An MPEC approach for the critical post-collapse behavior of rigid-plastic structures

This paper presents a numerical method to identify and trace the critical post-collapse response of rigid perfectly-plastic structures. To account for the possibility of multiple equilibrium paths, the critical one is directly identified using the minimum 2nd-order work criterion. Our proposed enhanced sequential limit analysis is formulated as an instance of the challenging class of optimization problems known as a mathematical program with equilibrium constraints (MPEC). This MPEC formulation minimizes the 2nd-order work expression subject to the set of constraints describing the complete complementarity system (in mixed static-kinematic variables) governing simultaneously the two adjacent equilibrium configurations, namely the current one and its neighboring state. We use a nonlinear programming based algorithm, involving relaxation of the complementarity terms, to solve the MPEC. Four numerical examples are provided to illustrate application of the proposed scheme.