THE SEARCH FOR SUBSTATIONARITY PAINTS IN THE UNILATERAL CONTACT PROBLEMS WITH NONMONOTONE FRICTION

Structures involving nonmonotone, possibly multivalued reaction-displa cement, or stress-strain laws cannot be effectively treated by the cla ssical numerical methods for nonlinear laws. This type of problems hav e as a variational formulation a hemivariational inequality, leading t o a nonconvex optimization problem. In this paper, a new method is pro posed which approximates the nonmonotone problem by a series of monoto ne ones. The method constitutes an iterative scheme for the approximat ion of the substationarity points, i.e., of all the solutions of the c orresponding hemivariational inequality. Numerical examples demonstrat e the properties of the proposed numerical method. (C) 1998 Elsevier S cience Ltd. All rights reserved.