A dissipated energy maximization approach to elastic-perfectly plastic analysis of planar frames

The optimization approaches, known as powerful tools in nonlinear analysis of structures, are considered in this paper for further development. Adopting linear kinematics, proportional loading, lumped plasticity, piecewise-linear yield loci, perfect plasticity and associated flow rule as the basic assumptions, the nonlinear analysis of a framed structure is formulated in the form of a mathematical programming problem. Dissipated energy is considered as the objective function and is maximized using the conventional simplex method with special provisions to obtain exact structural responses. The proposed algorithm is validated and outlined using several numerical examples taken from the literature.