Postbuckling behaviour of isotropic thin rectangular plates with one free edge

Abstract

This work aims to evaluate the individual stiffness of six plates’ boundary conditions with one free edge to obtain the specific mathematical models for predicting the postbuckling loads of the six plates’ boundary conditions under consideration. The shape profiles of each of the six plates were differentiated and substituted into the individual stiffness integrals to obtain the numerical values of the individual stiffness. The individual stiffness values were then substituted into the total bending and membrane stiffness expressions and evaluated. The resulting total and membrane stiffness expressions were thereafter substituted into the general postbuckling equation and evaluated to obtain specific mathematical models for the six plate types to predict the postbuckling loads of each plate. The newly formulated mathematical models were validated by carrying out numerical predictions of the postbuckling loads of each plate. The critical load obtained was compared with those in the literature and was found adequate. Additionally, the results showed a gradual increase in the strength of plate beyond the initial yield point which is in line with the behavior of plates. Based on these observations it was concluded that the newly formulated mathematical models for predicting the postbuckling strength of thin isotropic rectangular plates considered here were adequate and that the models will provide an easy means of analyzing thin plates for postbuckling loads.