A generalized approach for robust topology optimization using the first-order second-moment method for arbitrary response functions
A generalized approach for robust topology optimization using the first-order second-moment method for arbitrary response functions
复制标题
使用任意响应函数的一阶二阶矩方法进行鲁棒拓扑优化的通用方法
DOI：
10.1007/s00158-023-03540-w
复制
发表时间：
2023
影响因子：
3.9
通讯作者：
B. Kriegesmann
中科院分区：
文献类型：
--
作者：
M. Kranz;J. K. Lüdeker;B. Kriegesmann
本文提出了要使用一阶二阶矩方法求解鲁棒设计优化的伴随系统的严格公式。该公式允许将该方法应用于任何目标函数，这通过将特定点的变形和最大应力分别考虑为随机材料刚度和几何形状的目标来证明。与确定性情况相比，所提出的方法要求每个不确定系统响应最多三个附加伴随系统的解决方案。因此，要求解的伴随系统的数量与随机变量的数量无关。这是以牺牲准确性为代价的，因为假设目标函数相对于随机参数是线性的。然而，对两个标准案例的应用以及蒙特卡罗模拟的验证表明，该方法仍然能够找到稳健的设计。
The paper presents a rigorous formulation of adjoint systems to be solved for a robust design optimization using the first-order second-moment method. This formulation allows to apply the method for any objective function, which is demonstrated by considering deformation at certain point and maximum stress as objectives subjected to random material stiffness and geometry, respectively. The presented approach requires the solution of at most three additional adjoint systems per uncertain system response, when compared to the deterministic case. Hence, the number of adjoint systems to be solved is independent of the number of random variables. This comes at the expense of accuracy, since the objective functions are assumed to be linear with respect to random parameters. However, the application to two standard cases and the validation with Monte Carlo simulations show that the approach is still able to find robust designs.
影响因子：
3.9
作者：
Giraldo-Londono, Oliver;Paulino, Glaucio H.
通讯作者：
Paulino, Glaucio H.