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

• Interval limit analysis incorporates interval applied loads and plastic capacities.
• Efficient MP methods to obtain directly sharp collapse load bounds of structures.
• Optimal minimum collapse load bound is computed using a mixed 0–1 MP approach.
• Optimal maximum and minimum load bounds are captured using pairs of NLP approaches.
• Conditions under which accurate bounds are obtained at extreme limits of intervals.

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.