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Existence and uniqueness for frictional incremental and rate problems - sharp critical bounds
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
University of Lisbon, Portugal.
Zagazig University, Egypt.
2016 (English)In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 96, no 1, 78-105 p.Article in journal (Refereed) PublishedText
Abstract [en]

We investigate frictional contact problems for discrete linear elastic structures, in particular the quasistatic incremental problem and the rate problem. It is shown that sharp conditions on the coefficients of friction for unique solvability of these problems are the same. We also give explicit expressions of these critical bounds by using a method of optimization. For the case of two spatial dimensions the conditions are formulated as a huge set of non symmetric eigenvalue problem. A computer program for solving these problems was designed and used to compute the critical bounds for some structures of relative small size, some of which appeared in the literature. The results of a variety of numerical experiments with uniform and non uniform distributions of the frictional properties are presented. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Place, publisher, year, edition, pages
WILEY-V C H VERLAG GMBH , 2016. Vol. 96, no 1, 78-105 p.
Keyword [en]
Coulomb friction; quasistatic and rate problems; existence/uniqueness; sharp critical bounds; finite elements
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-124481DOI: 10.1002/zamm.201400143ISI: 000367732000007OAI: diva2:899709
Available from: 2016-02-02 Created: 2016-02-01 Last updated: 2016-02-09

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Andersson, Lars-Erik
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Mathematics and Applied MathematicsThe Institute of Technology
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