关键词: 可靠性分析, 水平集方法, 拓扑优化

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.

Key words: Level set method, Reliability analysis, Topology optimization