A novel method of non-probabilistic reliability-based topology optimization corresponding to continuum structures with unknown but bounded uncertainties

A new non-probabilistic reliability-based topology optimization (NRBTO) method for detailed design of continuum structures is proposed in this paper, in which the unknown but bounded (UBB) uncertainties existing in material and external loads are considered simultaneously. Based on the interval set-theoretic model, traditional displacement constraint is transformed into the non-probabilistic reliability format, in which a novel measuring index, namely, the optimization feature distance is defined by a combination of the area-ratio ideas. Thus, the optimal layout issue is converted by the lightweight design problem with displacement reliability constraints. Moreover, the interval parametric vertex approach and the adjoint vector method are also employed to obtain the sensitivity information between the reliability measurement and design variables. By utilizing the method of moving asymptotes (MMA), the optimization problem that is investigated can be solved iteratively. Two engineering examples are eventually presented to demonstrate the validity and effectiveness of the methodology that has been developed, and numerical results show that considering the UBB uncertainty effects during the whole procedure of topology optimization may have a significant influence on the final structural configurations.