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Bending Analytic Solutions of Anisotropic Rectangular medium-thickness Plate

DOI：

 作者 单位 E-mail 王春玲 西安建筑科技大学 wangchunlingjd@sina.com 张杰 西安建筑科技大学

本文先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将混合奇偶阶偏微分方程组进行求解，求得包括板的内力和支撑反力表达式的弯曲解析解。它取消了直法线假设，克服了数学上求解的困难，去除了数值法的弊端，得出的结果更贴近实际。不但用该方法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 variant bracing conditions with the boundary conditions of the free edges of a plate. Through symmetrical decomposition, it decomposed into superposition of central symmetry questions and central dissymmetry questions. By using triangular series method, the mixed order partial differential governing equations have been solved, obtaining the analytical bending solution of anisotropic rectangular medium-thickness plate with four free edges on the different bearing forms. It abandoned the assumption of method of line, overcome the difficulty in solving mathematical problems and the drawbacks of numerical method to make the results more accurate. This method can be used to study the bending and vibration characteristics of anisotropic medium-thickness plates with four free edges and also to analyze the static and dynamic characteristics of anisotropic rectangular medium-thickness plates under different boundary constraints.
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