The Principle of Virtual Work for Deformable Bodies and Its Application to Contact Problems

The theory of virtual work principles of deformable bodies and the technique to derive their expressions are studied and applied to contact problems to build FEM formulas. An infinitesimal element that constitutes a deformable body is taken as a particle, which is constrained elastically by the other particles around it but loses no degree of freedom. Accordingly, the whole deformable body becomes a particle system. The principles of virtual work for deformable bodies can be obtained with facility by taking advantage of the well-known principle of virtual displacement in analytical mechanics. The principles of virtualwork is applied to solve contact problems. Especially, the study focuses on the contact between a bodywith small stiffness and anotherwith very large stiffness, which leads to two special instances:(1) that between a deformable and a rigid bodies; and (2) that containing so-called external contact boundary between a deformable and a fixed rigid bodies. It would be convenient to solve some special contact problems in engineeringwith the method presented in this paper.