Exact solutions for nonlinear static responses of a shear deformable FGM beam | |
L.S. Ma1; D.W. Lee2 | |
2012-01 | |
发表期刊 | European Journal of Mechanics A/Solids |
ISSN | 0997-7538 |
卷号 | 31期号:1页码:13-20 |
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. |
关键词 | Functionally graded material beam Exact solution Static response In-plane thermal loading Transverse shear deformation |
学科门类 | 工学::力学(可授工学、理学学位) |
DOI | doi:10.1016/j.euromechsol.2011.06.016 |
收录类别 | SCI |
语种 | 英语 |
资助项目 | 功能梯度材料结构非线性力学行为的进一步研究 |
WOS记录号 | WOS:000298869400002 |
出版者 | ELSEVIERRADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS |
EI入藏号 | 20114814556405 |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | https://ir.lut.edu.cn/handle/2XXMBERH/118221 |
专题 | 理学院 |
通讯作者 | L.S. Ma |
作者单位 | 1.School of Science, Lanzhou University of Technology 2.bMEMS & Nanotechnology Laboratory, School of Mechanical Systems Engineering, Chonnam National University |
第一作者单位 | 兰州理工大学 |
通讯作者单位 | 兰州理工大学 |
第一作者的第一单位 | 兰州理工大学 |
推荐引用方式 GB/T 7714 | L.S. Ma,D.W. Lee. Exact solutions for nonlinear static responses of a shear deformable FGM beam[J]. European Journal of Mechanics A/Solids,2012,31(1):13-20. |
APA | L.S. Ma,&D.W. Lee.(2012).Exact solutions for nonlinear static responses of a shear deformable FGM beam.European Journal of Mechanics A/Solids,31(1),13-20. |
MLA | L.S. Ma,et al."Exact solutions for nonlinear static responses of a shear deformable FGM beam".European Journal of Mechanics A/Solids 31.1(2012):13-20. |
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