Hybrid 3D-plane finite element modeling for elastodynamics

The coupling of three-dimensional (3D) and plane (2D) finite element (FE) models to form a single hybrid 3D–2D model is considered for linear elastodynamic problems. The 2D model is used to represent a large thin 3D computational domain where the solution behaves approximately in a 2D (plane-elasticity) way. Problems where the normal displacement is important in the thin region (bending) are excluded. The hybrid model, if designed properly, is a more efficient way to solve the full 3D model over the entire problem. This paper focuses on the way the 3D–2D coupling is performed, and on the coupling error generated. The Panasenko technique is used to couple the 3D and 2D models. This method has been used previously for mixed-dimensional coupling in steady-state problems, as well as for 2D–1D coupling of acoustic waves. Here it is being used for the first time for the 3D–2D coupling of time-dependent elastic problems. The hybrid formulation is derived, and is shown to be well-posed. It is shown that the Panasenko method is extremely simple to implement in the framework of FE analysis, yet the resulting coupling yields a rather small error level, provided the 3D–2D interface is sensibly placed. The numerical accuracy and efficiency of the method are explored for a couple of example problems. In particular, it is shown that spurious reflections from the interface back into the 3D region are negligible.