A triangular plate bending element for contact problems

Abstract

A refined triangular plate bending element is developed for the problem of a thin elastic plate resting on an elastic half-space. The behaviour of the elastic half-space is described in terms of displacements at ten points in each triangular region into which the surface in contact with the plate is divided. The plate finite element similarly has ten nodes. The requirements of continuity of displacement and slope between adjacent plate elements are met by using a seventh order polynomial with 33 degrees of freedom. The behaviour of this element is tested on various plate bending problems and found to be satisfactory. The element is then applied to the problems of square, triangular and circular plates resting on an elastic half-space and on a foundation of Winkler type, and some comments are made on the problem of finding an equivalent Winkler foundation for a given elastic half-space.