For the time-dependent and field uncertainties in continuum structures, this paper proposes a novel time-dependent non-probabilistic reliability-based topology optimization (TNRBTO) method based the spatial points control technology (SPCT) method, where field uncertainty is characterized by a bounded field model. To transform the time-dependent reliability problem into a static one, the predictable time- dependent uncertainty is converted into static time parameter, thereby establishing a TNRBTO model that simultaneously considers both parametric and field uncertainties. The TNRBTO model is a nested optimization problem, where the inner-loop optimization determines the worst-case time instant and field uncertainty realization, while the outer-loop optimization identifies the optimal structural topology configuration based on SPCT method—an approach that constructs field functions via spatial arrangement of control points to define structural topology. The optimization model is solved using the gradient-based method of moving asymptotes (MMA) algorithm. To validate the effectiveness of the proposed optimization approach, three numerical examples are presented, including a three-dimensional cantilever beam structure. Furthermore, a comparative analysis between the SPCT method and the material field series expansion (MFSE) topology optimization algorithm is conducted in the second example to demonstrate the advantages and limitations of the proposed methodology.
Zhan et al. (Sat,) studied this question.