GENERAL MATHEMATICAL THEORY OF LARGE DEFLECTIONS OF THIN PLATES WITH SOME HOLES

The theoretical analysis and the numerical computations for the problem of a thin platewith large deflection and some holes become much more difficult due to the multi-valued propertiesof the stress function F and the single-valued demands on the displacements.The necessary andsufficient conditions which can assure F to be single-valued are obtained in this paper.At the sametime,we prove that the single-valued demands on the displacements are equivalent to 3m functionalconstraint equations DC(w,F)=0,where m is the number of holes.From these conclusions,thesingle-valued governing equations of the problem of plates with large deflection and some holes arederived.It is a system of fourth order partial differential equations with 3m unknown constants andconstrained equations.A numerical method for solving this problem is presented.The problem ofthe critical load is considered and an iterative scheme for computing the buckled states is given whena critical load λ is ‘single’.