基于面片删减的带孔结构等几何形状优化方法

Isogeometric Shape Optimization Method with Patch Removal for Holed Structures

等几何分析方法采用非均匀有理B样条(Nonuniform rational B-spline,NURBS)基函数作为待分析物理场的插值函数,使得等几何形状优化中的设计模型、分析模型和优化模型能够用NURBS统一进行表达,避免了模型转换过程。拓扑复杂结构的等几何形状优化常采用多块面片拼接方法进行建模,然而面片拼接方法需要将结构划分成多个适用于分析的完整面片,不便于建立带孔结构尤其是多孔结构模型。为此,提出一种基于面片删减的带孔结构等几何形状优化设计方法,依据带孔结构内外边界构造建模所使用的面片,并且给出灵敏度的解析计算方法。以经典转矩臂带孔结构为优化算例,表明本方法不仅建模直观,而且优化设计变量选择也十分便利。

Nonuniform rational B-spline （NURBS） basis function is used as the interpolation function of unknown physical field in isogeometric analysis （IGA） method. The model transformation process is avoided in isogeometric shape optimization, because design, analysis and optimization models can all be represented in the framework of NURBS. Previously, the multiple patches method is often adopted to model topologically complex structures in isogeometric shape optimization. However, it has been found inconvenient for holed structures, especially when multiholes are involved. The reason lies in that the structure needs to be partitioned into many intact patches suitable to structural analysis. Therefore, an isogeometric shape optimization method using patch removal is proposed. The patch partition is achieved on the basis of inner and outer boundaries of holed structures. Moreover, an analytical shape sensitivity approach is developed. By means of classical optimization example of torque arm, it proves that the present method can not only provide a concise modeling approach, but also favor the selection of design variables.