一种自由度缩减和收敛加速的高效等几何拓扑优化方法  

An Efficient Isogeometric Topology Optimization Method Using DOF Reduction and Convergence Acceleration

作　　者：杨雨豪 郑伟 王英俊 YANG Yuhao;ZHENG Wei;WANG Yingjun(National Engineering Research Center of Novel Equipment for Polymer Processing,South China University of Technology,Guangzhou,510641;State Key Laboratory of Digital Manufacturing Equipment and Technology,Huazhong University of Science and Technology,Wuhan,430074)

机构地区：[1]华南理工大学聚合物新型成型装备国家工程研究中心,广州510641 [2]华中科技大学数字制造装备与技术国家重点实验室,武汉430074

出　　处：《中国机械工程》2022年第23期2811-2821,共11页China Mechanical Engineering

基　　金：国家重点研发计划(2020YFB1708300);国家自然科学基金(52075184);数字制造装备与技术国家重点实验室开放基金(DMETKF2021020)。

摘　　要：为提高等几何拓扑优化效率,提出了一种高效等几何拓扑优化方法,从自由度缩减和收敛加速两个方面对等几何拓扑优化进行加速。自由度缩减算法包括基于位移变化的自由度缩减和基于空单元的自由度缩减,收敛加速算法包括设计变量缩减和灰度抑制算法。二维和三维算例结果表明,所提出的高效等几何拓扑优化方法在保证优化精度的同时,相对于传统等几何拓扑优化方法的加速比为1.56~6.02,显著提高了等几何拓扑优化的效率,为产品结构的高效高质量设计提供了有力支撑。In order to improve the efficiency of isogeometric topology optimization(ITO),an efficient ITO method was proposed,which accelerated ITO from DOF reduction and convergence acceleration.The DOF reduction algorithm included DOF reduction based on displacement changes and empty elements,and the convergence acceleration algorithm included design variable reduction and gray-scale suppression.Through 2D and 3D cases,it is demonstrated that the speedup ratio of the proposed efficient ITO method may reach to 1.56~6.02 compared with traditional ITO when optimization accuracy is ensured,which significantly improves the efficiency of ITO and provides a strong support for the efficient and high-quality design of product structures.

关 键 词：等几何分析 拓扑优化 高效优化方法 自由度缩减 收敛加速 

分 类 号：TH11[机械工程—机械设计及理论]