On the basis of the Kirchoff-K~rmhn h)Tothses for the nonlinear bending of thin plates, the three kinds of boundar), 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 yon Kfirmfin theory. These mathematical models can be applied to the β’nonlinear analysis and the stability analysis of perforated thin plates in arbitraryplane boundao, conditions.
Key words perforated thin plate, non-linear analysis, mathematical model, generalized variational principle
I. Introductic-~
There are some theories to be able to analyse the nonlinear bending of thin plates without holes, such that,β’ K/trm~n theory, Reissner theory and director theory ['] etc.. However, up to the beginning in the 80's of the 20th century, there is no simple and rational theory to be used to analyse the nonlinear problems of perforated thin plates and shells. In 1984, on the basis of the Kirchhoff-K~rmLm hypothses, the frame of the theory analysing the nonlinear problems of perforated thin plates was initially presented by Cheng Changjun. In 1985, the authors in [2] first established the. boundary value problem II (noted by BVP II)-when the given in-plane membrane forces X, on the edge ..F~(i= 1,2,-.. ,m)' are in self-equilibrium. After that, the authors in [ 3 ] established BVP II when the given in-plane membrane forces XΒ° on ; ,/-'~ are not in self-equilibrium and showed that in this case the stress function F may be divided into the sum of two parts, where one of them is a single valued function F* and the other part J~ is made of konwn multiple valued functions. In 1991, the authors in [4] presented three kinds of boundary value problems to analyse buckling and post-buckling of perforated thin plates. As application of the modelsi: there are many papers to analyse the buckling and post-buckling of annular plates CS"s]. And in [11], the existance of bifurcation solutions for BVP II has been shown and the corresponding variational principles and the finite element method are * Project supported by the State Education Commission of China and the Natural Science