An optimisation algorithm for the collapse detection of stone masonry structures

摘要

The paper presents a computer procedure to evaluate the collapse load and the collapse mechanism of three-dimensional structures made of rigid blocks with no-tension and frictional interfaces based on mathematical programming. Using the theorems of non-standard limit analysis, the algorithm searches the minimum statically admissible load factor, which ensures a possible mechanism. The presence of friction makes the problem non-linear and difficult to solve. The possibility to detect the optimal solution using a quasi-feasible initial estimate of the unknowns is shown. This is obtained as the solution of a linear programming problem corresponding to a system of blocks with dilatancy in the joints instead of friction. Various analyses show the validity of the procedure and the effectiveness of the non-standard limit analysis approach for studying the collapse behaviour of real stone masonry structures.