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An asymmetric Least‐Squares Mixed Finite Element for Elasto‐Plasticity at Small Strains
Author(s) -
Schwarz Alexander,
Schröder Jörg
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910091
Subject(s) - least squares function approximation , plasticity , finite element method , non linear least squares , mathematics , element (criminal law) , order (exchange) , generalized least squares , total least squares , mathematical analysis , explained sum of squares , algorithm , engineering , physics , structural engineering , statistics , thermodynamics , singular value decomposition , finance , estimator , political science , law , economics
We present a mixed finite element based on a modified least‐squares formulation for rate‐independent elasto‐plasticity. Due to kink‐like points in the least‐squares functional, the first variation is not always continuous and a standard Newton method could fail in order to minimize the least‐squares functional. In order to keep the availability of the Newton method, we introduce a modified least‐squares approach, which guarantees the continuity of the resulting weak form. Finally, a numerical example is presented to show the applicability and performance. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)