考虑材料性能空间分布不确定性的可靠度拓扑优化

论文研究了考虑材料性能空间分布不确定性的连续体结构可靠度拓扑优化问题。其中，材料的弹性模量视为具有给定概率分布特征的随机场，其离散采用级数最优线性估值法（EOLE）。随机结构的响应以及相应的灵敏度分析采用多项式混沌展开（PCE）近似表达，并采用Monte Carlo方法验证了该方法的精度。结构的可靠度分析采用一次可靠度方法（FORM），在优化问题的求解中，对双层嵌套方法和序列近似规划（SAP）方法进行了对比。数值算例中，该方法应用于二维和三维结构的拓扑优化问题，优化结果验证了方法的正确性和有效性。

Reliability-based Topology Optimization Considering Spatially Varying Uncertain Material Properties

Topology optimization aims to find the optimal distribution of a given amount of material in a design domain to maximize the structural performance. However, the deterministic topology optimization may generate a structural design that is not reliable or robust under uncertain parameter variations. The reliability-based topology optimization considering spatially varying uncertain material properties is developed in this paper. In practical engineering, some uncertain parameters fluctuate not only over the time domain but also in space. Therefore, an independent random variable is incapable of characterizing the structural uncertainty due to its spatially varying nature. In such circumstances, we introduce a random field model for the spatially varying physical quantities. The elastic modulus is modeled as a random field with a given probability distribution, which is discretized by means of an Expansion Optimal Linear Estimation (EOLE). The response statistics and their sensitivities are evaluated with the polynomial chaos expansions (PCE). The accuracy of the proposed method is verified by the Monte Carlo simulations. The reliability of the structure is analyzed using the first-order reliability method (FORM). Two approaches to solving the optimization problems are compared, which are the double-loop approach and the sequential approximate programming (SAP) approach. Numerical examples show that the proposed method is valid and efficient for both 2D and 3D topology optimization problems. The obtained results show that the SAP approach has higher efficiency than the double-loop approach, and can realize concurrent convergence of topology optimization and reliability analysis. In addition, it is found that the reliability-based topology optimization (RBTO) solutions considering the uncertain model (the random variable and the random field model) have different topologies and member sizes to improve the level of reliability as compared with the deterministic solutions. Also, the optimal designs considering the random field model require less material, compared with those obtained with random variables.