开孔簿板非线性分析的数学模型和广义变分原理*

基于薄板非线性弯曲的Kirchhoff-Kármán假设.本文提出了在任意中面边界条件下任意开孔薄板非线性分析的三类边值问题并建立了相应的广义变分原理.能够看到在本文中提出的数学模型完全是一种新的不同于Karman理论的模型.这些数学模型能够应用于任意中面边界条件下开孔薄板的非线性分析和稳定性分析.

The Mathematical Models and Generalized Variational Principles of Nonlinear Analysis for Perforated Thin Plates

On the basis of the Kirchhoff-Karmhn hypothses for the nonlinear bendingof thin plates, the three kinds of boundary value problems of nonlinear analysis for perforated thin plates are presented under the. different in-plane boundaryconditions and the corresponding- generalized variational principles are established. One can see that all mathematical models presented in this paper are com pletely new ones and differ from the ordinary von Karman theory. These mathematical models can be applied to the nonlinear analysis and the stability analysisof perforated thin plates in arbitrary plane boundary conditions.