各向异性板平面应力问题的一般解析解  

A GENERAL ANALYTICAL SOLUTION FOR ANISOTROPIC PLATE IN PLANE STRESS PROBLEM

作　　者：杨端生[1] 黄炎[2] 田蕾[2] 

机构地区：[1]长沙理工大学桥梁与结构工程学院,长沙410076 [2]国防科技大学航天与材料工程学院,长沙410073

出　　处：《工程力学》2006年第8期31-35,共5页Engineering Mechanics

基　　金：国家自然科学基金资助项目(19872076)

摘　　要：根据各向异性矩形板平面应力问题的基本方程精确地求得了位移函数的一般解。一般解包括三角函数和双曲线函数组成的解,还有代数多项式解。前者能满足四个边为任意边界条件问题;后者能满足四个角为任意边界条件等问题。这些边界条件用以决定一般解中的积分常数。因此一般解可用以求解任意边界条件下的平面应力问题。Based on the fundamental equation of an anisotropic rectangular plate in plane stress problem, an accurate general displacement solution is obtained. This general solution consists of either the combinations of trigonometric and hyperbolic functions, or algebraic polynomials. The first one can satisfy the problems with arbitrary boundary conditions along four edges; and the second one can satisfy the problems with arbitrary boundary conditions at four corners. Boundary conditions are used to determine the integral constants in the general solution. Consequently, the general solution can be used to solve plane stress problems with arbitrary boundary conditions. As an example, a symmetric angle-plied laminated composite plate with uniform distributed displacements and non-uniform distributed disolacements on four edges is analyzed.

关 键 词：各向异性板 平面应力 解析法 应变 位移 

分 类 号：O343.9[理学—固体力学]