Simultaneous ultimate load and deformation analysis of strain softening frames under combined stresses

This paper presents a method for carrying out, in a single step, an elastoplastic analysis to obtain simultaneously both the ultimate load and corresponding deformation of a strain softening structure. The effect of combined bending moment and axial force is also accounted for in the piecewise linearized softening yield condition. However, a monotonic loading process is assumed within a small displacement framework. We propose a mathematical programming approach to tackle this problem. In particular, the formulation leads to an instance of the challenging class of a so-called “mathematical program with equilibrium constraints” (MPEC). Various nonlinear programming based algorithms are proposed to solve the MPEC. Numerical examples are provided to illustrate the described analysis and also to highlight the effects of constitutive local softening instability and of axial forces on the overall structural behavior of the frames.