A Flexible Rectangular Plate on an Elastic Layer: Large Area Contact

Abstract

The unbonded frictionless receding contact problem of a symmetrically loaded thin rectangular plate resting on an elastic layer is solved in this paper. The contact is assumed to be tensionless. The problem is transformed into the solution of three coupled two-dimensional singular integral equations. The possible contact pressure singularities along the plate edges and at the corners are treated using adaptive discretization. The contact regions are found iteratively since the problem is nonlinear. Contact regions and numerical values of displacements and contact pressures are presented to illustrate the influences of uplift, layer depth, aspect ratio, stiffness ratio, Poisson’s ratio, and other quantities.