CLASSICAL AND HOMOGENIZED EXPRESSIONS FOR BUCKLING SOLUTIONS OF FUNCTIONALLY GRADED MATERIAL LEVINSON BEAMS

查看全文 作　　者：Shirong [1]Li;Xuan [1]Wang;Zeqing [1]Wan

机构地区：[1]Department of Civil Engineering, Yangzhou University

出　　处：《Acta Mechanica Solida Sinica》索引2015年第28卷第5期,共13页

基　　金：supported by the National Natural Science Foundation of China(No.11272278) 摘　　要：The relationship between the critical buckling loads of functionally graded material(FGM) Levinson beams(LBs) and those of the corresponding homogeneous Euler-Bernoulli beams(HEBBs) is investigated. Properties of the beam are assumed to vary continuously in the depth direction. The governing equations of the FGM beam are derived based on the Levinson beam theory, in which a quadratic variation of the transverse shear strain through the depth is included.By eliminating the axial displacement as well as the rotational angle in the governing equations,an ordinary differential equation in terms of the deflection of the FGM LBs is derived, the form of which is the same as that of HEBBs except for the definition of the load parameter. By solving the eigenvalue problem of ordinary differential equations under different boundary conditions clamped(C), simply-supported(S), roller(R) and free(F) edges combined, a uniform analytical formulation of buckling loads of FGM LBs with S-S, C-C, C-F, C-R and S-R edges is presented for those of HEBBs with the same boundary conditions. For the C-S beam the above-mentioned equation does not hold. Instead, a transcendental equation is derived to find the critical buckling load for the FGM LB which is similar to that for HEBB with the same ends. The significance of this work lies in that the solution of the critical buckling load of a FGM LB can be reduced to that of the HEBB and calculation of three constants whose values only depend upon the throughthe-depth gradient of the material properties and the geometry of the beam. So, a homogeneous and classical expression for the buckling solution of FGM LBs is accomplished. 关键词：临界屈曲载荷功能梯度材料欧拉-伯努利梁光束常微分方程解析表达式匀浆控制方程

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CLASSICAL AND HOMOGENIZED EXPRESSIONS FOR BUCKLING SOLUTIONS OF FUNCTIONALLY GRADED MATERIAL LEVINSON BEAMS

参考文献(31)

引证文献(6)

耦合文献(34)

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