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Non‐unique Equilibria of a Statically Indeterminate System with Coulomb Friction
Author(s) -
Steiner Wolfgang
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710146
Subject(s) - statically indeterminate , slipping , coulomb , coulomb friction , indeterminate , static friction , simple (philosophy) , coulomb's law , unilateral contact , mathematics , statistical physics , mathematical economics , classical mechanics , physics , materials science , thermodynamics , pure mathematics , geometry , nonlinear system , quantum mechanics , finite element method , composite material , electron , philosophy , epistemology
This contribution aims to show that the Coulomb friction model in a statically indeterminate system can result in ambiguous equilibrium states. We demonstrate that a simple framework may be in equilibrium and satisfy all inequalities, related to a unilateral contact, for several values of the reaction forces. A new method [3], which extends Castigliano's theorem to problems with Coulomb friction, is applied to analyze the cases of sticking, slipping or opening of the framework's supports. We think that our example is simpler and more illustrative than the rather mathematical examples in [1] or in [2] where non‐unique static solutions were found, too. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)