Constraint variational schemes for analysis of rectangular plates on an elastic half space

Abstract

The flexural interaction of a rectangular thin elastic plate resting in smooth contact with an isotropic homogeneous elastic half space is analysed by using constraint variational schemes. The deflected shape of the plate is represented by a double power series of spatial variables with a set of generalized coordinates. The contact stresses are expressed in terms of the generalized coordinates by discretizing the contact area into several rectangular regions and solving an appropriate flexibility equation based on generalized Boussinesq's solution. Using the representations adopted for displacement and contact stresses, a constraint energy functional is constructed to determine the generalized coordinates. The constraint term in the variational functional corresponds to plate edge boundary conditions and formulations corresponding to both Lagrange multiplier and penalty types are presented. It is noted that for the present class of problems, penalty type formulations are numerically efficient. The convergence and numerical stability of the solution scheme is confirmed. Selected numerical results are presented to illustrate the dependence of flexural response of plate on the governing parameters of the plate-half space system.