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General mathematical theory of large deflections of thin plates with some holes
Authors:Zhengyou  Zhu  Changjun  Cheng
Affiliation:(1) Lanzhou University, Lanzhou
Abstract:The theoretical analysis and the numerical computations for the problem of a thin plate with large deflection and some holes become much more difficult due to the multi-valued properties of the stress functionF and the single-valued demands on the displacements. The necessary and sufficient conditions which can assureF to be single-valued are obtained in this paper. At the same time, we prove that the single-valued demands on the displacements are equivalent to 3m functional constraint equationsDC(w,F)=0, wherem is the number of holes. From these conclusions, the single-valued governing-equations of the problem of plates with large deflection and some holes are derived. It is a system of fourth order partial differential equations with 3m unknown constants and constrained equations. A numerical method for solving this problem is presented. The problem of the critical load is considered and an iterative scheme for computing the buckled states is given when a critical load λ is ‘single’.
Keywords:large deflection  orthogenally anisotropic  plates with holes  multiply connected region  eigenvalue and eigenfunction  bifurcation theory
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