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A stable energy‐conserving approach for frictional contact problems based on quadrature formulas
Author(s) -
Hager C.,
Hüeber S.,
Wohlmuth B. I.
Publication year - 2007
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.2069
Subject(s) - lagrange multiplier , spurious relationship , quadrature (astronomy) , mass matrix , mathematics , mathematical optimization , numerical stability , numerical analysis , conservation of energy , stability (learning theory) , matrix (chemical analysis) , computer science , mathematical analysis , engineering , physics , materials science , statistics , electrical engineering , neutrino , nuclear physics , thermodynamics , machine learning , composite material
A common approach for the numerical simulation of non‐linear multi‐body contact problems is the use of Lagrange multipliers to model the contact conditions. The stability of standard algorithms is improved by introducing a modified mass matrix which assigns no mass to the potential contact nodes. By this, the spurious algorithmic oscillations in the multiplier do not occur any more, which facilitates the application of the primal–dual active set strategy to dynamical contact problems. The new mass matrix is calculated via a modified quadrature formula that needs no extra computational cost. In addition the conservation properties of the underlying algorithm are transferred to the modified mass version. Different numerical examples for frictional two‐body contact problems illustrate the improvement in the results for the contact stresses. Copyright © 2007 John Wiley & Sons, Ltd.