Energy‐momentum conserving discretization of mixed shell elements for large deformation problems

Abstract

AbstractIn the present paper we consider structure‐preserving integration methods in the context of mixed finite elements. The used low‐order mixed finite elements typically exhibit improved coarse mesh accuracy. On the other hand energy‐momentum (EM) consistent time‐stepping schemes have been developed in the realm of nonlinear structural dynamics to enhance the numerical stability properties. EM schemes typically exhibit superior robustness and thus offer the possibility to use large time steps while still producing physically meaningful results. Accordingly, combining mixed finite element discretizations in space with EM consistent discretizations in time shows great promise for the design of numerical methods with superior coarse mesh accuracy in space and time. Starting with a general Hu‐Washizu‐type variational formulation we develop a second‐order accurate structure‐preserving integration scheme. The present approach is applicable to a large number of mixed finite element formulations. As sample application we deal with a specific mixed shell element. Numerical examples dealing with large deformations will show the improved coarse mesh accuracy in space and time of the advocated approach. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)