A Generalized Method of Analysis of Large-deformed Elastic-Plastic Plate Problems

Abstract

This paper presents a generalized method of analysis of large-deformed elastic-plastic plate problems. The nonlinear geometric and material problems are solved by the incremental load procedure (step-by-step method).The method of solution is outlined as follows.(A) Plastic analysis is based on the flow theory of plasticity. The method of initial strains is applied considering the following characteristic feature. Structures can be treated by this method as if they had elastic stiffness and the effect of plastic deformation is transformed into the equivalent additional external force. So this method makes it possible for us to apply the principle of stationary potential energy of elastic plate with initial strains.(B) Finite deformation analysis is performed at the respective loading steps in the following way.(1) Incremental deflection Δw is expanded in a series of functions with unknown coefficients ΔC [m] .(2) Inplane incremental displacement Δue is expressed in terms of ΔC [m] , considering inplane equilibrium condition. The finite element method for plane stress problems can be used in this process.(3) ΔC [m] are determined to satisfy inplane and out-of-plane equilibrium conditions.This method has a special merit to require only a short computing time owing to expantion of Δw in a series of functions. Whole application of the finite element method would result in untolerable time-and core-consuming troubles.As numerical examples, two problems are studied with regards to the simply-supported square plates and the perforated square plates.(1) Laterally loaded plate(2) Ultimate compressive strength of the plates with various thickness and initial deflection.A few experiments were performed to investigate the applicability of the method of solution.