On the Extension of Mesh‐Distortion‐Insensitive Petrov‐Galerkin Finite Element Formulations to Linear Elastodynamics

Numerous mesh-distortion-insensitive Petrov-Galerkin finite element formulations have been developed for the simulation of elastostatic problems. This contribution presents initial results on how these formulations can be extended to linear elastodynamics. In this context, three different approaches are examined, building upon an established 8-node elastostatic formulation. The first two approaches demonstrate that preexisting strategies reach their limits when applied to such unsymmetric formulations. In contrast, the novel third approach enables stable simulations. Moreover, the resulting formulation appears to be less sensitive to mesh distortion than a standard 8-node Bubnov-Galerkin formulation.