Analytical solution for functionally graded anisotropic cantilever beam subjected to linearly distributed load  

作　　者：黄德进 丁皓江 陈伟球 

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

出　　处：《Applied Mathematics and Mechanics(English Edition)》2007年第7期855-860,共6页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.10472102 and 10432030)

摘　　要：The bending problem of a functionally graded anisotropic cantilever beam subjected to a linearly distributed load is investigated. The analysis is based on the exact elasticity equations for the plane stress problem. The stress function is introduced and assumed in the form of a polynomial of the longitudinal coordinate. The expressions for stress components are then educed from the stress function by simple differentiation. The stress function is determined from the compatibility equation as well as the boundary conditions by a skilful deduction. The analytical solution is compared with FEM calculation, indicating a good agreement.The bending problem of a functionally graded anisotropic cantilever beam subjected to a linearly distributed load is investigated. The analysis is based on the exact elasticity equations for the plane stress problem. The stress function is introduced and assumed in the form of a polynomial of the longitudinal coordinate. The expressions for stress components are then educed from the stress function by simple differentiation. The stress function is determined from the compatibility equation as well as the boundary conditions by a skilful deduction. The analytical solution is compared with FEM calculation, indicating a good agreement.

关 键 词：functionally graded plane stress problem stress function linearly distributed load analytical solution 

分 类 号：O342[理学—固体力学]