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

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

Abstract

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

CLC Number:

TP391

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.

Figures/Tables 15

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

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

Fig. 3 Initial cone-cylinder composite shell model

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

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)

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

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%

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

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

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

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)

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)

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

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

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

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