第一作者傅晓锦男，博士，教授，1964年11月生

基于等几何裁剪分析的拓扑与形状集成优化

傅晓锦1，龙凯2，周利明1，阙春兰1，叶航1

(1. 上海电机学院机械学院，上海200245； 2. 华北电力大学新能源电力系统国家重点实验室，北京102206)

摘要：提出了将设计和分析、拓扑与形状优化集成的思想，探索了基于等几何裁剪分析的拓扑与形状集成优化设计算法，该方法统一了结构优化的计算机辅助设计、计算机辅助工程分析和优化设计的模型，基于B样条的等几何裁剪分析既能准确表达几何形状，又可以用裁剪面分析方便处理任意复杂拓扑优化问题，由裁剪选择标准确定合理的拓扑结构变动方向，结构变动时无需重新划分网格，设计结果突破初始设计空间的限制，还可方便优化形状。建立了等几何裁剪灵敏度分析的计算方法，给出了等几何裁剪分析拓扑与形状集成优化算法，通过典型实例表明所用方法的正确性和有效性。

关键词：形状优化； 灵敏度分析； 拓扑优化； 等几何分析； 裁剪B样条； 有限元分析

基金项目：国家自然科学基金(11202078);上海市教委科研创新重点项目(13ZZ145);上海市自然科学基金(11ZR1413800)

收稿日期：2014-02-24修改稿收到日期：2014-04-21

中图分类号:O241；TH122

文献标志码：A

DOI:10.13465/j.cnki.jvs.2015.07.026

Abstract:An idea of integration of computer aided design, computer aided engineering analysis, topology and shape optimization design was introduced and a kind of optimization strategy for integation of topology and shape optimization design of continuum structure based on isogeometric trimmed surface analysis was explored. The proposed method offers a unified model of computer aided design, computer aided engineering and optimization design in structure optimization. The isogeometric trimmed surface analysis based on B splines has the capability of both expressing the geometry shape accurately and solving arbitrarily complex topology optimization problem. The trimmed criteria selected determine the reasonable direction of topology changes. It does not need to remesh during structural optimization process. The design results can be beyond the limitations of initial design space. It is also convenient in shape optimization. In the integration method, the calculation approach for sensitivity analysis of isogeometric trimmed surface, and the algorithm for integation of topology and shape optimization design based on isogeometric trimmed analysis were developed. A numerical example illustrates the correctness and effectiveness of the method.

Integration of topology and shape optimization design of continuum structure based on isogeometric trimmed surface analysis

FUXiao-jin1,LONGKa2,ZHOULi-ming1,QUEChun-lan1,YEHang1(1. School of Mechanical Engineering, Shanghai Dianji University, Shanghai 200245,China 2.State Key Laboratory for Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206,China)

Key words:shape optimization; sensitivity analysis; topology optimization; isogeometric analysis; trimmed B-spline; finite element analysis

计算机辅助结构优化设计是一项多学科相交叉的新技术。它的研究领域涉及到力学、机械、结构工程、数学和信息技术，具有巨大的发展潜力[1-3]。我国程耿东院士和郭旭在布局优化研究中提出求解奇异最优解的松弛算法，是具有重要意义的贡献[4]。……