A unilateral discrete contact problem for a stratified elastic strip

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Abstract

The problem is considered for the indentation of a stratified elastic strip by a rigid punch of finite dimension with a surface microrelief. Boundary variational formulations of the problem are given using the Poincaré-Steklov operator that maps normal stresses to normal displacements. To approximate this operator the discrete Fourier transform is used. The fast Fourier transform algorithms are applied for numerical realization. A variational formulation of a boundary value problem for transforms of displacements is used to calculate a transfer function. A quadratic programming problem with equality and inequality restrictions is obtained by approximating the original contact problem. To solve this problem numerically an algorithm based on the conjugate gradient method is used. Some regularities of contact interaction have been established.

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About the authors

A. A. Bobylev

Lomonosov Moscow State University; Moscow Centre for Fundamental and Applied Mathematics

Author for correspondence.
Email: abobylov@gmail.com
Russian Federation, Moscow; Moscow

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