Existence and Uniqueness of the Solution for a Two-Dimensional Elastic Frictional Contact Problem

The elasticity contact problems with friction give rise to variational inequalities as their mathematical models. The main technical difficulties in solving these problems are to find their variational functions and numerical methods. The main numerical methods of variational inequalities contain finite element method and boundary element method - each has its advantages and disadvantages - and fast mutipole boundary element method, which overcomes the lack of traditional boundary element method in a certain extent and can be used to solve the large scale numerical computation and improve computation speed. Existence and uniqueness of the solution for a two-dimensional elastic contact problem with friction is made meaningfully in this paper. First, we give the partial differential equation for 2-D elastic frictional contact problem and boundary condition, also corresponding to variational inequality. Then, the existence condition of its solution is proved, which provides strong mathematical support for the solution of elastic frictional contact engineering problems.