基于调和函数的复合材料弹性力学解析

Analysis of Elastic Mechanics for Composite Materials Based on the Harmonious Function

摘要: 本文按照实变函数分析理念推导出复合材料弹性力学偏微分方程的通解，利用坐标变换法与调和函数求解各向异性板应力边值问题。通过典例阐明解决弹性力学应力边值问题的具体办法。为了满足给定应力边界条件要求，必须选择合适的调和函数，进而推导出各向异性材料确切的应力场表达式。

Abstract: In this paper, based on the analytic conception of real variable function, the general solution of the partial derivative equation has been determined on the elastic mechanics for composite materials. By the method of the coordinate transition and the use of the harmonious functions, some stress boundary problems of the anisotropic plate are solved. The practical course to solve the boundary problem of elastic mechanics can be proved clearly from several typical examples. By way of selecting reasonable harmonious functions in order to satisfy the needs of the given stress boundary conditions, the specific formulae of the stress fields are derived for the anisotropic materials.