扁球壳的边界元几何非线性分析

本文从壳体位移的三个微分方程出发，采用付立叶积分变换的基本解，利用加权残值法推导了几何非线性边界积分方程。这种基本解的壳体边界元法类似于板的非线性边界元法，各种变量物理意义明确，能方便地处理各种复杂边界条件及有开口情况。文末算例说明本文方法的可行性、收敛性和精确性，并与二变量边界单元法或有限元结果相比较，吻合较好。

Boundary element nonlinear analysis for shallow spherical shells

In this paper,bounary integral equations are derived applying weighted residual mthod and fundamental solutions which are obtained by using Fourier integrals for independent dif-ferential equations for three displacements components.This method for shallow shell is sim-ilar to one in the nonlinear analysis for plates. It has advantages that physical meanings for each variable are clear,various complicated boundary conditions and existence of openings can be treated simply and unfriendly.Examples at end of the paper show applicability,conver-gency and accuracy of the method.Results obtained are in good agreement with that of two-variables(stress function and normal displacement)BE analysis or FEM for shallow spheri-cal shell.