A neural network approach for the solution of frictional contact problems with nonconvex superpotentials

Abstract

A neural network approach is proposed for the numerical treatment of frictional contact problems. A nonmonotone friction law is assumed to describe the stick-slip process which leads to the formulation of a computational intensive nonconvex-nonsmooth optimization problem. The problem is addressed by a heuristic method which effectively replaces the nonmonotone law by a sequence of monotone friction laws, leading to quadratic programming problems with inequality constraints. The resulting quadratic optimization problems are transformed into a system of appropriately defined differential equations. Then, an appropriate neural network is applied for the solution of the problem. The proposed method is illustrated through the solution of the engineering problem of the frictional contact between two shear walls. (C) 2002 Elsevier Science Ltd. All rights reserved.