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Structure‐preserving space‐time discretization of nonlinear structural dynamics based on a mixed variational formulation
Author(s) -
Janz Alexander,
Betsch Peter,
Hesch Christian
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610091
Subject(s) - discretization , nonlinear system , finite element method , robustness (evolution) , displacement field , stability (learning theory) , mathematics , control theory (sociology) , computer science , physics , mathematical analysis , engineering , structural engineering , biochemistry , quantum mechanics , chemistry , control (management) , machine learning , artificial intelligence , gene
The present work deals with the design of structure‐preserving numerical methods in the field of nonlinear elastodynamics and structural dynamics. Structure‐preserving schemes such as energy‐momentum consistent (EMC) methods are known to exhibit superior numerical stability and robustness. Most of the previously developed schemes are relying on a displacement‐based variational formulation of the underlying mechanical model. In contrast to that we present a mixed variational framework for the systematic design of EMC schemes. The newly proposed mixed approach accomodates high‐performance mixed finite elements such as the shell element due to Wagner & Gruttmann [1] and the brick element due to Kasper & Taylor [2]. Accordingly, the proposed approach makes possible the structure‐preserving extension to the dynamic regime of those high‐performance elements. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)