Simple Formulation for the Flexure of Plates on Nonlinear Foundation

Abstract

Plates resting on an elastic medium are normally analyzed in a simplified way using the linear Winkler foundation approach. Nevertheless, plates resting on layered medium with vast differences in their moduli exhibit nonlinear behavior under pressure. The present technical note deals with a nonlinear finite-element procedure to analyze plates with linear strain displacement relations resting on a nonlinear elastic media. The coupled problem is formulated using the total potential energy (TPE) concept. The nonlinear foundation stiffness matrices have been derived using the Taylor expansion of the TPE at equilibrium and a symbolism of grouping the energy contributions. The nonlinear foundation stiffness matrices derived in the present technical note have been demonstrated to yield results that agree well with published results in the literature. A brief parametric study on the effects of nonlinearity of the foundation is also presented using the proposed foundation stiffness matrices.