对称迭层矩形板的平面应力分析

常用的对称迭层板为各向异性板．根据平面应力问题的基本方程精确地用应力函数解法求得了各向异性板的一般解析解．推导出平面内应力和位移的一般公式，其中积分常数由边界条件来决定．一般解包括三角函数和双曲函数组成的解，它能满足4个边为任意边界条件的问题．还有代数多项式解，它能满足4个角的边界条件．因此一般解可用以求解任意边界条件下的平面应力问题．以4边承受均匀法向和切向载荷以及非均匀法向载荷的对称迭层方板为例，进行了计算和分析．

Analysis of Symmetric Laminated Rectangular Plates in Plane Stress

Symmetric laminated plates usually used are anisotropic plates. Based on fundamental equation for anisotropic rectangular plates in plane stress problem, a general general solution was established by method of stress function accurately. Therefore it gives the general formula of stress and displacement in plane. The integral constants in general formula can be determined by boundary conditions. This general solution composes the conoosite solution made by trigonometric function and hyperbolic function which can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial solutions which can satisfy the problem of boundary conditions at four corners. Consquently this general solution can be used to solve the plane stress problem with arbirary boundary conditions. For example, a symmetric laminated square plate acted with uniform normal load and tangential load and non-uniform normal load on four edges has been calculated and analyzed.