基于可靠性的连续体结构拓扑优化设计

STRUCTURAL TOPOLOGY OPTIMIZATION OF CONTINUOUS STRUCTURES BASED ON RELIABILITY

建立水平集函数为设计变量、刚度极小化为目标、具有可靠性约束的连续体结构拓扑优化模型,并提出相应的优化算法。文中提出的基于可靠性的结构拓扑优化算法方法分为两个步骤,结构可靠性分析和结构拓扑优化。可靠性分析采用计算简便、效率高的一次二阶矩法,结构拓扑优化设计则应用稳定高效、最优结构清晰的水平集方法。最后以悬臂梁结构的可靠性拓扑优化为例,表明文中提出的方法既简单又有效。

A new structural topology algorithm based on reliability is proposed. Moreover, the mathematical model of topology optimization based on the reliability for continuous structures is developed, in which the level set function is taken as design variables, minimization of the compliance is taken as objective function, reliability constraint is included. For solving reliability-based topology optimization problem of continuous structures, the proposed methodology is combined with the reliability analysis and the topology optimization. The reliabihty analysis is carried out with the first-order reliability method for the reduction of the compute time, while the optimization part is performed with the level set method in order to obtain a better optimum material distribution. Finally, two examples show that the approach proposed is simple and efficient.