正交各向异性椭圆板弹性失稳的定性分析

Qualitative Analysis on Elastic Instability of an Orthotropic Elliptic Plate

本文利用分支理论讨论了正交各向异性椭圆板在面内边缘均布压力作用下的弹性失稳.首先借助于 Sobolev 空间的基本理论将问题化力一个等价的算子方程,讨论了线性化问题和特征值,并利用 Liapunov—Schmidt 过程把求算子方程的分支解化为寻求分支方程的问题.并给出了分支点处分支解的渐近表达式.

The elastic instability of an orthotropic elliptic plate subjected to auniform plane compression is discussed by means of the bifurcation theory.According to the theory of Sobolev Space,the problem reduces to an equi-valent operator equation.The linearized problem and the correspondingeigenvalue are studied.By the Liapunov-Schmidt procedure,the bifurca-tion equation is obtained to be equivalent to the operator equation.Theasymptotic expression of the bifurcation solution is given.