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A formulation of arbitrarily shaped surface elements for three‐dimensional large deformation contact with friction
Author(s) -
Parisch H.,
Lübbing Ch.
Publication year - 1997
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/(sici)1097-0207(19970930)40:18<3359::aid-nme217>3.0.co;2-5
Subject(s) - finite element method , contact analysis , coulomb friction , convergence (economics) , deformation (meteorology) , quadratic equation , surface (topology) , penalty method , stiffness , unilateral contact , contact force , contact mechanics , coulomb , contact theory , mechanics , mathematical analysis , mathematics , classical mechanics , geometry , structural engineering , engineering , materials science , physics , mathematical optimization , nonlinear system , composite material , quantum mechanics , economics , economic growth , electron
Abstract The paper introduces a general theory for the numerical simulation of large deformation contact problems. The contacting bodies under consideration may be of two‐ or three‐dimensional shape modelled by finite elements. A contact finite element which can be applied to handle multi‐body contact as well as contact with rigid bodies is developed. The element is universal in the sense that it can be used as a surface element for any known finite element model and includes friction. The frictional behaviour of the model obeys Coulomb's law of friction distinguishing between sticking and sliding contact. The algorithmic treatment is based on a penalty formulation for the normal and sticking contact. The corresponding consistent tangential stiffness matrices are derived, leading to an overall quadratic convergence behaviour for the method. This feature is demonstrated in a number of representative examples. © 1997 by John Wiley & Sons, Ltd.