弹性地基上各向异性板的静力分析

根据弹性地基上各向异性矩形板弯曲挠度的微分方程精确的求得了适用于各种载荷的非齐次解和各类齐次解。其中由三角函数和双曲线函数组成的齐次解能满足四个边为任意边界条件的问题;由代数多项式和双正弦级数组成的齐次解能满足四个角为任意边界条件的问题。通过适当选取建立了满足任意边界条件和任意载荷作用的一般解。解中的积分常数完全由边界条件来决定。以四边简支承受均布载荷和局部分布载荷的对称迭层复合材料方板为例进行了计算和分析。其结果与已有文献结果是一致的。由于集中载荷不能求得作用点的弯矩,故在例题中改用局部分布载荷因而求得了最大弯矩。

Static Analysis of Anisotropic Plates on Elastic Foundation

Based on the differential equation for bending momemt deflection of anisotropic rectangular plates on elastic foundation,the nonhomogeneous solution for arbitrary loads and varions homogeneous solutions are obtained accurately. The homogeneous solutions composed of trigonometric functions and hyperbolic function can satisfy the problems with arbitrary boundary conditions along four edges. The homogeneous solutions of algebraic polynomial and double sine series can satisfy the problems with arbitrary boundary conditions at four corners,thus a general solution for arbitrary loads and boundary conditions is found via a proper selection,and all integral constants in the solution can be determined by the boundary conditions. An example of symmetric laminated composite square plate with four edges simply supported and uniformly or partly load verifies the result in the references.