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本文基于薄壳结构最小势能变分原理,建立了薄壳结构一种新的边界积分方程法的公式。平面波分解法提供了一个强有力的数学工具,使我们找到一个通过处理常微分方程来求解偏微分方程的方法,本文将重点予以介绍。这个新的方法,不同于传统的边界积分方程法,可以不需要问题的基本解,也不需要处理高阶奇异性。采用这种方法很容易列出总体系数矩阵,相对来说是比较经济的,可在微机上算题。最后,本文给出了数值例题,以说明本方法的有效性。
In this paper, based on the principle of variational principle of minimum potential energy of thin shell structure, a new formula of boundary integral equation method for thin shell structure is established. The plane wave decomposition method provides a powerful mathematical tool that allows us to find a way to solve partial differential equations by processing ordinary differential equations. This article will focus on the introduction. This new method, unlike the traditional boundary integral equation method, does not require the fundamental solution of the problem, nor does it need to deal with higher order singularities. Using this method it is easy to list the overall coefficient matrix, which is relatively economical and can be calculated on a microcomputer. Finally, numerical examples are given in this paper to illustrate the effectiveness of the method.