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Hybrid‐mixed discretization of elasto‐dynamic contact problems using consistent singular mass matrices
Author(s) -
Tkachuk A.,
Wohlmuth B. I.,
Bischoff M.
Publication year - 2013
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4457
Subject(s) - discretization , mathematics , mass matrix , truss , mathematical analysis , numerical analysis , matrix (chemical analysis) , physics , engineering , materials science , structural engineering , nuclear physics , neutrino , composite material
SUMMARY An alternative spatial semi‐discretization of dynamic contact based on a modified Hamilton's principle is proposed. The modified Hamilton's principle uses displacement, velocity and momentum as variables, which allows their independent spatial discretization. Along with a local static condensation for velocity and momentum, it leads to an approach with a hybrid‐mixed consistent mass matrix. An attractive feature of such a formulation is the possibility to construct hybrid singular mass matrices with zero components at those nodes where contact is collocated. This improves numerical stability of the semi‐discrete problem: the differential index of the underlying differential‐algebraic system is reduced from 3 to 1, and spurious oscillations in the contact pressure, which are commonly reported for formulations with Lagrange multipliers, are significantly reduced. Results of numerical experiments for truss and Timoshenko beam elements are discussed. In addition, the properties of the novel discretization scheme for an unconstrained dynamic problem are assessed by a dispersion analysis.Copyright © 2013 John Wiley & Sons, Ltd.