Design optimization considering uncertainties arising from different sources has been one of the hotspots in the area of structural optimization. This paper presents a robust topology optimization method for structures with bounded loads and spatially correlated material uncertainties. We first develop a new model for random structural loads with bounded nature, in which the uncertain load components are assumed to be uniformly distributed within a convex set represented by an ellipsoid model. This model is then combined with the random field discretized by means of the expansion optimized linear estimation to provide uncertainty modelling of structures exhibiting both load and material uncertainties. The robust topological design problem is formulated as a bi-criteria optimization problem for minimizing the mean value and standard deviation of the structural compliance under these uncertainties. The polynomial chaos expansion, in conjunction with the sparse grid quadrature rule, is employed for calculating the statistical moments of the structural responses. The adjoint sensitivity analysis scheme is derived, and a gradient based optimizer is employed for updating the design variables. Numerical examples show that the structural designs obtained by the proposed robust topology optimization method exhibit higher robustness against uncertainties as compared with their deterministic counterpart.

考虑来自不同来源的不确定性的设计优化一直是结构优化领域的热点之一。本文针对具有有限载荷和空间相关材料不确定性的结构提出了一种鲁棒的拓扑优化方法。我们首先针对具有有限性质的随机结构载荷开发了一个新模型，其中不确定载荷分量被假定为均匀分布在以椭圆模型表示的凸集内。然后将此模型与借助扩展优化线性估计离散化的随机场组合，以提供同时显示载荷和材料不确定性的结构的不确定性模型。鲁棒的拓扑设计问题被公式化为双准则优化问题，以使在这些不确定性下结构顺应性的平均值和标准偏差最小。结合稀疏网格正交规则，使用多项式混沌展开来计算结构响应的统计矩。推导了伴随灵敏度分析方案，并采用了基于梯度的优化器来更新设计变量。数值算例表明，与确定性方法相比，所提出的鲁棒拓扑优化方法获得的结构设计具有更高的鲁棒性。用于计算结构响应的统计矩。推导了伴随灵敏度分析方案，并采用了基于梯度的优化器来更新设计变量。数值算例表明，与确定性方法相比，所提出的鲁棒拓扑优化方法获得的结构设计具有更高的鲁棒性。用于计算结构响应的统计矩。推导了伴随灵敏度分析方案，并采用了基于梯度的优化器来更新设计变量。数值算例表明，与确定性方法相比，所提出的鲁棒拓扑优化方法获得的结构设计具有更高的鲁棒性。