An enriched finite element method for general wave propagation problems using local element domain harmonic enrichment functions

Abstract

We present an enriched finite element (FE) formulation applicable for general wave propagation problems in one- and two-dimensional domains, using local element domain spatial harmonic enrichment functions which satisfy the partition of unity condition. It allows prescription of boundary conditions in the same way as in the conventional FE method. The method is assessed for different classes of wave propagation problems such as impact and high frequency-guided wave propagation in bars and plates, and surface and body wave propagation in semi-infinite solid media for which the classical FE method either fails to yield accurate results or is prohibitively expensive. It is shown that the present formulation gives accurate solutions to the former and shows significant improvement in computational efficiency for the latter category of problems. The performance is also assessed against other special FEs such as the spectral FE and a recently proposed enriched FE with global harmonic basis functions.