基于等几何分析的复杂部件智能优化设计方法

An intelligent optimization design method for complex components based on isogeometric analysis

摘要

传统复杂部件的设计研发方法中存在CAD(computer-aided design)与CAE(computer-aided engineering)模型转换繁琐、自动化和智能化程度低、设计-仿真-优化方法协同性不足等问题,导致研发效率低下且成本增加。为此,本文基于等几何分析,提出针对复杂部件的智能优化设计方法,实现基于约束变体技术的等几何模型参数化修改与重用、多物理场下变体模型等几何分析仿真验证与力学性能预测优化。通过不同应用场景下的3种典型模型案例,验证参数化约束变体后等几何模型的拓扑一致性与可仿真性,以防撞梁等几何模型优化设计为例,通过可视化平台集成上述方法与求解器,验证数据与模型融合驱动的智能优化设计方法,提高复杂部件优化迭代效率与自主研发能力。

Abstract

Traditional design and development methods for complex components face challenges including CAD-CAE model conversion, low levels of automation and intelligence, and insufficient integration of the design-simulation-optimization workflow. These issues reduce R&D efficiency and drive up costs. Therefore, this paper proposes intelligent parametric-optimization design method for complex components based on isogeometric analysis (IGA). The method achieves parametric modification and reuse of IGA models through constraint morphing, simulation verification of IGA morphed models under multi-physics fields, and optimization of mechanical property predictions. Using three representative models across diverse application scenarios, we validated the topological consistency and suitability for simulation of geometric models after parametric constraint morphing. In a case study on the optimization of a collision-beam IGA model, integrating the proposed methods and solvers within a visualization platform demonstrates the effectiveness of an intelligent optimization approach driven by the fusion of data and models. This method enhances optimization iteration efficiency for complex components and strengthens independent research and development capabilities.

关键词

等几何分析 / 智能优化 / 约束变体 / 拓扑一致性 / 集成设计

Key words

isogeometric analysis / intelligent optimization / constraint morphing / topological consistency / integration design

参考文献

[1] GUO X, ZHANG W S, ZHONG W L. Doing topology optimization explicitly and geometrically: a new moving morphable components based framework[J]. Journal of Applied Mechanics, 2014, 81(8): 081009.

[2] 徐岗, 李新, 黄章进, 等. 面向等几何分析的几何计算[J]. 计算机辅助设计与图形学学报, 2015, 27(4): 570-581.

[3] XU Gang, LI Xin, HUANG Zhangjin, et al. Geometric computing for isogeometric analysis[J]. Journal of Computer—Aided Design & Computer Graphics, 2015, 27(4): 570-581.

[4] CHEN L L, LIAN H, LIU Z, et al. Structural shape optimization of three dimensional acoustic problems with isogeometric boundary element methods[J]. Computer Methods in Applied Mechanics and Engineering, 2019, 355: 926-951.

[5] MA Y, SONG X W, JIA Q Q, et al. Isogeometric interval size optimization of beam structures[J]. Computer Methods in Applied Mechanics and Engineering, 2022, 395: 115003.

[6] HU P, XIA Y, WANG C S. Exact geometry based quasi—conforming analysis for Euler—Bernoulli beam[J]. Theoretical and Applied Mechanics Letters, 2012, 2(5): 051002.

[7] FUßEDER D, SIMEON B, VUONG A V. Fundamental aspects of shape optimization in the context of isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 286: 313-331.

[8] ZHAO H, KAMENSKY D, HWANG J T, et al. Automated shape and thickness optimization for non—matching isogeometric shells using free—form deformation[J]. Engineering with Computers, 2024, 40(6): 3495-3518.

[9] 张贝, 张代雨, 王志东, 等. 基于自由变形的自主水下航行器壳体优化设计方法研究[J]. 船舶力学, 2022, 26(9): 1315-1325.

[10] ZHANG Bei, ZHANG Daiyu, WANG Zhidong, et al. A free—form deformation optimization design approach for AUV hull shape[J]. Journal of Ship Mechanics, 2022, 26(9): 1315-1325.

[11] DANG T J, LI B F, HU D K, et al. Aerodynamic design optimization of a hypersonic rocket sled deflector using the free—form deformation technique[J]. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2021, 235(15): 2240-2248.

[12] EVANGELOS BIANCOLINI M , CELLA U . Radial basis functions update of digital models on actual manufactured shapes[J]. Journal of Computational and Nonlinear Dynamics, 2019, 14(2): 021013.

[13] SIEGER D, MENZEL S, BOTSCH M. RBF morphing techniques for simulation—based design optimization[J]. Engineering with Computers, 2014, 30(2): 161-174.

[14] YANG L, LI B J, LV Z Q, et al. Finite element mesh deformation with the skeleton—section template[J]. Computer—Aided Design, 2016, 73: 11-25.

[15] RENDALL T C S, ALLEN C B. Unified fluid—structure interpolation and mesh motion using radial basis functions[J]. International Journal for Numerical Methods in Engineering, 2008, 74(10): 1519-1559.

[16] 姚远, 任靖雯, 颜佳聪, 等. 基于势流模型与等几何配点法的机翼翼型优化[J]. 计算机辅助设计与图形学学报, 2023, 35(12): 1993-2002.

[17] YAO Yuan, REN Jingwen, YAN Jiacong, et al. Airfoil optimization with isogeometric collocation based on potential flow model[J]. Journal of Computer—Aided Design & Computer Graphics, 2023, 35(12): 1993-2002.

[18] FUßEDER D, SIMEON B, VUONG A V. Fundamental aspects of shape optimization in the context of isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering, 2015, 286: 313-331.

[19] RAISSI M, YAZDANI A, KARNIADAKIS G E. Hidden fluid mechanics: learning velocity and pressure fields from flow visualizations[J]. Science, 2020, 367(6481): 1026-1030.

[20] NIE Z G, JIANG H L, KARAL B. Stress field prediction in cantilevered structures using convolutional neural networks[J]. Journal of Computing and Information Science in Engineering, 2020, 20: 011002.

[21] 韩丽, 朴京钰, 兰鹏燕, 等. 结构感知深度学习的三维形状分类方法[J]. 计算机辅助设计与图形学学报, 2021, 33(1): 29-38.

[22] HAN Li, PIAO Jingyu, LAN Pengyan, et al. 3D shape classification method based on shape—aware deep learning[J]. Journal of Computer—Aided Design & Computer Graphics, 2021, 33(1): 29-38.

[23] WANG D D, XU J L, GAO F, et al. IGA—reuse—NET: a deep—learning—based isogeometric analysis—reuse approach with topology—consistent parameterization image 1[J]. Computer Aided Geometric Design, 2022, 95: 102087.

[24] ZHU X F, JI Y, ZHU C G, et al. Isogeometric analysis for trimmed CAD surfaces using multi—sided toric surface patches[J]. Computer Aided Geometric Design, 2020, 79: 101847.

[25] ZHU X F, REN G W, ZHANG X K, et al. Conforming embedded isogeometric analysis for B—Rep CAD models with strong imposition of Dirichlet boundary conditions using trivariate B++ splines[J]. Computers & Structures, 2024, 305: 107586.

[26] 姜凯, 祝雪峰, 侯文彬. 基于B++样条的改进扩展等几何分析对强不连续问题强加Dirichlet边界[C]// 中国力学大会—2021(第1册). 深圳:中国力学学会, 2022: 714.

[27] JIANG Kai, ZHU Xuefeng, HOU Wenbin. Improved extended isogeometric analysis based on B++ splines for imposing dirichlet boundaries in strong discontinuity problems[C]// Proceedings of the China Mechanics Conference—2021(Volume I). Shenzhen: CSTAM, 2022: 714.

[28] LI Z Y, KOVACHKI N, AZIZADENESHELI K, et al. Fourier neural operator for parametric partial differential equations[EB/OL]. (2020—11—18] [2025—12—18]. http://arxiv.org/abs/2010.08895.

基金资助

国家重点研发计划项目(2021YFB3300600)