Limit analysis of elastoplastic frames considering 2nd-order geometric nonlinearity and displacement constraints

The present paper extends the classical limit analysis of plane frames to account for 2nd-order geometric nonlinearity. Any specified displacement limits can also be included in the proposed analysis. The effect of combined bending moment and axial force is accommodated in the adopted piecewise linearized yield condition, albeit still assumed as perfectly plastic. The main feature of the novel approach proposed is to compute simultaneously, in a single step, the maximum load and corresponding deformations of the structure under limited displacement conditions. The problem is cast as an instance of the challenging class of (nonconvex and nonsmooth) mathematical programs with equilibrium constraints (MPECs). Various nonlinear programming based algorithms are proposed to solve the MPEC. Four numerical examples are provided to illustrate application of the proposed limit analysis approach and to highlight the necessity of considering geometric nonlinearity for a more realistic assessment of structural behavior.