Approximate large-deflection analysis of simply supported rectangular plates under transverse loading using plate post-buckling solutions

This paper describes an approximate analytical method to determine the large-deflection behaviour of rectangular simply supported thin plates under transverse loading. The method is based on a simple trial function to describe the shape of the initial and total deflections of the plate, corresponding to the first buckling mode shape of the plate when subjected to uniform in-plane compression. Therefore, the large-deflection behaviour of the plate under transverse loading can be expressed as a function of the ratio of the pre- to post-buckling in-plane stiffness of the plate, which is given in literature for plates with various membrane boundary conditions of the plate edges. Due to the simplicity of the trial function flexural and membrane actions of the plate are decoupled. It was found that the approximate method gives good insight into the large-deflection behaviour. The results of the approximate method have been compared to the results of finite element solutions and solutions available in literature. For uniformly distributed loads the approximate method gives deflections which differ less than about 10% from the finite element simulation values.