论文标题
在随机场材料模型下基于可靠性可靠性的拓扑优化
Robust reliability-based topology optimization under random-field material model
论文作者
论文摘要
本文提出了一种算法，以在随机场材料模型下找到基于可靠性的拓扑优化设计。初始设计域是由线性弹性材料制成的，其特性（即Young的模量）由随机字段建模。为了促进计算，Karhunen-Loève扩展将建模随机场离散为少数随机变量。鲁棒性是通过优化一定数量的平均值和标准偏差的加权总和，而可靠性是通过概率约束来实现的。 Smolyak型稀疏网格和随机响应表面方法用于降低计算成本。此外，一种有效的逆稳定性算法可用于将可靠性分析的双回路结构解除。该算法对文献中的两个常见基准问题进行了测试。最后，使用蒙特卡洛模拟来验证优化设计的鲁棒性和可靠性。
This paper proposes an algorithm to find robust reliability-based topology optimized designs under a random-field material model. The initial design domain is made of linear elastic material whose property, i.e., Young's modulus, is modeled by a random field. To facilitate computation, the Karhunen-Loève expansion discretizes the modeling random field into a small number of random variables. Robustness is achieved by optimizing a weighted sum of mean and standard deviation of a quantity of interest, while reliability is employed through a probabilistic constraint. The Smolyak-type sparse grid and the stochastic response surface method are applied to reduce computational cost. Furthermore, an efficient inverse-reliability algorithm is utilized to decouple the double-loop structure of reliability analysis. The proposed algorithm is tested on two common benchmark problems in literature. Finally, Monte Carlo simulation is used to validate the claimed robustness and reliability of optimized designs.
