Plastic optimization of 3D steel frames under fixed or repeated loading: Reduction formulation

This paper present a new algorithm of plastic optimization for 3D steel frames under fixed loading (limit optimization) or repeated loading (shakedown optimization). The weights of the frames are minimized under constraints of plastic collapse (instantaneous mechanics/alternating plasticity). A 3D plastic-hinge considering two bending moments and axial force is taken into account by 16-facet polyhedrons. The static theorem of limit analysis is adopted and the formulations are written under a linear programming problem that is solved by using the simplex method. Several useful techniques of reducing the problem sizes are proposed. Some numerical examples are presented to demonstrate the efficiency of the proposed algorithm.