Extended Limit Analysis of Strain Softening Frames Involving 2nd-Order Geometric Nonlinearity and Limited Ductility

Abstract

Classical limit analysis is extended to include the effects of 2nd-order geometric and material nonlinearities, as well as the inclusion of limited ductility constraints. For the class of frame structures considered, the material constitutive model adopted can simultaneously accommodate the effects of combined axial and flexural force as well as local softening instability through the use of piecewise linearized yield surfaces. The main feature of the approach developed is to compute, in a single step, an upper bound to the maximum load. Corresponding displacements and stresses can be obtained as a by-product of the analysis. The problem is formulated as an instance of the challenging class of so-called mathematical programs with equilibrium constraints (MPECs). A number of numerical examples are provided to validate the robustness and efficiency of the current approach, and to illustrate some key mechanical features expected of realistic frames that exhibit local softening behavior and geometric nonlinearity.