Nonlinear Postbuckling Behavior of a Simply Supported, Uniformly Compressed Rectangular Plate

Abstract

The geometrically nonlinear deformation theory is used for the far post-buckling analysis of a uniformly compressed rectangular plate. The plate geometrically nonlinear deformation theory is developed using the right stretch tensor and the Biot stress tensor. The plate is assumed thin such that the Kirchhoff hypothesis are applied. The plate material is assumed linear elastic. The simply supported boundary conditions are assumed for the plate deflection function. The in-plane displacements of a plate are not constrained except for the prescribed uniform shortening along the opposite edges. The weak solution is constructed using the Ritz method. The basis functions in the displacement function approximations are assumed as Legendre polynomials and their linear combinations. The nonlinear simultaneous equations are solved by the Newton method. Three equilibrium paths are determined, which originate from the first three bifurcation points; two additional equilibrium paths are found to appear during the post-buckling deformation, which correspond to the formation of the buckle-waves (wrinkles) along the non-loaded edges. Stable and unstable branches of the equilibrium paths are determined, as well the bifurcation and limit points. The variation of the potential energy is demonstrated and the possible points of jump-like transitions between the adjacent buckled configurations are identified, including those with where wrinkles are formed. The high accuracy and convergence rate of the numerical solution are demonstrated.