Nonprobabilistic reliability oriented topological optimization for multi-material heat-transfer structures with interval uncertainties

Abstract

This study presents a nonprobabilistic reliability-based topology optimization (NRBTO) framework that combines a multi-material interpolation model and interval mathematics to achieve an optimal layout design for heat-transfer structures under unknown but bounded (UBB) uncertainties. In terms of the uncertainty quantification (UQ) issue, the interval dimension-wise method (IDWM) based on set collocation theory is first proposed to effectively determine the bounds of nodal temperature responses. For safety reasons, the interval reliability (IR) index corresponding to the thermal constraint is defined, and then a new design policy, i.e., the strategy of nonprobabilistic reliability oriented topological optimization is established. To circumvent problems of large-scale variable updating in a multi-material topology optimization procedure, theoretical deductions of the design sensitivity analysis are further given based on the adjoint-vector criterion and the chain principle. The validity and feasibility of the developed methodology are eventually demonstrated by several application examples.