考虑惯性载荷的结构热力耦合拓扑优化

doi:10.3901/JME.2024.13.130

机械工程学报 ›› 2024, Vol. 60 ›› Issue (13): 130-140.doi: 10.3901/JME.2024.13.130

• 多学科仿真与优化设计 • 上一篇下一篇

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考虑惯性载荷的结构热力耦合拓扑优化

郑静¹, 荣轩霈¹, 姜潮¹, 米栋^1,2, 李加强²

1. 湖南大学特种装备先进设计技术与仿真教育部重点实验室长沙 410082;
2. 中国航发湖南动力机械研究所株洲 412002

收稿日期:2023-10-09 修回日期:2024-01-05 出版日期:2024-07-05 发布日期:2024-08-24
作者简介:郑静,女,1990年出生,博士,助理教授,硕士研究生导师。主要研究方向为结构拓扑优化、可靠性分析与设计。E-mail:jingzheng@hnu.edu.cn;荣轩霈,男,1994年出生,博士研究生。主要研究方向为结构拓扑优化。E-mail:xuanpeirong@hnu.edu.cn;姜潮(通信作者),男,1978年出生,博士,教授,博士研究生导师。主要研究方向为结构优化设计、可靠性分析与设计、结构强度设计。E-mail:jiangc@hnu.edu.cn;米栋,男,1973年出生,硕士,研究员。主要研究方向为结构拓扑优化、结构强度设计。E-mail:capimd@163.com;李加强,男,1993年出生,博士,工程师。主要研究方向为结构拓扑优化、结构强度设计。E-mail:lijq20@tsinghua.org.cn
基金资助:
国家自然科学基金资助项目(52005172,52235005)。

Thermal-mechanical Coupled Topology Optimization for Structures with Inertial Loads

ZHENG Jing¹, RONG Xuanpei¹, JIANG Chao¹, MI Dong^1,2, LI Jiaqiang²

1. Key Laboratory of Advanced Design and Simulation Techniques for Special Equipment of Ministry of Education, Hunan University, Changsha 410082;
2. AECC Hunan Aviation Powerplant Research Institute, Zhuzhou 412002

Received:2023-10-09 Revised:2024-01-05 Online:2024-07-05 Published:2024-08-24

摘要/Abstract

摘要： 现代复杂装备结构通常不仅处于热力耦合的复杂环境，而且承受着不可忽视的惯性力作用。针对这一类问题，提出了一种考虑拓扑相关惯性载荷的热力耦合拓扑优化高效求解方法。首先，构建了考虑热载荷、机械载荷以及惯性载荷的热力耦合拓扑优化模型，在体积约束条件下优化结构的柔顺度；其次，给出了惯性载荷的计算方法，针对低密度区域材料分布不收敛的问题提出了一种改进的材料插值惩罚模型，并基于此推导了结构柔顺度关于拓扑设计变量的敏度；最后，采用了基于梯度的移动渐近线法(Method of moving asymptotes, MMA)更新拓扑设计变量。此外，开发了基于MATLAB和ABAQUS的热力耦合拓扑优化平台，可适用于复杂工程中不规则结构设计域的拓扑优化问题。数值算例结果表明，所提出方法可有效避免低密度区域结构分布模糊的现象，具有良好的收敛性。

关键词: 拓扑优化, 热力耦合, 惯性载荷

Abstract: Modern complex equipment structures are usually not only in a complex environment of thermal-mechanical coupling, but also subject to inertial forces that cannot be ignored. A high-efficiency solution method for thermoelastic topology optimization considering topology related inertial loads is proposed for this type of problem. First, a thermoelastic topology optimization model considering thermal, mechanical, and inertial loads is constructed to optimize the compliance of the structure under volume constraints; Secondly, a calculation method for inertial loads is provided, and an improved material interpolation penalty model is proposed to address the issue of non-convergence of material distribution in low density areas. Based on this, the sensitivity of structural compliance to topological variables is derived. Finally, the gradient based Method of Moving Asymptotes is used to update the topology design variables. In addition, a thermal coupling topology optimization platform based on MATLAB and ABAQUS has been developed, which can be applied to topology optimization problems of irregular structural design domains in complex engineering. The numerical example results show that the proposed method can effectively avoid the phenomenon of fuzzy structural distribution in low density areas and has good convergence.

Key words: topology optimization, thermal-mechanical coupled, inertial load

中图分类号:

O343.6

郑静, 荣轩霈, 姜潮, 米栋, 李加强. 考虑惯性载荷的结构热力耦合拓扑优化[J]. 机械工程学报, 2024, 60(13): 130-140.

ZHENG Jing, RONG Xuanpei, JIANG Chao, MI Dong, LI Jiaqiang. Thermal-mechanical Coupled Topology Optimization for Structures with Inertial Loads[J]. Journal of Mechanical Engineering, 2024, 60(13): 130-140.

参考文献

[1] BENDSØE M P, KIKUCHI N. Generating optimal topologies in structural design using a homogenization method[J]. Computer Methods in Applied Mechanics and Engineering, 1988, 71(2)：197-224.
[2] BENDSØE M P. Optimal shape design as a material distribution problem[J]. Structural Optimization, 1989, 1：193-202.
[3] XIE Yimin, STEVEN G P. A simple evolutionary procedure for structural optimization[J]. Computer & Structures, 1993, 49：885-896.
[4] HUANG Xiaodong, XIE Yimin. Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method[J]. Finite Elements in Analysis and Design, 2007, 43：1039-1049.
[5] WANG M Y, WANG Xiaoming, GUO Dongming. A level set method for structural topology optimization[J]. Computer Methods in Applied Mechanics and Engineering, 2003, 192：227-246.
[6] GUO Xu, ZHANG Weisheng, ZHANG Jian, et al. Explicit structural topology optimization based on moving morphable components (MMC) with curved skeletons[J]. Computer Methods in Applied Mechanics and Engineering, 2016, 310：711-748.
[7] YU Minghao, RUAN Shilun, WANG Xinyu, et al. Topology optimization of thermal–fluid problem using the MMC-based approach[J]. Structural and Multidisciplinary Optimization, 2019, 60：151-165.
[8] GUIRGUIS D, HAMZA K, ALY M, et al. Multi-objective topology optimization of multi-component continuum structures via a Kriging-interpolated level set approach[J]. Structural and Multidisciplinary Optimization, 2015, 51：733-748.
[9] ZUO Wenjie, SAITOU K. Multi-material topology optimization using ordered SIMP interpolation[J]. Structural and Multidisciplinary Optimization, 2017, 55：477-491.
[10] BRUYNEEL M, DUYSINX P. Note on topology optimization of continuum structures including self-weight[J]. Structural and Multidisciplinary Optimization, 2005, 29：245-256.
[11] LEE E, JAMES K A, MARTINS J R R A. Stress-constrained topology optimization with design-dependent loading[J]. Structural and Multidisciplinary Optimization, 2012, 46：647-661.
[12] FÉLIX L, GOMES A A, SULEMAN A. Topology optimization of the internal structure of an aircraft wing subjected to self-weight load[J]. Engineering Optimization, 2020, 52(7)：1119-1135.
[13] ZHU Jihong, ZHANG Weihong, BECKERS P. Integrated layout design of multi-component system[J]. International Journal for Numerical Methods in Engineering, 2009, 78(6)：631-651.
[14] ZHU Jihong, GUO Wenjie, ZHANG Weihong, et al. Integrated layout and topology optimization design of multi-frame and multi-component fuselage structure systems[J]. Structural and Multidisciplinary Optimization, 2017, 56：21-45.
[15] ZHANG Shanshan, LI Houmin, HUANG Yicang. An improved multi-objective topology optimization model based on SIMP method for continuum structures including self-weight[J]. Structural and Multidisciplinary Optimization, 2021, 63：211-230.
[16] KUMAR P. Topology optimization of stiff structures under self-weight for given volume using a smooth Heaviside function[J]. Structural and Multidisciplinary Optimization, 2022, 65(4)：128.
[17] 张晖, 刘书田, 张雄. 考虑自重载荷作用的连续体结构拓扑优化[J]. 力学学报, 2009(1)：98-104. ZHANG Hui, LIU Shutian, ZHANG Xiong. Topology optimization of continuum structures subjected to self-weight loads[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009(1)：211-230.
[18] 高彤, 张卫红, 朱继宏. 惯性载荷作用下结构拓扑优化[J]. 力学学报, 2009, 41(4): 530-541. GAO Tong, ZHANG Weihong, ZHU Jihong. Structural topology optimization under inertial loads[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(4)：530-541.
[19] HUANG Xiaodong, XIE Yimin. Evolutionary topology optimization of continuum structures including design-dependent self-weight loads[J]. Finite Elements in Analysis and Design, 2011, 47(8)：942-948.
[20] XU Huayang, GUAN Liwen, CHEN Xiang, et al. Guide-weight method for topology optimization of continuum structures including body forces[J]. Finite Elements in Analysis and Design, 2013, 75：38-49.
[21] 陈祥, 刘辛军. 基于RAMP插值模型结合导重法求解拓扑优化问题[J]. 机械工程学报, 2012, 48(1)：135-140. CHEN Xiang, LIU Xinjun. Solving topology optimization problems based on RAMP method combined with guide-weight method[J]. Journal of Mechanical Engineering, 2012, 48(1)：135-140.
[22] 任毅如, 向剑辉, 何杰, 等. 基于导重法的自重载荷下悬臂梁结构拓扑优化[J]. 北京航空航天大学学报, 2021, 47(7)：1338-1344. REN Yiru, XIANG Jianhui, HE Jie, et al. Topology optimization of cantilever structure with self-weight load based on guide-weight method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(7)：1338-1344.
[23] 朱继宏, 张卫红, 王丹. 航空发动机柔性部件结构的热力耦合优化设计技术[J]. 航空制造技术, 2013, 429(9)：26-30. ZHU Jihong, ZHANG Weihong, WANG Dan. Coupled thermal and mechanical optimization design for flexible structure of aeroengine[J]. Aeronautical Manufacturing Technology, 2013, 429(9)：26-30.
[24] SHI Guanghui, GUAN Chengqi, QUAN Dongliang, et al. An aerospace bracket designed by thermo-elastic topology optimization and manufactured by additive manufacturing[J]. Chinese Journal of Aeronautics, 2020, 33(4)：1252-1259.
[25] GAO Tong, ZHANG Weihong. Topology optimization involving thermo-elastic stress loads[J]. Structural and Multidisciplinary Optimization, 2010, 42(5)：725-738.
[26] YANG Xiongwei, LI Yueming. Topology optimization to minimize the dynamic compliance of a bi-material plate in a thermal environment[J]. Structural and Multidisciplinary Optimization, 2013, 47(3)：399-408.
[27] MENG Qingxuan, XU Bin, HUANG Chenguang, et al. Topology optimization of thermo-elastic structures considering stiffness, strength and temperature constraints over a wide range of temperatures[J]. International Journal for Numerical Methods in Engineering, 2022, 123(7)：1627-1653.
[28] CHUNG H, AMIR O, KIM H A. Level-set topology optimization considering nonlinear thermoelasticity[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 361：112735.
[29] GAN Ning, WANG Qianxuan. Topology optimization design of porous infill structure with thermo-mechanical buckling criteria[J]. International Journal of Mechanics and Materials in Design, 2022, 18：267-288.
[30] DENG Shiguang, SURESH K. Topology optimization under thermo-elastic buckling[J]. Structural and Multidisciplinary Optimization, 2016, 55(5)：1759-1772.
[31] OGAWA S, YAMADA T. Topology optimization for transient response problems involving thermoelastic materials[J]. Finite Elements in Analysis and Design, 2022, 201：103695.
[32] LIU Xinjun, WANG Chao, ZHOU Yanhua. Topology optimization of thermoelastic structures using the guide-weight method[J]. Science China Technological Sciences, 2014, 57：968-979.
[33] GAO Tong, XU Pengli, ZHANG Weihong. Topology optimization of thermo-elastic structures with multiple materials under mass constraint[J]. Computers & Structures, 2016, 173：150-160.
[34] ALACOQUE L, WATKINS R T, TAMIJANI A Y. Stress-based and robust topology optimization for thermoelastic multi-material periodic microstructures[J]. Computer Methods in Applied Mechanics and Engineering, 2021, 379：113749.
[35] XU Bin, HUANG Xiaodong, ZHOU Shiwei, et al. Concurrent topological design of composite thermoelastic macrostructure and microstructure with multi-phase material for maximum stiffness[J]. Composite Structures, 2016, 150：84-102.
[36] YAN Jun, SUI Qianqian, FAN Zhirui, et al. Clustering-based multiscale topology optimization of thermo-elastic lattice structures[J]. Computational Mechanics, 2020, 66(4)：979-1002.
[37] HANG Li, HAO Li, XIAO Mi, et al. Robust topology optimization of thermoelastic metamaterials considering hybrid uncertainties of material property[J]. Composite Structures, 2020, 248：112477.
[38] ZHENG Jing, CHEN Hong, JIANG Chao. Robust topology optimization for structures under thermo-mechanical loadings considering hybrid uncertainties[J]. Structural and Multidisciplinary Optimization, 2022, 65(1)：29.
[39] WANG Bo, WANG Guangming, SHI Yongxin, et al. Stress-constrained thermo-elastic topology optimization of axisymmetric disks considering temperature-dependent material properties[J]. Mechanics of Advanced Materials and Structures, 2022, 29(28)：7459-7475.
[40] RODRIGUES H, FERNANDES P. A material based model for topology optimization of thermoelastic structures[J]. International Journal for Numerical Methods in Engineering, 1995, 38(12)：1951-1965.
[41] 曾攀. 有限元分析及应用[M]. 北京：清华大学出版社, 2004. ZENG Pan. Finite element analysis and applications[M]. Beijing：Tsinghua University Press, 2004.
[42] PEDERSON N L. Maximization of eigenvalues using topology optimization[J]. Structural and Multidisciplinary Optimization, 2000, 20(1)：2-11.
[43] BRUYNEEL M, DUYSINX P. Note on topology optimization of continuum structures including self-weight[J]. Structural and Multidisciplinary Optimization, 2005, 29(4)：245-256.
[44] ZHENG Jing, RONG Xuanpei, JIANG Chao. Thermoelastic topology optimization for structures with temperature-dependent material properties[J]. SCIENCE CHINA Technological Sciences, 2023, 66(12)：3488-3503.

考虑惯性载荷的结构热力耦合拓扑优化

Thermal-mechanical Coupled Topology Optimization for Structures with Inertial Loads

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