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An improved mixed finite element based on a modified least‐squares formulation for hyperelasticity
Author(s) -
Schwarz Alexander,
Steeger Karl,
Schröder Jörg,
Starke Gerhard,
Müller Benjamin
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410109
Subject(s) - finite element method , hyperelastic material , mathematics , least squares function approximation , displacement (psychology) , mixed finite element method , nonlinear system , non linear least squares , stress (linguistics) , total least squares , mathematical analysis , algorithm , physics , estimation theory , structural engineering , engineering , psychology , linguistics , statistics , philosophy , quantum mechanics , estimator , psychotherapist , singular value decomposition
Abstract The present work deals with the solution of geometrically nonlinear elastic problems solved by the least‐squares finite element method (LSFEM). The main goal is to obtain an improved performance and an accurate approximation in particular for lower‐order elements. Basis for the mixed element is a first‐order stress‐displacement formulation resulting from a classical least‐squares method. Similar to the ideas in SCHWARZ ET AL. [1] a modified weak form is derived by the introduction of an additional term controlling the stress symmetry condition. The approximation of the unknowns follows the same procedures as for a conventional least‐squares method, see e.g. CAI & STARKE [2]. The proposed modified formulation is compared to recently developed classical LSFEMs, in order to show the improvement of performance and accuracy. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)