On the influence of elasticity on the large deflections response of circular plates to uniform quasi-static pressure

This work presents an approximate theory to predict the large deflections and elastic spring-back of circular plates made of elastic, perfectly plastic material when subjected to uniform quasi-static pressure. A non-linear interaction between the membrane force and bending moment is assumed when the radial displacements are included in the analysis in order to obtain realistic strain distributions. It is shown that the stored elastic energy in the plate has a limit for the particular material model when sufficiently large deflection occurs and the plate becomes entirely plastic. Therefore, the spring-back of the plate during unloading decreases with the increase of the pressure level. It is also revealed that a plate thinning occurs at sufficiently large deflections, which has a non negligible effect on the plate stiffness. The plate deflections predicted by the proposed elastic-plastic theoretical model in the loading phase are compared with those given by a rigid-plastic analysis reported in the literature so as to estimate the loading range where the material elasticity has an important effect. In parallel, numerical simulations are conducted using the commercial software package ABAQUS to verify the proposed theoretical model. It is shown that the theoretical predictions are in good agreement with the results from the numerical simulations in terms of the pressure-displacement dependence, accumulated elastic energy, elastic spring-back and permanent displacements. (C) 2017 Elsevier Ltd. All rights reserved.