Page 24 - 《振动工程学报》2025年第9期
P. 24
1954 振 动 工 程 学 报 第 38 卷
及不同约束区间相对宽度的算例,本文发现约束区 reaction forces[J]. Structural and Multidisciplinary Optimiza-
间相对宽度对于最终优化结果的动柔度模值影响不 tion,2017,56(4):755-765.
[11] CAO Y F,GU X J,ZHU J H,et al. Precise output loads
大,外载荷频率与体积分数比对于优化结果会产生
control of load-diffusion components with topology optimiza-
一定影响。拓扑优化对传力路径的规划不仅可以实 tion[J]. Chinese Journal of Aeronautics,2020,33(3):933-946.
现最小动柔度设计,还可以通过边界条件等效与合 [12] CAO Y F,ZHU J H,GUO W J,et al. Structure topology
理的约束建模实现精确的动载荷输出设计。 optimization method for output loads precise control[J]. Scien-
tia Sinica Physica, Mechanica & Astronomica, 2018,
综上所述,本文提出的拓扑优化方法充分考虑
48(1):014606.
了周围结构对局部结构的影响,从而保证了结构优 [13] HOU J,GU X J,ZHU J H,et al. Topology optimization of
化的正确性。由于边界条件等效本身存在一定的误差, joint load control with geometrical nonlinearity[J]. Chinese
Journal of Aeronautics,2020,33(1):372-382.
这会对优化结果不可避免地产生一定影响,如何更
[14] TANG L,GAO T,SONG L L,et al. Thermo-elastic topol-
加准确地进行边界条件等效将成为今后的研究目标。
ogy optimization of continuum structures subjected to load
allocation constraints[J]. Structural and Multidisciplinary Opti-
参考文献: mization,2022,65(12):344.
[15] 谷小军,徐珉轲,张薇,等. 重型运载火箭发动机机架与
舱段传力结构一体化拓扑优化设计 [J]. 火箭推进,2022,
[1] BENDSØE M P, SIGMUND O. Material interpolation
48(2):27-35.
schemes in topology optimization[J]. Archive of Applied
GU Xiaojun, XU Minke, ZHANG Wei, et al. Integrated
Mechanics,1999,69(9):635-654.
topology optimization design of heavy rocket engine frame and
[2] QUERIN O M,YOUNG V,STEVEN G P,et al. Computa-
segment force transmission structure[J]. Journal of Rocket
tional efficiency and validation of bi-directional evolutionary
Propulsion,2022,48(2):27-35.
structural optimisation[J]. Computer Methods in Applied
[16] 李佳霖,赵剑,孙直,等. 基于移动可变形组件法(MMC)
Mechanics and Engineering,2000,189(2):559-573.
的运载火箭传力机架结构的轻量化设计 [J]. 力学学报,
[3] ZHANG W S,YUAN J,ZHANG J,et al. A new topology
2022,54(1):244-251.
optimization approach based on Moving Morphable Compo-
LI Jialin,ZHAO Jian,SUN Zhi,et al. Lightweight design
nents (MMC) and the ersatz material model[J]. Structural and
of transmission frame structures for launch vehicles based on
Multidisciplinary Optimization,2016,53(6):1243-1260.
moving morphable components(MMC) approach[J]. Chinese
[4] 范瑞祥,姚瑞娟,朱振涛,等. 一种新型 7 台火箭发动机并
Journal of Theoretical and Applied Mechanics, 2022,
联推力传递结构方案 [J]. 载人航天,2020,26(5):630-634.
54(1):244-251.
FAN Ruixiang,YAO Ruijuan,ZHU Zhentao,et al. A new
[17] 王一航,彭珍瑞. 基于 Kriging 模型和分层模型修正技术的
type of thrust transmission structure of paralleled seven rocket
结构边界条件识别 [J]. 振动与冲击,2023,42(6):134-142.
engines[J]. Manned Spaceflight,2020,26(5):630-634.
WANG Yihang, PENG Zhenrui. Identification of structural
[5] WANG C,ZHU J H,WU M Q,et al. Multi-scale design
boundary conditions based on the Kriging model and the hier-
and optimization for solid-lattice hybrid structures and their
archical model updating technique[J]. Journal of Vibration and
application to aerospace vehicle components[J]. Chinese Jour-
Shock,2023,42(6):134-142.
nal of Aeronautics,2021,34(5):386-398.
[18] POON N M K,MARTINS J R R A. An adaptive approach to
[6] WANG J,ZHU J H,HOU J,et al. Lightweight design of a
constraint aggregation using adjoint sensitivity analysis[J].
bolt-flange sealing structure based on topology optimi-
Structural and Multidisciplinary Optimization, 2007,
zation[J]. Structural and Multidisciplinary Optimization,
34(1):61-73.
2020,62(6):3413-3428.
[7] 王志祥,雷勇军,段静波,等. 重型运载火箭集中力扩散 [19] STOLPE M, SVANBERG K. An alternative interpolation
舱段多区域联合设计与优化 [J]. 航空学报,2022,43(3): scheme for minimum compliance topology optimization[J].
Structural and Multidisciplinary Optimization, 2001,
225135.
22(2):116-124.
WANG Zhixiang, LEI Yongjun, DUAN Jingbo, et al.
[20] LAZAROV B S,SIGMUND O. Filters in topology optimiza-
Multi-region integrated design and optimization of concen-
tion based on Helmholtz-type differential equations[J]. Interna-
trated-force diffusion component in heavy-lift launch
tional Journal for Numerical Methods in Engineering,2011,
vehicle[J]. Acta Aeronautica et Astronautica Sinica, 2022,
86(6):765-781.
43(3):225135.
[8] WANG C, ZHOU E L, WU Y, et al. Transient stress- [21] XU S L, CAI Y W, CHENG G D. Volume preserving
nonlinear density filter based on Heaviside functions[J]. Struc-
constrained topology optimization of impacted structures[J].
Structural and Multidisciplinary Optimization, 2023, tural and Multidisciplinary Optimization, 2010, 41( 4) :
495-505.
66(4):94.
[9] 张家鑫,王博,牛飞,等. 分级型放射肋短壳结构集中力 [22] SVANBERG K. MMA and GCMMA-two methods for nonlin-
扩散优化设计 [J]. 计算力学学报,2014,31(2):141-148. ear optimization[C/OL][2023-09-18]. 2014.
ZHANG Jiaxin,WANG Bo,NIU Fei,et al. Optimal design
of concentrated force diffusion for short shell structure using 第一作者:张理昊(2000—),男,硕士研究生。
hierarchical radial ribs[J]. Chinese Journal of Computational
E-mail:3216045zlh@163.com
Mechanics,2014,31(2):141-148.
[10] GAO T,QIU L B,ZHANG W H. Topology optimization of 通信作者:于开平(1968—),男,博士,教授。
continuum structures subjected to the variance constraint of E-mail:yukp@hit.edu.cn