特征驱动的结构拓扑优化方法

Feature-driven method for structural topology optimization

本文提出一种以特征作为结构拓扑优化基本设计要素的方法.该方法从CAD特征设计概念出发,通过采用隐式水平集函数建立结构的特征模型,将结构拓扑优化转化为设计域内特征布局和形状优化问题,避免了传统拓扑优化方法仅从力学性能角度寻优材料分布,导致拓扑优化结果过于抽象、工程特征差的弊端.本文针对给定体积约束条件下的结构柔顺度最小化问题,发展了固定网格框架下结构响应分析与形状灵敏度分析计算方法,理论上保证了灵敏度计算精度与结构水平集函数的数学表达形式无关.最后以带孔悬臂梁结构与飞机发动机支架结构为例,采用超椭圆/球特征设计要素验证了该方法的有效性与优越性.

We propose a new method by which features are regarded as the basic design primitives for structural topology optimization. This method originates from the concept of feature-based design in CAD community. Implicit level-set functions such as Max-Min function, R function, KS function or Ricci function are used to describe the feature model of a structure. Structural topology optimization is converted into layout and shape optimization of features within the prescribed design domain. This method makes it possible to avoid the drawbacks of traditional topology optimization methods that seek the material distribution only for the optimization of mechanical performance and thus result in abstract topology optimization results with the lack of engineering features. The minimum compliance problem subjected to volume constraint is considered. Structural response analysis and sensitivity analysis are formulated within the framework of fixed mesh. It is shown that the sensitivity accuracy is independent of the mathematical expressions of the related level-set function. Finally, a holed cantilever beam structure and aero-engine bracket structure are studied as numerical examples. By means of super-elliptical/super-ellipsoidal features, the effectiveness and advantage of the developed method are demonstrated.