An efficient approach for reliability-based topology optimization
An efficient approach for reliability-based topology optimization
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DOI：
10.1080/0305215x.2014.992890
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发表时间：
2016-01
影响因子：
2.7
通讯作者：
Pugazhendhi Kanakasabai;A. Dhingra
中科院分区：
文献类型：
--
作者：
Pugazhendhi Kanakasabai;A. Dhingra
本文提出了一种基于可靠性的拓扑优化方法，其计算量与求解确定性拓扑优化问题的计算量相当。所提出的方法是建立在用于解决确定性优化问题的双向渐进结构优化（BESO）方法。所提出的方法适用于具有独立和正态分布载荷的线弹性问题，并受到挠度和可靠性约束。利用挠度矩阵和刚度矩阵之间的线性关系沿着叠加原理来处理可靠性约束，发展了求解RBTO问题的有效算法。四个例子的各种随机变量和单一或多个施加载荷的问题，以证明所提出的方法在解决RBTO问题的适用性。这篇文章的主要贡献来自所提出的算法的效率提高时，测量的有限元分析运行所需的计算最优解的计算工作量。对于一个单一的应用负载的例子，它表明，在计算RBTO问题的最佳解决方案所需的CPU时间是15-30%，解决DTO问题所需的时间少。改进的计算效率允许在拓扑优化中纳入可靠性考虑，而不增加解决DTO问题所需的计算时间。
This article presents an efficient approach for reliability-based topology optimization (RBTO) in which the computational effort involved in solving the RBTO problem is equivalent to that of solving a deterministic topology optimization (DTO) problem. The methodology presented is built upon the bidirectional evolutionary structural optimization (BESO) method used for solving the deterministic optimization problem. The proposed method is suitable for linear elastic problems with independent and normally distributed loads, subjected to deflection and reliability constraints. The linear relationship between the deflection and stiffness matrices along with the principle of superposition are exploited to handle reliability constraints to develop an efficient algorithm for solving RBTO problems. Four example problems with various random variables and single or multiple applied loads are presented to demonstrate the applicability of the proposed approach in solving RBTO problems. The major contribution of this article comes from the improved efficiency of the proposed algorithm when measured in terms of the computational effort involved in the finite element analysis runs required to compute the optimum solution. For the examples presented with a single applied load, it is shown that the CPU time required in computing the optimum solution for the RBTO problem is 15–30% less than the time required to solve the DTO problems. The improved computational efficiency allows for incorporation of reliability considerations in topology optimization without an increase in the computational time needed to solve the DTO problem.