Postbuckling of a Uniformly Compressed Simply Supported Plate with Free In-Plane Translating Edges

The postbuckling of a Kirchhoff isotropic simply supported plate is considered in detail. The in-plane displacements on the edges of the plate are not constrained. The solution is obtained using the principle of the total potential energy stationarity. The expression for energy is written in the three versions: in terms of the Biot strains, the Cauchy-Green strains, and the strains corresponding to Füppl-von Kármán plate theory. Some approximate solution is constructed by the classical Ritz method. The basis functions are taken in the form of Legendre polynomials and their linear combinations. The obtained diagram of equilibrium states is rather similar to the classical diagrams of compressed shells. We show the failure of Föppl-von Kármán theory under large deflections. Using the Biot strains and the Cauchy-Green strains leads to the discrepancy between the results of at most 5 %. We demonstrate the high accuracy and convergence of the approximate solution.