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A NOVEL FINITE ELEMENT APPROACH TO FRICTIONAL CONTACT PROBLEMS
Author(s) -
REFAAT M. H.,
MEGUID S. A.
Publication year - 1996
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(19961130)39:22<3889::aid-nme29>3.0.co;2-6
Subject(s) - variational inequality , finite element method , quadratic programming , mathematical optimization , regularization (linguistics) , convergence (economics) , penalty method , mathematics , minification , algorithm , computer science , engineering , artificial intelligence , structural engineering , economics , economic growth
Existing solution techniques which are based upon the variational inequalities description of frictional contact problems mostly adopt penalty and regularization methods. The convergence and accuracy of these methods are governed by user defined parameters . To overcome the difficulties associated with the ad hoc use of such parameters, the variational inequality of the general frictional contact problem is treated through a two‐step algorithm using mathematical programming. In the first, the technique of Quadratic Programming (QP) is used to identify the developing contact surface and to determine the normal stresses acting on it. In the second, a novel minimization algorithm is devised to treat the Non‐Differential Optimization (NDO) problem arising from the use of Coulomb's friction law. This novel algorithm solves the NDO problem through a sequence of convex QP sub‐problems in a sequential search strategy. The validity of the method is established by treating two test cases, where the main features and difficulties of contact problems can be examined.