Earthquake interaction between adjacent buildings under friction effects

A numerical approach is presented for an inequality problem arising in the earthquake analysis of adjacent buildings. This problem concerns the unilateral contact-impact between neighboring buildings, when friction and P-delta effects are taken into account. The proposed numerical approach is based on a double discretization, in space and time, and on optimization methods. First, the Finite Element Method is applied in space. A piecewise linearization for the nonconvex contact laws and for the Coulomb frictional behaviour is used. Next, with the aid of Laplace transform, the linear equality problem conditions are transformed to convolutional ones, involving as unknowns the unilateral quantities only. So the number of unknowns is significantly reduced. Then, by using a time marching scheme, in each time step a nonconvex linear complementarity problem is solved. Finally, the proposed method is illustrated by means of a numerical example and some conclusions useful for the civil engineering praxis are discussed.