正交各向异性椭圆板的弹性失稳

Elastic Instability of an Orthotropic Elliptic Plate

本文以von Kármán型方程为基础并利用一般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.利用Liapunov-Schmidt过程证明了单特征值处分支解的存在性并利用小摄动展开得到了分支解的渐近表达式.最后利用有限单元法计算了正交各向异性椭圆板的临界载荷并进行了板的过屈曲分析,还考察了材料和几何参数对稳定性的影响.

On the basis of von Karman equations and using the general bifurcation theory, the elastic instability of an orthotropic elliptic plate whose edge is subjected to a uniform plane compression is discussed. Following the well-known Liapunov-Schmidt process the exiscance of bifurcation solution at a simple eigenvalue is shown and the asymptotic expression is obtained by means of the perturbation expansion with a small parameter. Finally, by using the finite element method, the critical loads of the plate are computed and the post-buckling behaviour is analysed. And also the effect of material and geometric parameters on the stability is studied.