四边自由各向异性矩形中厚板弯曲解析解

Analytic solutions for bending of anisotropic rectangular medium-thickness plate with four free edges

将基于阿穆巴诸米扬各向异性中厚板理论的控制方程、不同支撑下建立的板与支撑的协调方程以及板的自由边界条件,通过对称性分解成中心对称问题和中心反对称问题的叠加。利用傅立叶三角级数求解混合奇偶阶偏微分方程组,求得包括板的内力和支撑反力表达式的弯曲解析解。本文方法取消了直法线假设,克服了数学上的求解困难,去除了数值法的弊端,得出的结果更贴近实际。用该方法不但可以研究四边自由各向异性中厚板的弯曲特性和振动特性,而且还可分析不同边界约束下各向异性矩形中厚板的静动力特性。

This paper is based on the governing equation of AM6apuyMяH＇s anisotropic medium-thickness plate theory.It combines the compatibility equation under various support conditions with the boundary conditions of free edges.Through symmetrical decomposition, the plate bending is decomposed into a central symmetry problem and a central dissymmetry problem.By using triangular series method, the mixed-order governing partial differential equations are solved, obtaining the analytical bending solution of an anisotropic rectangular medium-thickness plate with four free edges.It abandons the assumption of method of line, overcomes difficulty in mathematical solutions and the drawbacks of a numerical method to make the results more accurate.This method can be used to study the static and dynamic bending characteristics of anisotropic medium-thickness plates with four free edges and under different boundary constraints.