Numerical methods for analysis of plates on tensionless elastic foundations

A numerical methodology for analysis of plates resting on tensionless elast ic 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 plat e and foundation. To overcome the difficulties in solving the plate-foundat ion equilibrium equations together with the inequality constraints due to t he frictionless unilateral contact condition, a variational formulation equ ivalent to these equations is presented from which three alternative linear complementary problems (LCP) are derived and solved by Lemke's complementa ry 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 thi rd formulation, the variables are the elastic foundation displacements and the gap between the bodies. Once the LCP is solved the no-contact regions w here 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 compar ed with existing analytical and numerical results found in the literature. (C) 2001 Elsevier Science Ltd. All rights reserved.