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.
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