Collapse behaviour of three-dimensional brick-block systems using non-linear programming

A two-step procedure for the application of non linear constrained programm ing to the limit analysis of rigid brick-block systems with no-tension and frictional interface is implemented and applied to various masonry structur es. In the first step, a linear problem of programming, obtained by applyin g the upper bound theorem of limit analysis to systems of blocks interactin g through no-tension and dilatant interfaces, is solved. The solution of th is linear program is then employed as initial guess for a non linear and no n convex problem of programming, obtained applying both the 'mechanism' and the 'equilibrium' approaches to the same block system with no-tension and frictional interfaces. The optimiser used is based on the sequential quadra tic programming. The gradients of the constraints required are provided dir ectly in symbolic form. Ln this way the program easily converges to the opt imal solution even for systems with many degrees of freedom. Various numeri cal analyses showed that the procedure allows a reliable investigation of t he ultimate behaviour of jointed structures, such as stone masonry structur es, under statical load conditions.