The Boundary Element Method For Three Dimensional Elastic Contact Problem With Friction

A boundary element method based on an iterative technique for solving the three-dimensional elastic contact problem without sliding is presented. The boundary integral equation for elasticity is derived through the general Green's formula and the corresponding fundamental solution. The paper represents the contact conditions, which are essential for the coupling of the boundary integral equations of the two different elastic contact bodies, in a local coordinate system properly chosen. In this paper, an iterative procedure, which seeks the increments of boundary values for displacements and tractions compatible with the contact conditions, is applied to determine the correct contact zone without sliding. Due to the existence of friction, the paper utilizes a method of simulating the increments of the external load to trace the history of loading taking account of the irreversible character of the history of loading. In numerical calculation, the paper employs the collocation method to compute the coupled boundary integral equations with quadrangle constant elements. The singular integrals are carried out by analytical integration. A general Fortran90 program for computing the 3-D frictional elastic contact problem without sliding by Boundary Element Method is compiled and some numerical examples including conforming and advancing contact problems are offered to examine the convergence and feasibility of the described method. The numerical experiments illustrate that the method presented in the paper works well.