An improved mixed finite element based on a modified least-squares formulation for hyperelasticity |
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| Authors: | Alexander Schwarz Karl Steeger Jörg Schröder Gerhard Starke Benjamin Müller |
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| Affiliation: | 1. Institute of Mechanics, Faculty of Engineering, University of Duisburg-Essen, Universitätsstr. 15, 45117 Essen, Germany;2. Arbeitsgruppe Numerische Mathematik, Faculty of Mathematics, University of Duisburg-Essen, Thea-Leymann-Str. 9, 45127 Essen, Germany |
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| 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) |
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