Conjugated infinite elements for two-dimensional time-harmonic elastodynamics

Wave propagation problems in unbounded domains require the handling of appropriate radiation conditions (Sommerfeld). Various absorbing boundary conditions are available for that purpose. In a discrete finite element context, local and global Dirichlet-to-Neumann (DtN) and infinite element methods have shown their efficiency for the scalar wave equation. The paper concentrates on the extension of an infinite element method to the elastodynamic vector wave equation. The extension is developed in the frequency domain for 2-D problems. The paper focuses on the development of a conjugated formulation using the Helmholtz decomposition theorem of smooth vector fields. The accuracy of the developed formulation is assessed through the study of benchmarks. The computed results are shown to be in good agreement with the analytical solution for a multi-pole field along a circular cavity and with the results produced by other numerical methods.