Limit analysis of frictional block assemblies as a mathematical program with complementarity constraints

The computation of the collapse loads of discrete rigid block systems, characterized by frictional (nonassociative) and tensionless contact interfaces, is formulated and solved as a special constrained optimization problem known as a Mathematical Program with Equilibrium Constraints (MPEC). In the present instance, some of the essential constraints are defined by a complementarity system involving the orthogonality of two sign-constrained vectors. Due to its intrinsic complexity, MPECs are computationally very hard to solve. In this paper, we investigate a simple numerical scheme, involving appropriate relaxation of the complementarity term, to solve this nonstandard limit analysis problem. Some computational results are presented to illustrate potentialities of the method.