Periodic BEM and FEM-BEM coupling - Application to seismic behaviour of very long structures

The main motivation of this work is the dynamic behavior of very long structures such as diaphragm and quay walls. Indeed despite a seemingly bi-dimensional or periodic geometry, a true three dimensional analysis has to be carried out since the seismic loading is fully three-dimensional. Unfortunately usual 3D models are not able to account for such large structures either from the theoretical or the numerical point of view. The development of a periodic approach accounting for general 3D loadings and using a Boundary Element Method is addressed in this paper. After introducing geometrical and functional frameworks, a generalised theory for periodicity fields and operators is given. It accounts for periodic domains and fields decompositions in view of a subdomain approach. Periodic boundary elements and special Green functions are then worked out. The third part points out some numerical validations and results issued from this theory applied to a real quay wall.