The mathematical models and generalized variational principles of nonlinear analysis for perforated thin plates

Abstract

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