基于功能度量法的桁架结构非概率可靠性拓扑优化方法研究

在结构优化中,拓扑优化相比于尺寸优化和形状优化,设计空间更加广泛,因而能够取得更大的效益.近年来,结构拓扑优化逐渐成为人们研究的热点和难点.随着科学技术的发展,工程结构越来越复杂,材料本身和外部环境的不确定性影响加剧,因此在拓扑优化中需要考虑不确定性的影响.本文研究了桁架结构的非概率可靠性拓扑优化问题,用区间模型来量化不确定性,并利用参数顶点组合法来完成不确定性的传播分析,利用基于面积比的非概率可靠性指标构建可靠性拓扑优化模型,提出了功能度量法对原可靠性约束进行等价转化,从而克服了收敛性问题.采用移动渐近方法(MMA)对优化问题进行了求解.数值算例表明,本文提出的功能度量法能够很好地适用于桁架结构的非概率可靠性拓扑优化问题.

Non-probabilistic reliability topology optimization of truss structures based on performance measure approach

Compared with size and shape optimizations of structures, topology optimization has more design variables and can achieve more benefits. In recent years, topology optimization has become a hot topic. With the development of science and technology, engineering structures are more and more complex, and the effects of uncertainties in material of and the external environment increase. Therefore, uncertainties must be considered in topology optimization. In this paper, an interval model is used to quantify the uncertainties, and the parameter vertex combination method is used to accomplish the propagation of interval uncertainties. The area-ratio based non-probabilistic reliability index is used to construct the reliability-based topology optimization formulation, and the performance measure approach is proposed to equivalently transform the original reliability constraints to overcome the convergence problem. The moving asymptotic method (MMA) is used to solve the optimization problem. The non-probabilistic reliability topology optimization of a truss structure is studied. The results of two numerical examples show that the proposed method is applicable to the non-probabilistic reliability topology optimization of truss structures.