Effective Seismic Input

When incorporating earthquake excitation into the soil-structure model, we not only have to apply effective forces that are equivalent to the incoming earthquake, but we also have to account for the non-linearity of the structure, or in other words, start the transient earthquake analysis from a static state of the structure. 

The effective forces to be applied to the model are derived from the scattering analysis framework described earlier, wherein we consider the difference  between the ground motion with the structure and without, and this scattered motion - entirely outgoing from the structure - is absorbed by a PML boundary.

scattered motion in the soil domain is absorbed by the boundary

The non-linear analysis of the structure can also be incorporated in the same context, as described later.