Rocking response of masonry block structures using mathematical programming

In this paper a variational formulation for dynamic analysis is adopted to investigate rock-ing behaviour of masonry block structures under lateral loads. The model is composed of rigid bodies interacting at potential contact points located at the vertexes of the block inter-faces. A no-tension and associative frictional behaviour with infinite compressive strength is assumed at contact interfaces. The contact dynamic problem is governed by equilibrium equations, which relate external, inertial and contact forces, and by kinematic equations, which ensure compatibility between contact displacement rates and block degrees of free-dom. Mathematical programming is used to solve the optimization problem arising from the formulation of the variational problem associated to dynamics of the block assemblages. To evaluate the accuracy and computational efficiency of the implemented formulation, a vali-dation study is presented for rigid blocks subjected to rocking behaviour under different ac-celeration pulse types and for an in-plane wall panel problem from the literature. A good agreement in terms of failure mechanism and response time histories was observed. The computational efficiency and the stability of the implemented procedure were found to be encouraging, thus suggesting that the proposed model may be used to model dynamic behav-iour of masonry block assemblages with a large number of rigid bodies.