%A Michael C. Ferris
%A Francis Tin-Loi
%T Limit analysis of frictional block assemblies as a mathematical program with complementarity constraints
%D February 1999
%R 99-01
%I COMPUTER SCIENCES DEPARTMENT, UNIVERSITY OF WISCONSIN
%C MADISON, WI
%X
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.