A Smooth System of Equations Approach to Complementarity Problems for Frictionless Contacts

Abstract

Frictionless contact problems are the simplest and classical contact problems, and the contact conditions of sticking, slipping, and separation mode all can be ascribed to complementary problems. Consequently, a smooth system of equations approach for the design and analysis of complementarity problems for frictionless contacts is presented. A compute program based on boundary element technique is given and applied to two practical contact examples. The validity and accuracy of the proposed method are demonstrated.

Boundary Element and Augmented Lagrangian Methods for Contact Problem with Coulomb Friction

“…We note that there exist two types of approaches for the numerical solution of the contact problem. An option is to discrete the problem by the finite element method (FEM) [2][3][4][5] or the boundary element method (BEM) [6][7][8][9][10] and obtain a convex optimization problem in the finite dimensional space. Another option is to use the Lagrange multiplier which replaces the nonlinear problem with a sequence of linear problems in function spaces, and this idea has been introduced in [11][12][13][14][15][16][17][18].…”

“…For contact problems, the key unknowns are displacement and stress on the contact boundary, which are considered as primary variables and can be obtained directly in the BEM [28][29][30]. erefore, the BEM seems to be the natural way for these problems [6][7][8][9][10][31][32][33][34][35][36][37].…”