Structure-preserving space-time discretization of nonlinear structural dynamics based on a mixed variational formulation

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)