Variational Formulation of Interaction between Elastic Plate and Elastic Medium under the Influence of Surface Energy

Abstract

A variational formulation of interaction problem is presented in this paper for the analysis of an elastic circular plate under axisymmetric vertical loading resting on an isotropic elastic half-space under the influence of surface energy. The Gurtin-Murdoch surface elasticity theory is adopted to take into account the surface energy effects. The contact surface between the plate and the half-space is assumed to be smooth, and the deflected shape of the plate is represented by a power series of the radial coordinate. The undetermined coefficients in the series are determined through the minimization of the total potential energy functional of the plate-half-space system. The accuracy of the present solution is verified by comparing with existing solutions, and selected numerical results are presented to portray the influence of surface energy effects on interaction between an elastic circular plate and an elastic half-space.