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Recovery of equilibrium on star patches using a partition of unity technique
Author(s) -
Moitinho de Almeida J. P.,
Maunder E. A. W.
Publication year - 2009
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.2623
Subject(s) - finite element method , partition of unity , element (criminal law) , mixed finite element method , partition (number theory) , extended finite element method , mathematics , displacement (psychology) , mathematical optimization , mathematical analysis , structural engineering , engineering , combinatorics , psychology , political science , law , psychotherapist
A technique for recovering equilibrated element stresses is developed for finite element models of structural mechanics problems. The data for the method consist of the prescribed loading and the stress and displacement fields resulting from a conventional compatible finite element model. Local problems are defined for each star of elements, via the introduction of fictitious body forces and strains. These problems can be solved independently for equilibrium in a process that can be easily parallelized. The quality of the solutions is assessed, for two‐dimensional linear elastic problems, by using them to compute bounds of the error of the finite element solutions, in terms of both global and local quantities of interest. Copyright © 2009 John Wiley & Sons, Ltd.