Exact solutions for nonlinear static responses of a shear deformable FGM beam under an in-plane thermal loading

doi:10.1016/j.euromechsol.2011.06.016

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	Exact solutions for nonlinear static responses of a shear deformable FGM beam under an in-plane thermal loading
	Ma, L.S.1,2; Lee, D.W.2
刊名	European Journal of Mechanics, A/Solids
	2012
卷号	31 期号:1 页码:13-20
关键词	Beams and girders Boundary conditions Buckling Eigenvalues and eigenfunctions Functionally graded materials Numerical methods Plates (structural components) Shear deformation Thermal load
ISSN号	09977538
DOI	10.1016/j.euromechsol.2011.06.016
英文摘要	An exact, closed-form solution is obtained for the nonlinear static responses of beams made of functionally graded materials (FGM) subjected to a uniform in-plane thermal loading. The equations governing the axial and transverse deformations of FGM beams are derived based on the nonlinear first-order shear deformation beam theory and the physical neutral surface concept. The three equations are reduced to a single nonlinear fourth-order integral-differential equation governing the transverse deformations. For a fixed-fixed FGM beam, the equation and the corresponding boundary conditions lead to a differential eigenvalue problem, while for a hinged-hinged FGM beam, an eigenvalue problem does not arise due to the inhomogeneous boundary conditions, which result in quite different behavior between clamped and simply supported FGM beams. The nonlinear equation is directly solved without any use of approximation and a closed-form solution for thermal post-buckling or bending deformation is obtained as a function of the applied thermal load. The exact solutions explicitly describe the nonlinear equilibrium paths of the deformed beam and thus are able to provide insight into deformation problems. To show the influence of the material gradients, transverse shear deformation, in-plane loading, and boundary conditions, numerical examples are given based on exact solutions, and some properties of the post-buckling and bending responses of FGM beams are discussed. The exact solutions obtained herein can serve as benchmarks to verify and improve various approximate theories and numerical methods. © 2011 Elsevier Masson SAS. All rights reserved.
WOS研究方向	Mechanics
语种	英语
出版者	Elsevier Ltd
WOS记录号	WOS:000298869400002
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/151553]
专题	理学院
作者单位	1.School of Science, Lanzhou University of Technology, Lanzhou 730050, China; 2.MEMS and Nanotechnology Laboratory, School of Mechanical Systems Engineering, Chonnam National University, Gwangju 500-757, Korea, Republic of
推荐引用方式 GB/T 7714	Ma, L.S.,Lee, D.W.. Exact solutions for nonlinear static responses of a shear deformable FGM beam under an in-plane thermal loading[J]. European Journal of Mechanics, A/Solids,2012,31(1):13-20.
APA	Ma, L.S.,&Lee, D.W..(2012).Exact solutions for nonlinear static responses of a shear deformable FGM beam under an in-plane thermal loading.European Journal of Mechanics, A/Solids,31(1),13-20.
MLA	Ma, L.S.,et al."Exact solutions for nonlinear static responses of a shear deformable FGM beam under an in-plane thermal loading".European Journal of Mechanics, A/Solids 31.1(2012):13-20.