Abstract: To meet the robustness requirements of the structure,a robust topology optimization method of orthotropic material structures considering loading uncertainties was proposed.Considering the uncertainties of loading magnitude and direction,the uncertain load were composed of a deterministic part and a random fluctuation part.The uncertainties of the applied load were expressed by the second order Taylor series expansion,and the expectation and standard deviation of the compliance of orthotropic structures were calculated.The modified solid anisotropic material interpolation model was applied to perform robust topology optimization of orthotropic structures.The expectation and standard deviation of the compliance of orthotropic structures was minimized under the volume constraint.Compared with the results of deterministic results,there were significant differences in the topological configurations of orthotropic structures attained by robust design.The orthotropic structures could better resist the component forces of uncertain loads in the horizontal direction.The orthotropic structures obtained by robust topology optimization considering variable fiber angle had higher robustness against loading uncertainties.

Key words: orthotropic material structures, robust topology optimization, load uncertainties, perturbation method

摘要： 为了满足结构稳健性要求,提出一种考虑载荷大小和方向不确定性的正交各向异性材料结构拓扑优化设计方法。考虑载荷大小和方向不确定性,将不确定载荷表示为确定性部分与随机扰动部分,对作用载荷进行二阶泰勒级数展开,计算正交各向异性结构柔顺度的期望和标准差。采用改进的固体各向异性材料插值模型进行正交各向异性结构稳健性拓扑优化设计,在体积约束条件下寻求正交各向异性结构的柔顺度期望和标准差加权和最小化。结果表明:与确定性设计结果比较,稳健性设计的正交各向异性材料结构拓扑构型存在明显差异,可以更好地抵抗不确定载荷在水平方向的分力;并且考虑变化纤维角度的稳健性拓扑优化获得的正交各向异性结构更加稳健。

关键词: 正交各向异性结构, 稳健性拓扑优化, 载荷不确定性, 摄动法