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Computational Mechanics
Erschienen in: Computational Mechanics 1/2015

01.07.2015 | Original Paper

Bifurcations in piecewise-smooth steady-state problems: abstract study and application to plane contact problems with friction

verfasst von: T. Ligurský, Y. Renard

Erschienen in: Computational Mechanics | Ausgabe 1/2015

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Abstract

The paper presents a local study of bifurcations in a class of piecewise-smooth steady-state problems for which the regions of smooth behaviour permit analytical expressions. A system of piecewise-linear equations capturing the essential features of branching scenarios around points of non-smoothness is derived under the assumptions that (i) the points lie in the intersection of the boundaries of the regions where the gradients of the respective smooth selections have the full rank, (ii) there is no solution branch whose tangential direction is tangent to the boundary of any of the regions. The simplest cases of this system are studied in detail and the most probable branching scenarios are described. A criterion for detecting bifurcation points is proposed and a procedure for its realisation in the course of numerical continuation of solution curves is designed for large problems. Application of the general frame to discretised plane contact problems with Coulomb friction is explained. Simple as well as more realistic model examples of bifurcations are shown.
Vorheriger Artikel A displacement smoothing induced strain gradient stabilization for the meshfree Galerkin nodal integration method
Nächster Artikel A semi-numerical algorithm for instability of compressible multilayered structures

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Metadaten
Titel
Bifurcations in piecewise-smooth steady-state problems: abstract study and application to plane contact problems with friction
verfasst von
T. Ligurský
Y. Renard
Publikationsdatum
01.07.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 1/2015
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-015-1154-1

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