A compliance based topology optimization design of structures considering non-probabilistic reliability.

*(Chinese. English summary)*Zbl 1265.74073Summary: In practical engineering, existing uncertainties may play an important role in structural topology optimization. Based on the multi-ellipsoid convex model for uncertainties and the definition of the non-probabilistic reliability index, a mathematical model for non-probabilistic reliability based topology optimization is proposed. The optimization objective is to minimax the structural compliance with the constraints on the material volume and the bounds of uncertainties. The single loop strategy combining with the method of moving asymptotes is adopted for the solution of the optimization problem. Then the advantages of the proposed topology optimization are illustrated by a classical example of size optimization design. Numerical investigations underline the validity of the present model as well as the proposed numerical techniques.