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Total FETI for contact problems with additional nonlinearities
Author(s) -
Dobiáš Jiří,
Pták Svatopluk,
Vondrák Vít,
Dostál Zdeněk
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810269
Subject(s) - feti , a priori and a posteriori , lagrange multiplier , finite element method , nonlinear system , mortar methods , mathematics , grid , tearing , constraint algorithm , mathematical analysis , mathematical optimization , computer science , domain decomposition methods , geometry , structural engineering , engineering , mechanical engineering , physics , philosophy , epistemology , quantum mechanics
The paper is concerned with application of a new variant of the Finite Element Tearing and Interconnecting (FETI) method, referred to as the Total FETI (TFETI), to the solution to contact problems with additional nonlinearities. While the standard FETI methods assume that the prescribed Dirichlet conditions are inherited by subdomains, TFETI enforces both the compatibility between subdomains and the prescribed displacements by the Lagrange multipliers. If applied to the contact problems, this approach not only transforms the general nonpenetration constraints to the bound constraints, but it also generates an enriched natural coarse grid defined by the a priori known kernels of the stiffness matrices of the subdomains exhibiting rigid body modes. We combine our in a sense optimal algorithms for the solution to bound and equality constrained problems with geometric and material nonlinearities. The section on numerical experiments presents results of solution to bolt and nut contact problem with additional geometric and material nonlinear effects. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)