F. Kosel, and M. Brojan. Large deflections of nonlinearly elastic functionally graded composite beams. Archives of Civil and Mechanical Engineering, 14(4):700–709, 2014., doi: 10.1016/j.acme.2013.11.007.
[27] D.K. Nguyen. Large displacement behaviour of tapered cantilever Euler–Bernoulli beams made of functionally graded material. Applied Mathematics and Computation, 237:340–355, 2014. doi: 10.1016/j.amc.2014.03.104.
[28] S. Ghuku and K.N. Saha. A theoretical and experimental study on geometric nonlinearity of initially curved cantilever beams. Engineering Science and Technology, an International Journal, 19(1):135–146, 2016. doi: 10.1016/j.jestch.2015.07.006.
[29] A.M. Tarantino, L. Lanzoni, and F.O. Falope. The Bending Theory of Fully Nonlinear Beams. Springer, Cham, 2019. doi: 10.1007/978-3-030-14676-4.
[30] S.J. Salami. Large deflection geometrically nonlinear bending of sandwich beams with flexible core and nanocomposite face sheets reinforced by nonuniformly distributed graphene platelets. Journal of Sandwich Structures & Materials, 22(3):866–895, 2020. doi: 10.1177/1099636219896070.
[31] T.T. Akano. An explicit solution to continuum compliant cantilever beam problem with various variational iteration algorithms. Advanced Engineering Forum, 32:1–13, 2019. doi: 10.4028/www.scientific.net/aef.32.1.
[32] J.K. Zhou. Differential Transformation and its Applications for Electrical Circuits. Huazhong University Press, Wuhan, China, 1986.
[33] S.K. Jena and S. Chakraverty. Differential quadrature and differential transformation methods in buckling analysis of nanobeams. Curved and Layered Structures, 6(1)68–76, 2019. doi: 10.1515/cls-2019-0006.
[34] M. Kumar, G.J. Reddy, N.N. Kumar, and O A. Bég. Application of differential transform method to unsteady free convective heat transfer of a couple stress fluid over a stretching sheet. Heat Transfer – Asian Research, 48(2):582–600, 2019. doi: 10.1002/htj.21396.
[35] G.C. Shit and S. Mukherjee. Differential transform method for unsteady magnetohydrodynamic nanofluid flow in the presence of thermal radiation. Journal of Nanofluids, 8(5):998–1009, 2019. doi: 10.1166/jon.2019.1643.
[36] D. Nazari and S. Shahmorad. Application of the fractional differential transform method to fractional-order integro-differential equations with nonlocal boundary conditions. Journal of Computational and Applied Mathematics, 234(3):883–891, Jun. 2010. doi: 10.1016/j.cam.2010.01.053.
[37] M.A. Rashidifar and A.A. Rashidifar. Analysis of vibration of a pipeline supported on elastic soil using differential transform method. American Journal of Mechanical Engineering, 1(4):96–102, 2013. doi: 10.12691/ajme-1-4-4.
[38] Y. Xiao. Large deflection of tip loaded beam with differential transformation method. Advanced Materials Research, 250-253:1232–1235, 2011. doi: 10.4028/www.scientific.net/AMR.250-253.1232.
[39] Z.M. Odibat, C. Bertelle, M.A. Aziz-Alaoui, and G.H.E. Duchamp. A multi-step differential transform method and application to non-chaotic or chaotic systems. Computers & Mathematics with Applications, 59(4):1462–1472, 2010. doi: 10.1016/j.camwa.2009.11.005.
[40] A. Arikoglu and I. Ozkol. Solution of differential-difference equations by using differential transform method. Applied Mathematics and Computation, 181(1):153–162, 2006. doi: 10.1016/j.amc.2006.01.022.

Data

2020.12.22

Typ

Artykuły / Articles

Identyfikator

DOI: 10.24425/ame.2020.131703 ; ISSN 0004-0738, e-ISSN 2300-1895

Źródło

Archive of Mechanical Engineering; 2020; vol. 67; No 4; 471-489
×