基于扩展等几何分析和混沌离子运动算法的带孔结构形状优化设计

为了解决带孔结构形状优化问题，提出了一种将扩展等几何分析方法和混沌离子运动算法相结合的优化求解模式。针对带孔结构的力学计算，采用扩展等几何分析方法，以几何体外轮廓划分背景网格，利用非均匀有理B样条描述带孔边界，其中在劲度矩阵组装过程中，孔内区域不做积分。另外，为获得高精度的积分计算，与孔边界相关的单元采用自适应四叉树细化规则。在优化模型中，以描述结构形状的控制点作为设计变量，以结构质量最小作为优化目标；利用离子运动优化算法代替传统的敏感性移动渐进法对优化模型进行求解。带孔无限平板算例的扩展等几何分析计算结果和转矩臂结构优化算例的计算结果证明了本文方法的有效性。

DESIGN AND SHAPE OPTIMIZATION OF HOLED STRUCTURE BY EXTENDED ISOGEOMETRIC ANALYSIS AND CHAOTIC ION MOTION OPTIMIZATION

To solve the problem of the shape optimization of holed structure, a method that integrates extended isogeometric analysis and a chaotic ion motion algorithm is proposed. For mechanical calculations of holed structure, extended isogeometric analysis is used to divide the background meshes in geometric shape, and to describe the boundary of the holes with non-uniform rational B-splines where there is no integral in the area of the holes in the assembly of the stiffness matrix. In addition, to obtain high precision integral calculations, refinement by the adaptive four-forked tree is performed in the element related to the hole boundary. In the optimization model, the control points for describing the structure are set to be the design variables, and the optimization objective is to minimize the mass of the structure. The optimization model is then solved by using the ion motion optimization algorithm instead of the traditional asymptotic method based on sensitivity analysis. The calculation results of the infinite plate with a circular hole by extended isogeometric analysis and the optimization result of a torque arm structure proved the validity of this method.