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基于水平集方法的结构可靠性拓扑优化
引用本文:欧阳高飞,张宪民. 基于水平集方法的结构可靠性拓扑优化[J]. 机械工程学报, 2008, 44(10): 60-65
作者姓名:欧阳高飞  张宪民
作者单位:华南理工大学机械工程学院,广州,510640;华南理工大学机械工程学院,广州,510640
基金项目:国家自然科学基金,国家自然科学基金,国家自然科学基金
摘    要:基于水平集方法,建立以水平集函数为优化变量、结构柔度极小化为目标、具有可靠性约束的结构拓扑优化模型,并提出一种基于可靠性的结构拓扑优化算法。首先,采用计算效率高的一次二阶矩法进行可靠性分析,编制计算可靠性指标的最优化方法。然后,根据结构可靠性指标的几何意义,优化求解符合可靠性约束的随机变量。将修正后的随机变量作为确定性变量进行结构拓扑优化设计,使基于可靠性的结构拓扑优化模型转为常规的结构拓扑优化模型,采用稳定、高效的水平集方法进行结构拓扑优化。最后以悬臂梁结构的可靠性拓扑优化为例,说明文中所提算法的简便性与有效性。

关 键 词:可靠性分析  拓扑优化  水平集方法

Reliability-based Topology Optimization of Structures Using the Level Set Method
OUYANG Gaofei,ZHANG Xianmin. Reliability-based Topology Optimization of Structures Using the Level Set Method[J]. Chinese Journal of Mechanical Engineering, 2008, 44(10): 60-65
Authors:OUYANG Gaofei  ZHANG Xianmin
Affiliation:School of Mechanical Engineering, South China University of Technology
Abstract:Based on the level set method, the mathematical model of topology optimization is developed, in which the level set function is taken as design variable, minimization of the compliance is taken as objective function, the structural reliability is taken as constraint function, and a novel reliability-based topology optimization algorithm is proposed. First, the reliability analysis is carried out by using the first-order second-moment method with high computation efficiency, and the optimization method of computing the reliability index is worked out. Second, according to the geometric meaning of the structural reliability index , the solution of random variables that conform to the reliability constraint is optimized. The modified random variables are used in topology optimization as determined parameters, so the original optimization model based on reliability is transformed into the conventional topology optimization model. And the topology optimization is performed by using a stable and efficient level set method. Finally, the topology optimization of a cantilever beam shows that the proposed algorithm is simple and efficient.
Keywords:Level set method  Reliability analysis  Topology optimization  
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