基于等几何法和模拟退火的复杂壳结构分析及优化

doi:10.11996/JG.j.2095-302X.2024030575

图学学报 ›› 2024, Vol. 45 ›› Issue (3): 575-584.DOI: 10.11996/JG.j.2095-302X.2024030575

基于等几何法和模拟退火的复杂壳结构分析及优化

薛雨彤¹^,²(), 王爱增¹^,²(), 岳怡珂¹^,², 何川¹^,², 赵罡¹^,²

1.北京航空航天大学机械工程及自动化学院，北京 100191
2.北京航空航天大学航空高端装备智能制造技术工信部重点实验室，北京 100191

收稿日期:2023-11-22 接受日期:2024-02-29 出版日期:2024-06-30 发布日期:2024-06-12
通讯作者:王爱增(1982-)，男，副教授，博士。主要研究方向为几何造型、CAE等。E-mail：azwang@buaa.edu.cn
第一作者:薛雨彤(1999-)，女，硕士研究生。主要研究方向为等几何分析。E-mail：xyt18811733395@163.com
基金资助:
航空科学基金项目(2023Z068051002);国家自然科学基金项目(52175213);工信部2021民用飞机专项科研技术研究项目

Complex shell structure analysis and optimization based on isogeometric analysis and simulated annealing algorithm

XUE Yutong¹^,²(), WANG Aizeng¹^,²(), YUE Yike¹^,², HE Chuan¹^,², ZHAO Gang¹^,²

1. School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
2. Key Laboratory of Aeronautics Smart Manufacturing, Beihang University, Beijing 100191, China

Received:2023-11-22 Accepted:2024-02-29 Published:2024-06-30 Online:2024-06-12
First author：XUE Yutong (1999-), master student. Her main research interest covers isogeometric analysis. E-mail：xyt18811733395@163.com
Supported by:
Aeronautical Science Foundation of China(2023Z068051002);National Natural Science Foundation of China(52175213);2021 Special Scientific Research on Civil Aircraft Project

摘要/Abstract

摘要：

本文提出了一种基于等几何法和模拟退火的壳结构分析及优化算法，旨在提高复杂壳结构的CAD与CAE一体化设计效率。首先基于NURBS技术对薄壳结构进行适分析参数化建模，然后基于Kirchhoff-Love壳理论实现等几何分析。接着，基于模拟退火算法以壳体的几何参数为设计变量，以多项力学性能为目标函数进行优化，实现了等几何分析与智能优化算法相结合的壳结构分析与优化。最后，通过2个算例验证了该算法的有效性。相对于传统有限元方法，该算法具有高精度、高效率的优势。

关键词: 等几何分析, 模拟退火算法, Kirchhoff Love壳, 结构优化设计, CAD

Abstract:

This paper proposed a shell structure analysis and optimization algorithm based on the isogeometric method and simulated annealing, aiming to enhance the efficiency of CAD and CAE integrated design for complex shell structures. Firstly, based on NURBS technology, the parametric modeling of the thin shell structure was carried out, and then the isogeometric analysis was realized based on the Kirchhoff-Love shell theory. Then, based on the simulated annealing algorithm, the geometric parameters of the shell served as the design variables, while multiple mechanical properties acted as the objective functions for optimization, thus realizing the integration of isogeometric analysis and intelligent optimization algorithm for shell structure analysis and optimization. Finally, the effectiveness of the algorithm was verified through two examples. Compared with traditional finite element methods, this algorithm has the advantages in precision and efficiency.

Key words: isogeometric analysis, simulated annealing algorithm, Kirchhoff Love shell, optimization design, CAD

中图分类号:

TP391

薛雨彤, 王爱增, 岳怡珂, 何川, 赵罡. 基于等几何法和模拟退火的复杂壳结构分析及优化[J]. 图学学报, 2024, 45(3): 575-584.

XUE Yutong, WANG Aizeng, YUE Yike, HE Chuan, ZHAO Gang. Complex shell structure analysis and optimization based on isogeometric analysis and simulated annealing algorithm[J]. Journal of Graphics, 2024, 45(3): 575-584.

图/表 15

图1 含交点与映射点的参数曲面

Fig. 1 Parameter surface containing both intersection points and mapping points

图2 基于模拟退火的壳结构等几何优化算法流程图

Fig. 2 Isogeometric optimization algorithm flowchart based on simulated annealing for shell structures

图3 初始锥柱组合壳模型

Fig. 3 Initial cone-cylinder composite shell model

图4 锥柱壳等几何分析结果图((a)等几何分析应力云图；(b)等几何分析位移云图)

Fig. 4 Isogeometric analysis results of conical-cylindrical shell ((a) Stress contour plot of isogeometric analysis; (b) Displacement contour plot of isogeometric analysis)

图5 锥柱壳有限元分析结果图((a)有限元分析应力云图；(b)有限元分析位移云图)

Fig. 5 Finite element analysis results of conical-cylindrical shell ((a) Stress contour plot from finite element analysis; (b) Displacement contour plot from finite element analysis)

表1 锥柱壳有限元分析与等几何分析结果对比

Table 1 Comparison of finite element analysis and isogeometric analysis results for conical-cylindrical shell

实验名称	最大应力/ MPa	最大位移/ mm	总时长/ s
一次有限元分析 (单元数：13 320)	813.24	1.143 4	18.23
二次有限元分析 (单元数：23 664)	810.67	1.149 5	44.95
三次有限元分析 (单元数：96 731)	804.30	1.153 3	268.18
四次有限元分析 (单元数：153 655)	802.68	1.153 7	508.69
等几何分析	801.11	1.155 5	44.16

表2 锥柱壳优化结果

Table 2 The optimized results of the conical-cylindrical shell

参数	最大位移/mm	应力方差×10⁻⁴	质量/g
初始值	1.73	2.54	441.02
优化值	0.76	0.17	432.41
变化量	−56.07%	−93.31%	−1.95%

图6 优化后锥柱壳等几何分析位移云图

Fig. 6 The displacement contour plot of the optimized conical-cylindrical shell in isogeometric analysis

图7 锥柱壳优化迭代曲线

Fig. 7 The optimization iteration curve of the conical-cylindrical shell

图8 s-t参数平面内带孔薄壁曲面

Fig. 8 A thin-walled surface with a hole in the s-t parameter plane

图9 带孔柱壳等几何分析结果图((a)等几何分析应力云图；(b)等几何分析位移云图)

Fig. 9 Isogeometric analysis results of a shell with a hole ((a) Stress contour plot of isogeometric analysis; (b) Displacement contour plot of isogeometric analysis)

图10 带孔柱壳有限元分析结果图((a)有限元分析应力云图；(b)有限元分析位移云图)

Fig. 10 Finite element analysis results of a shell with a hole ((a) Stress contour plot from finite element analysis; (b) Displacement contour plot from finite element analysis)

表3 带孔柱壳有限元分析与等几何分析结果对比

Table 3 Comparison between finite element analysis and isogeometric analysis results for a shell with a hole

实验名称	最大应力/ MPa	最大位移/ mm	总时长/ s
一次有限元分析 (单元数：3 884)	432.80	0.620 0	10.97
二次有限元分析 (单元数：15 511)	441.13	0.626 0	31.46
三次有限元分析 (单元数：63 316)	445.42	0.626 4	161.64
四次有限元分析 (单元数：98 998)	446.59	0.629 8	282.10
等几何分析	452.47	0.631 1	49.67

图11 优化后带孔柱壳等几何分析应力云图

Fig. 11 Stress contour plot of the isogeometric analysis for the optimized shell with a hole

图12 带孔柱壳优化迭代曲线

Fig. 12 The iteration curve of the optimization process for the shell with a hole

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基于等几何法和模拟退火的复杂壳结构分析及优化

Complex shell structure analysis and optimization based on isogeometric analysis and simulated annealing algorithm

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