﻿ Comparison of Lagrange Multiplier Method Implementation for Solving Two-Dimensional Contact Problems | Herald of the Bauman Moscow State Technical University. Natural Sciences
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# Comparison of Lagrange Multiplier Method Implementation for Solving Two-Dimensional Contact Problems

 Authors: Galanin M.P., Gliznutsina P.V., Lukin V.V., Rodin A.S. Published: 27.09.2017 Published in issue: #5(74)/2017 DOI: 10.18698/1812-3368-2017-5-35-48 Category: Mechanics | Chapter: Mechanics of Deformable Solid Body Keywords: deformable solid, contact problem, finite element method, Lagrange multiplier method

We consider a two-dimensional contact problem involving two deformable solids. We used the finite element method based on quadrilateral bilinear elements to approximate our elastic problem. Three implementations of the Lagrange multiplier method account for contact conditions: node-to-surface, surface-to-surface and surface-to-surface employing sub-segments. We carried out test calculations, solving the Hertz problem and comparing our results to the analytical solution. A comparative analysis of these methods shows that the two surface-to-surface contact implementations are more accurate than the node-to-surface implementation. The surface-to-surface contact method that employs sub-segments makes it possible to smooth out stress field fluctuations, but this effect only works for a limited number of problems

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