ALGORITHM FOR SOLVING UNILATERAL DISCRETE CONTACT PROBLEMS FOR A MULTILAYER ELASTIC STRIP

Abstract

This paper touches upon problems of a rigid punch of finite dimensions with a surface microrelief pressed into a multilayer elastic strip. A Poincaré–Steklov operator that maps contact stresses into displacements is applied to present boundary variational formulations of these problems. This operator is approximated using the discrete Fourier transform. The transfer function is calculated using an algorithm based on the variational formulation of the boundary value problem for displacement transforms. The original contact problem is approximated in order to obtain a quadratic programming problem with constraints in the form of equalities and inequalities. Its numerical solution is performed using an algorithm based on the conjugate gradient method. Many contact interaction spots are established.