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Numerical analysis of a lumped parameter friction model. (English) Zbl 1363.74066

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, November 18–21, 2015. In honor of the birthday anniversaries of Ivo Babuška (90), Milan Práger (85), and Emil Vitásek (85). Prague: Czech Academy of Sciences, Institute of Mathematics (ISBN 978-80-85823-65-3). 63-76 (2015).
Summary: We consider a contact problem of planar elastic bodies. We adopt Coulomb friction as (an implicitly defined) constitutive law. We will investigate highly simplified lumped parameter models where the contact boundary consists of just one point. In particular, we consider the relevant static and dynamic problems. We are interested in numerical solution of both problems. Even though the static and dynamic problems are qualitatively different, they can be solved by similar piecewise-smooth continuation techniques. We will discuss possible generalizations in order to tackle more complex structures.
For the entire collection see [Zbl 1329.00187].

MSC:

74M10 Friction in solid mechanics
65P40 Numerical nonlinear stabilities in dynamical systems
37M05 Simulation of dynamical systems
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
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