Mathematical programming approaches for obtaining sharp collapse load bounds in interval limit analysis

Abstract

The paper presents novel mathematical programming approaches for interval limit analysis that are guaranteed to furnish sharp (extreme) bounds to the collapse load of structures subjected to uncertain but bounded parameters. The formulation is cast as a pair of linear programs with interval coefficients. We discuss when sharp collapse load bounds occur when the interval parameters are at the extreme limits of their respective intervals. A mixed 0–1 programming approach is first proposed to compute the minimum collapse limit, and, more importantly, we then develop a pair of robust and efficient nonlinear programming schemes that capture maximum collapse loads in one case and minimum collapse loads in the other.