MULTILEVEL FORMULATIONS IN THE LIMIT ANALYSIS AND DESIGN OF STRUCTURES WITH BILATERAL CONTACT CONTACT CONSTRAINTS

In this paper, we study the rich class of formulations that arise in t he limit analysis and design of elastic/plastic structures in the pres ence of contact constraints. It is well-known that in the absence of c ontacts, both the limit analysis and limit design problems can be writ ten as linear programs. However, when contact constraints are present, the structure effectively exhibits:both softening and stiffening beha viour under monotonically increasing loading. The resulting limit anal ysis and limit design problems are non-convex and are difficult to sol ve due to the presence of complementary type of equality constraints. We show that by using a mixed form of the minimum principle, we can re state the limit analysis and limit design problems as two- and three-l evel formulations, respectively. Further, under a strong assumption on the problem and solution data, we can take advantage of the underlyin g convexity td reduce both these multilevel formulations to equivalent linear programs. While it may not be possible to always verify this a ssumption in practice, we show that a two-step iterative procedure is effective in reaching a solution to the limit design problem.