Numerical methods for analysis of plates on tensionless elastic foundations

Abstract

A numerical methodology for analysis of plates resting on tensionless elastic foundations, described either by the Winkler model or as an elastic half-space, is presented in this paper. The contact surface is assumed unbonded and frictionless. The finite element method is used to discretize the plate and foundation. To overcome the difficulties in solving the plate–foundation equilibrium equations together with the inequality constraints due to the frictionless unilateral contact condition, a variational formulation equivalent to these equations is presented from which three alternative linear complementary problems (LCP) are derived and solved by Lemke’s complementary pivoting algorithm. In the first formulation, the LCP variables are the plate displacements and the elastic foundation reaction, in the second, the LCP is derived in terms of the elastic foundation reaction and, in the third formulation, the variables are the elastic foundation displacements and the gap between the bodies. Once the LCP is solved the no-contact regions where the plate lifts up away from the foundation and the sub-grade reaction, as well as the plate displacements and stresses, can be easily obtained. The methodology is illustrated by three examples and the results are compared with existing analytical and numerical results found in the literature.