Numerical performance of two formulations of truss topology optimization

Abstract

The present paper studies topology optimization of truss structures in multiple loading cases and with stress constraints. It is pointed out in the paper that the special difficulty of adding bars and/or deleting bars from structure in the numerical algorithm of truss topology optimization is caused by the discontinuity of stress functions at the zero cross sectional area in the conventional formulation. In a new formulation, we replace the stress constraints by new constraints. The new constraints retain the same feasibility of the stress constraints, but are continuous in the closed interval up to zero cross sectional area. The new formulation enables us to solve topology optimization problem in the frame of the existing FEM software and mathematical programming techniques. Powell constrained variable metric method is applied to a number of examples of truss topology optimization. Numerical performances of the two formulations are compared. It is shown that in the conventional formulation the iteration of numerical algorithm may be blocked by discontinuity of the stress constraint and often stops at a nonoptimum solution. And in the new formulation the bar adding and bar deleting is done rationally and a local optimum, even the global optimum can be obtained by iteration.