Application of the wave finite elements for calculating dynamic responses of 2D structures of arbitrary shapes subjected to external loads

The wave finite element method (WFE) has been developed originally for one dimensional periodic structures with advantage in calculation time. However, this method cannot apply easily for 2D structures of arbitrary shape. This communication presents a new technique of WFE to calculate the dynamic responses of such a structure subjected to external loads. The structure is decomposed into rectangular domains which can be considered as periodic structures subjected to external loads and nodal reaction forces at the domains boundaries. Then, by using the WFE for theses domains, we can obtain a relation between the external loads, the DOF and the nodal reaction forces at the boundaries of the domains. Finally, by combining this relation with the dynamic equation of the rest of the structure, we obtain an equation of the whole structure to compute its response. This technique permits to reduce all the DOF of the rectangular domains of the structure. Examples showing the efficiency of the method are presented.