New analytic solutions for elastic buckling of isotropic plates

This chapter aims to derive a new analytical solution for determining the elastic buckling loads of thin isotropic rectangular plates with different combinations of boundary conditions. Thin plates are structural elements used in various fields, including civil, aeronautical and mechanical engineering. The first solution was obtained by Navier, and his solution was for a simply supported plate along all four edges. Many methods have been used for the approximate solution of buckling in plates. The chapter presents a new method of finding the exact buckling load for isotropic thin plates by using a superposition method. The solution for the buckling load of the plates is found using a static analysis. The analytic solution can predict the "exact" values of the critical buckling loads. The partial differential equations satisfy the equation of equilibrium of a plate, for most of its boundary conditions.