Worst scenario detection in limit analysis of trusses against deficiency of structural components

This paper addresses the plastic limit analysis of a truss with some deficient structural components. Given the upper bound for the number of deficient members, we consider uncertainty in the locations of deficient members, i.e., the set of deficient members is not specified in advance. Then we attempt to find the worst scenario of deficiency, in which the limit load factor attains the minimum value. We formulate this combinatorial optimization problem as a mixed integer linear programming problem and solve it by using an algorithm with guaranteed global convergence. The deficient structural components in the worst scenario are regarded as key elements which cause the largest degradation of structural performance. Numerical examples illustrate that the set of key elements, as well as the collapse mode in the worst scenario, depends on the number of deficient structural components.