Postbuckling Analysis of Plates Resting on a Tensionless Elastic Foundation

The buckling and large deflection postbuckling behavior of plates laterally constrained by a tensionless foundation and subjected to in-plane compressive forces are investigated. A nonlinear finite-element formulation based on Marguerre’s nonlinear shallow shell theory, modified by Mindlin’s hypothesis, is employed to model the plate response. To overcome difficulties in solving the plate–foundation equilibrium equations together with the inequality constraints due to the unilateral contact condition, two different approaches are used: (1) the unilateral constraint is accounted for indirectly by a bilinear constitutive law and (2) the problem is formulated as a mathematical programming problem with inequality constraints from which a linear complementarity problem is derived and solved by the Lemke algorithm. To obtain the nonlinear equilibrium paths, the Newton–Raphson algorithm is used together with path-following strategies. Plate–foundation interaction leads to interesting deformation sequences, characterized by the variation of the contact and noncontact zones along the postbuckling path, leading sometimes to sudden changes in the deformation pattern. The results have a remarkable dependence on the plate aspect ratio, foundation stiffness, and buckling shape. The effects of geometric imperfections on the nonlinear response of the plate are also investigated. From these results, a number of insightful conclusions regarding the behavior of such plate–foundation systems are drawn.