Application of the wave finite element method to multi-span bridges

The Wave Finite Element (WFE) method is based on wave propagation in periodic structures. Starting from a Finite Element (FE) analysis of a single period (sub-structure) we are able to derive the dynamic behaviour relative to the entire structure. Thanks to a reduction in the degrees of freedom (dofs) of the system and by decomposing the response of the structure on a wave basis, the calculation time is considerably reduced compared to the classic FEM. Numerous structures have been solved with this method but it can not deal easily on the boundary conditions. In this study, we develop a technique of WFE to deal with more general cases of structures constrained in a arbitrary manner as a multiple supported bridge. By using the WFE method, the vectors of dofs and loads will be decomposed on the wave basis in function of loads and reaction forces of the supports. Then, by substituting the boundary condition in this wave decomposition, we obtain a relation between the reaction forces and the loads which permits to calculate the structure response. The numerical applications show that the WFE and FEM agree well and the new method permits to reduce significantly the calculation time.