A lagrange multiplier solution method for pounding of buildings during earthquakes

An effective solution method for studying the pounding response of two or more adjacent buildings during earthquakes is presented. The method is based on the Lagrange multiplier approach by which the geometric compatibility conditions due to contact are enforced. The energy and momentum balance criteria for the contacting bodies are satisfied according to the laws of impact with proper post-impact conditions, which can also take into account local energy absorption phenomena during impact. A solution scheme is proposed which can be incorporated easily into existing computer programs for static and dynamic analysis of structures. The applicability of the algorithm is illustrated in a number of selected sample problems and the correlation of numerical results to analytical solutions, whenever possible, is very satisfactory.