Collaborative robust topology optimization of FGMs considering hybrid bounded uncertainties based on the distance to ideal solution

In this article, an efficient collaborative robust topology optimization (CRTO) method is proposed for functionally graded materials (FGMs) considering hybrid bounded uncertainties (HBU). Firstly, to realize the collaborative optimization of the structural topology and volume fraction of reinforcement in FGMs, two sets of design variables are defined following the SIMP framework. Secondly, with the uncertain material properties and external loads mathematically modeled as random and interval uncertain parameters respectively, the objective performance of FGMs are described as the implicit function of two sets of design variables and uncertain parameters. In contrast to the classical method of weighting the mean and standard deviation of objective performance, the robust objective function is constructed based on a novel distance to ideal solution to avoid the manually setting of weight parameters. The sensitivity analysis of the objective and constraint function with regard to the two sets of design variables is derived explicitly and a realization vector set is defined for bounded probabilistic uncertainties to parallelize the sensitivity analysis. In addition, an adaptive density shift algorithm is proposed to produce a clear topological profile and accelerate the convergence of the optimization. The effectiveness of the proposed method is demonstrated by both numerical and engineering examples.