Some recent advances in the wave finite element method

The wave finite element (WFE) method is now an established numerical method for obtaining the structural response of periodic structures. From a model of a substructure obtained from any finite element software, it allows to get dispersion curves and responses of finite periodic structures with a low calculation cost. Here, we consider some recent improvements of the method. First of all, the original WFE is often formulated with some point loads on the structure, but we show that it is possible to extend this to the consideration of general loads as pressure waves or moving loads for which external loads are applied on each substructure. Second, the classical WFE deals with structures in the frequency domain. It would be interesting to consider the analysis of periodic structures in the time domain, for instance to deal with blast loads. We present here one possibility to do so by computing absorbing boundary conditions in the time domain. By considering supplementary variables at the boundary, a new formulation can be obtained and a classical equation with extended mass, damping and stiffness matrices can be formulated in the time domain and solved by classical algorithms like the Newmark scheme.