QIU J Y , FAN Y T , WEI H L , et al. Lightweight design of aircraft truss based on topology and size optimization [J ] . Journal of Physics: Conference Series , 2021 , 1986 ( 1 ): 012094 . DOI: 10.1088/1742-6596/1986/1/012094 http://doi.org/10.1088/1742-6596/1986/1/012094 Truss structure is widely used in aircraft design. In this paper, the lightweight design of a certain type of aircraft truss structure is carried out through topology analysis and size optimization to improve the performance of the aircraft. The original truss model is established based on ABAQUS, and its static strength is checked and analyzed. According to the design domain of the original model, a topology optimization method is used to obtain a new material distribution. Then the section size of each truss member is taken as the optimization variable, the maximum deformation of the structure is taken as the constraint, and the overall model volume is the minimum as the optimization goal, the genetic algorithm is used to obtain the new structure size. The results show that the truss members after the second optimization can meet the requirements of use and have a 75.15% reduction in mass compared to the original structure, which verifies that the method is feasible and provides a new idea for the lightweight design of truss structures.

DONG H , GAO H , FENG X L , et al. Shape optimization of acoustic horns for improved directivity control and radiation efficiency based on the multimodal method [J ] . The Journal of the Acoustical Society of America , 2021 , 149 ( 3 ): 1411 - 1424 . DOI: 10.1121/10.0003568 http://doi.org/10.1121/10.0003568 https://asa.scitation.org/doi/10.1121/10.0003568 https://asa.scitation.org/doi/10.1121/10.0003568

荣见华 , 赵圣佞 , 李方义 , 等 . 涉及空腔制造的最小长度尺寸限制的清晰结构拓扑优化设计 [J ] . 机械工程学报 , 2019 , 55 ( 19 ): 174 - 185 . DOI: 10.3901/JME.2019.19.174 http://doi.org/10.3901/JME.2019.19.174 针对以结构柔顺度最小为目标函数，涉及空腔制造的最小长度尺寸限制的结构拓扑优化设计问题，提出了一种新的拓扑优化求解方法。首先，为了消除现有的结构实体相及空洞相的相同的光滑Heaviside映射导致的强烈对立矛盾，引入光滑Heaviside映射和修改的光滑Heaviside映射分别进行实体相及空洞相的设计变量过滤；而后，构建了合理和协同的涉及实体相和空洞相的几何最小长度尺寸限制的结构拓扑优化模型；利用MMA算法，形成了一种新的涉及实体相和空洞相的几何最小长度尺寸限制的结构拓扑优化算法。给出的算例结果表明，与现有方法比，该方法可解决结构实体相和空洞相的几何最小长度尺寸控制问题。且所提方法可获得清晰0/1分布的优化结构拓扑。

RONG J H , ZHAO S N , LI F Y , et al. Clear structural topology optimization design involving the minimum length and size limit of cavity manufacturing [J ] . Journal of Mechanical Engineering , 2019 , 55 ( 19 ): 174 - 185 . (in Chinese)

丁卯 . 基于变密度法的结构强度拓扑优化策略 [J ] . 上海交通大学学报 , 2021 , 55 ( 6 ): 764 - 773

DING M . Topology optimization strategy of structural strength based on variable density method [J ] . Journal of Shanghai Jiao Tong University , 2021 , 55 ( 6 ): 764 - 773 . (in Chinese)

陈俊男 , 陈吉清 , 兰凤崇 . 基于响应面与遗传算法的前副车架轻量化优化 [J ] . 机械设计与制造工程 , 2019 , 48 ( 4 ): 73 - 78 .

CHEN J N , CHEN J Q , LAN F C . Lightweight optimization of front subframe based on response surface and genetic algorithm [J ] . Mechanical Design and Manufacturing Engineering , 2019 , 48 ( 4 ): 73 - 78 . (in Chinese)

张新建 . 某火炮上架多工况拓扑优化设计 [J ] . 火炮发射与控制学报 , 2019 , 40 ( 3 ): 56 - 60 .

ZHANG X J . Topology optimization design of a gun under multiple working conditions [J ] . Journal of Gun Launch and Control , 2019 , 40 ( 3 ): 56 - 60 . (in Chinese)

钟焕杰 . 薄壁加筋结构的拓扑优化方法研究 [D ] . 南京 : 南京航空航天大学 , 2015 .

ZHONG H J . Research on topology optimization method of thin-walled stiffened structure [D ] . Nanjing : Nanjing University of Aeronautics and Astronautics , 2015 . (in Chinese)

吴胜军 , 叶欣钰 , 江兴洋 . 混合动力客车车身骨架轻量化设计 [J ] . 机械设计与制造 , 2021 ( 7 ): 221 - 224 .

WU S J , YE X Y , JIANG X Y . Lightweight design of hybrid electric bus body frame [J ] . Mechanical Design and Manufacturing , 2021 ( 7 ): 221 - 224 . (in Chinese)

王博 , 周子童 , 周演 , 等 . 薄壁结构多层级并发加筋拓扑优化研究 [J ] . 计算力学学报 , 2021 , 38 ( 4 ): 487 - 497 .

WANG B , ZHOU Z T , ZHOU Y , et al. Research on topology optimization of multi-layer concurrent reinforcement of thin-walled structures [J ] . Journal of Computational Mechanics , 2021 , 38 ( 4 ): 487 - 497 . (in Chinese)

TIAN D Y , HAN X H , HUA L , et al. A novel process for axial closed extrusion of ring part with mesh-like ribs [J ] . International Journal of Mechanical Sciences , 2019 , 165 : 105186 . (in Chinese) DOI: 10.1016/j.ijmecsci.2019.105186 http://doi.org/10.1016/j.ijmecsci.2019.105186 https://linkinghub.elsevier.com/retrieve/pii/S0020740319316960 https://linkinghub.elsevier.com/retrieve/pii/S0020740319316960

牛斌 . 面向动力学性能的薄壁加筋板结构阻尼与筋条布局协同优化 [J ] . 中国机械工程 , 2021 , 32 ( 16 ): 1912 - 1920 .

NIU B . Collaborative optimization design of damping and rib layout of thin-walled stiffened plate structure for dynamic performance [J ] . China Mechanical Engineering , 2021 , 32 ( 16 ): 1912 - 1920 . (in Chinese)

谌炎辉 , 周德俭 . 基于BOM的复杂产品模块划分方法研究 [J ] . 中国机械工程 , 2012 , 23 ( 21 ): 2590 - 2593 . 提出了一种基于产品物料清单(BOM)且适合于复杂产品的模块划分方法。首先基于复杂产品的BOM,形成以零部件为节点的产品结构树(PST),然后通过分析同一节点内零部件的几何、功能和物理相关性得到关联矩阵(CM)并生成关联图(CG),根据关联图计算在不同划分情况时的模块化度(DM),在结构树范围内选择最优的模块化度确定模块的划分。最后以轮式装载机的工作装置为例说明该方法的合理性和有效性。

CHEN Y H , ZHOU D J . Research on module division method of complex products based on BOM [J ] . China Mechanical Engineering , 2012 , 23 ( 21 ): 2590 - 2593 . (in Chinese)

兰凤崇 , 赖番结 . 考虑动态特性的多工况车身结构拓扑优化研究 [J ] . 机械工程学报 , 2014 , 50 ( 20 ): 122 - 128 . DOI: 10.3901/JME.2014.20.122 http://doi.org/10.3901/JME.2014.20.122 由于车身结构在汽车行驶过程中主要是保证其静动态承载性能，因此在概念设计阶段考虑其多种承载工况，特别是车身的动态性能要求来确定车身结构的最佳拓扑形式十分重要。结合整车多工况多体动力学分析，运用折衷规划法定义整车实际行驶工况下车身结构静态刚度和动态振动频率最大化的综合目标函数，通过层次分析法确定各工况的最优权重系数，进行车身结构的综合目标优化设计。以方程式赛车的车身结构设计为例，进行综合目标的拓扑优化设计，结果表明该方法进行车身结构的概念设计可行且有效。同时，经对比根据设计经验和基于正交试验定义权重系数的两种方法得出的优化结果，其车身的刚度和前6阶频率均有不同程度的提高，且结构更加合理，同时提高了计算效率。

LAN F C , LAI F J . Research on topology optimization of multi condition body structure considering dynamic characteristics [J ] . Journal of Mechanical Engineering , 2014 , 50 ( 20 ): 122 - 128 . (in Chinese)

GJB 150.16A—2009 . 军用装备实验室环境试验方法.第18部分:振动试验 [S ] . 北京 : 中国人民解放军总装备部 , 2009 .

GJB 150.18A—2009 . Laboratory environmental test methods for military equipment Part 18:impact test [S ] . Beijing : General Armament Department of the Chinese people's Liberation Army , 2009 . (in Chinese)

孙攀旭 , 杨红 , 吴加峰 , 等 . 基于频率相关黏性阻尼模型的复模态叠加法 [J ] . 力学学报 , 2018 , 50 ( 5 ): 1185 - 1197 . DOI: 10.6052/0459-1879-18-170 http://doi.org/10.6052/0459-1879-18-170 黏性阻尼模型存在每周期耗散能量与外激励频率相关的缺陷, 复阻尼模型时域计算结果存在发散现象. 为克服上述两种阻尼模型的不足, 在复阻尼模型基础上, 依据时频域转化原则推导了频率相关黏性阻尼模型. 频率相关黏性阻尼模型不仅具有每周期耗散能量与外激励频率无关的优点, 还保证了结构位移时程的稳定收敛. 混合结构由具有不同阻尼特性的材料组成, 其阻尼矩阵为非比例矩阵, 无法直接采用实模态叠加法. 根据频率相关黏性阻尼模型与复阻尼模型的转换关系, 提出了适用于混合结构的基于频率相关黏性阻尼模型的复模态叠加法. 算例分析结果表明, 与基于黏性阻尼模型的复模态叠加法相比, 基于频率相关黏性阻尼模型的复模态叠加法不仅计算结果唯一, 且不增加矩阵维度, 具有较高的计算效率. 小阻尼情况下, 两种方法的计算结果近似相等, 且与复阻尼模型的频域计算结果一致. 当阻尼比较大时, 两种方法的计算结果差异增大, 但频率相关黏性阻尼模型的复模态叠加法与复阻尼模型的频域计算结果仍保持一致.

SUN P X , YANG H , WU J F , et al. Complex mode superposition based on frequency dependent viscous damping model [J ] . Chinese Journal of Mechanics , 2018 , 50 ( 5 ): 1185 - 1197 . (in Chinese)

姚卫星 , 顾怡 . 飞机结构设计 [M ] . 北京 : 国防工业出版社 , 2016 .

YAO W X , GU Y . Aircraft structural design [M ] . Beijing : National Defense Industry Press , 2016 . (in Chinese)

李播博 . 基于子结构模态综合法的重型牵引车优化 [J ] . 东北大学学报(自然科学版) , 2019 , 40 ( 4 ): 531 - 536 ,542.

LI B B . Optimization design of heavy tractor based on substructure modal synthesis method [J ] . Journal of Northeast University (Natural Science Edition) , 2019 , 40 ( 4 ): 531 - 536 ,542. (in Chinese)

GJB 150.18A—2009 . 军用装备实验室环境试验方法.第18部分:冲击试验 [S ] . 北京 : 中国人民解放军总装备部 , 2009 .

GJB 150.18A—2009 . Laboratory environmental test methods for military equipment Part 18:impact test [S ] . Beijing : General Armament Department of the Chinese People's Liberation Army , 2009 . (in Chinese)

王超 . 某型遥控武器站关键结构设计问题研究 [D ] . 长沙 : 国防科技大学 , 2018 .

WANG C . Research on key structure design of a remote control weapon station [D ] . Changsha : National University of Defense Technology , 2018 . (in Chinese)

廖洪波 . 武器站伺服装置的性能分析与控制问题研究 [D ] . 长沙 : 国防科技大学 , 2018 .

LIAO H B . Performance analysis and control research of servo device in weapon station [D ] . Changsha : National University of Defense Technology , 2018 . (in Chinese)