Algorithm for solving problems of one-way discrete contact for a multilayer elastic strip
A. A. Bobylev1,2
1Lomonosov Moscow State University, Moscow, Russia
2Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia
Keywords: one-sided discrete contact, multilayer elastic strip, boundary variational inequality, Poincare-Steklov operator, Fourier transform
Abstract
The problems of indentation of a rigid stamp of finite dimensions with a surface microrelief into a multilayer elastic strip are considered. Boundary variational formulations of problems using the Poincare-Steklov operator, which maps contact stresses into displacements, are presented. When approximating this operator, a discrete Fourier transform was used; to calculate the transfer function, an algorithm based on the variational formulation of the boundary value problem for displacement transformants was used. As a result of approximation of the original contact problem, a quadratic programming problem with constraints in the form of equalities and inequalities was obtained, for the numerical solution of which an algorithm based on the conjugate gradient method was used. A number of patterns of contact interaction have been established.
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