基于近似模型辅助智能算法的变截面点阵结构优化设计方法

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (16) : 181-188.

论文

向艳1,2，蒋国璋1,2,3，张严1,2,3，徐曼曼1,2,3

作者信息 +

An optimization design method of variable cross-section lattice structures based on an approximate model-assisted intelligent algorithm

XIANG Yan1,2,JIANG Guozhang1,2,3,ZHANG Yan1,2,3,XU Manman1,2,3

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文章历史 +

摘要

桁架类点阵结构具有质量轻、比强度/比刚度高、减振吸能性好，且拓扑构型简单、增材成型可靠性高等优点，被广泛应用于航天器各关键承载部件设计。传统桁架类点阵设计大多囿于等截面设计约束，严重制约了优化设计的寻优潜能，难以满足航天器结构超轻质、高强度的性能要求。为突破传统点阵的等截面形状约束，构建基于显式拓扑描述函数的变截面几何描述模型，实现变截面点阵几何形状的自由描述；采用能量均匀化方法精确计算变截面点阵单胞宏观等效弹性张量，并建立变截面点阵几何描述参数关于其宏观等效弹性张量的近似响应模型；以变截面点阵的几何描述参数为设计变量，材料用量为约束条件，最大体积模量或最大剪切模量为目标函数，建立变截面点阵几何描述参数的优化数学模型，并采用基于近似模型辅助的粒子群优化算法实现上述优化模型的高效求解。数值算例表明，相较于等截面点阵，在相同材料用量下，优化后的变截面点阵的体积模量和剪切模量性能更优。所提方法进一步拓展了桁架类点阵的设计空间，有效提升其力学性能，在航天器结构轻量化设计方面具有应用推广前景。

Abstract

Truss lattice structures have the advantages of light weight, high specific strength/specific stiffness, good vibration and energy absorption, as well as simple topological configuration, high reliability of additive manufacturing, which have been widely used in the design of key load-bearing components of spacecrafts. The traditional truss lattice design is mostly limited by the constraint of constant cross-section, and the potential of optimization design method is also seriously restricted, which makes it difficult to meet the performance requirements of super light and high strength of spacecraft structures. In order to break through the constraint of constant cross-section shape of traditional lattice, a geometric description model of variable cross-section based on explicit topological description function is constructed to realize the free description of geometric shape of variable cross-section lattice. The macroscopic equivalent elastic tensor of the variable cross-section lattice unit cell is accurately calculated by using an energy-based homogenization method, and the approximate response model of geometric description parameters of the variable cross-section lattice about its macroscopic equivalent elastic tensor is established. Taking the geometric description parameters of variable cross-section lattice as design variables, material consumption as constraint conditions, and maximum bulk modulus or maximum shear modulus as objective functions, an optimization mathematical model of geometric description parameters of variable cross-section lattice is established, and the particle swarm optimization algorithm assisted by approximate model is adopted to realize the efficient solution of the above optimization model. Numerical examples show that compared with the lattice with constant cross-section, the optimized lattice with variable cross-section has better bulk modulus and shear modulus under the same material usage. The proposed method further expands the design space of truss lattice, and effectively improves its mechanical properties, as well as shows an application prospect in lightweight design of spacecrafts.

导出引用

向艳1,2，蒋国璋1,2,3，张严1,2,3，徐曼曼1,2,3. 基于近似模型辅助智能算法的变截面点阵结构优化设计方法[J]. 振动与冲击, 2023, 42(16): 181-188

XIANG Yan1,2,JIANG Guozhang1,2,3,ZHANG Yan1,2,3,XU Manman1,2,3. An optimization design method of variable cross-section lattice structures based on an approximate model-assisted intelligent algorithm[J]. Journal of Vibration and Shock, 2023, 42(16): 181-188

参考文献

[1] X. Zheng, H. Lee, T.H. Weisgraber, et al. Ultralight, ultrastiff mechanical metamaterials, Science, 344 (2014) 1373-1377.
[2] D.P. Anton, S.M.J. Razavi, M. Benedetti, et al. Properties and applications of additively manufactured metallic cellular materials: a review, Prog Mater Sci, (2021) 100918.
[3] 熊健, 杜昀桐, 杨雯, 等. 轻质复合材料夹芯结构设计及力学性能最新进展, 宇航学报, 41 (2020) 749-760.
Xiong Jian, Du Zantong, Yang Wen, et al. Latest progress in structural design and mechanical properties of lightweight composite sandwich, Journal of Aerospace, 41 (2020) 749-760.
[4] 蔡金虎,王春洁. 基于映射的梯度点阵结构设计方法[J]. 振动与冲击,2020,39(20):74-81.
Cai Hu, Wang Chunjie. Design method of gradient lattice structure based on mapping [J]. Vibration and Impact, 2020,39(20):74-81.
[5] 冀宾, 顾铖璋, 韩涵, 等. 几种变截面点阵承受面外压缩载荷的力学行为, 固体力学学报, 39 (2018) 394-402.
Ji Bin, Gu Chengzhang, Han Han, et al.Mechanical Behavior of Several Lattices with Variable Cross Sections under Out-of-Plane Compression Load, Journal of Solid Mechanics, 39 (2018) 394-402.
[6] 朱凌雪, 朱晓磊, 芯体截面梯度变化的点阵夹层结构吸能特性研究, 振动与冲击, 37 (2018) 115-121.
Zhu Lingxue, Zhu Xiaolei, Study on Energy Absorption Characteristics of Lattice Sandwich Structure with Gradient Change of Core Section, Vibration and Impact, 37 (2018) 115-121.
[7] X. Cao, S. Duan, J. Liang, et al. Mechanical properties of an improved 3D-printed rhombic dodecahedron stainless steel lattice structure of variable cross section, International Journal of Mechanical Sciences, 145 (2018) 53-63.
[8]雷鹏福, 戴宁, 汪志鹏. 基于复杂点阵结构的节点强化技术研究[J]. 机械设计与制造工程,2018, 47(12): 1-4.
Lei Pengfu, Nina Dai, Abollo Wang. Research on node strengthening technology based on complex lattice structure [J]. Mechanical Design and Manufacturing Engineering, 2018, 47(12): 1-4.
[9] Ren X, Xiao L, Hao Z. Multi-Property Cellular Material Design Approach Based on the Mechanical Behaviour Analysis of the Reinforced Lattice Structure[J]. Materials & Design, 2019, 174(3): 107785.
[10]汪飞雪,姚龙飞,张天翊,等.基于SLM工艺的变截面四棱锥点阵结构建模与试验研究[J].机械工程学报.2021,57(24).
Wang Feixue, Yao Longfei, Zhang Tianyi, et al. Modeling and experimental study of variable cross-section pyramid lattice structure based on SLM technology [J]. Journal of Mechanical Engineering. 2021,57(24).
[11] L.J. Feng, J. Xiong, L.H. Yang, et al. Shear and bending performance of new type enhanced lattice truss structures, International journal of mechanical sciences, 134 (2017) 589-598.
[12] Y. Liu, Z. Dong, J. Liang, et al. Determination of the strength of a multilayer BCC lattice structure with face sheets, International Journal of Mechanical Sciences, 152 (2019) 568-575.
[13] M.J. Powell, Radial basis functions in 1990, Adv. Numer. Anal., 2 (1992) 105-210.
[14] S. Kitayama, M. Arakawa, K. Yamazaki, Sequential approximate optimization using radial basis function network for engineering optimization, Optimization and Engineering,12 (2011) 535-557.
[15] Wang M Y, Wang X, Guo D. A level set method for structural topology optimization[J]. Computer Methods in Applied Mechanics and Engineering, 2003, 192(1-2):227-246.
[16] 聂利娟. 基于参数化水平集的微结构与结构--材料一体化拓扑优化方法研究[D]. 广东:华南理工大学,2020.
Nie Lijuan. Topological optimization method of microstructure and structure-material integration based on parametric level set [D]. Guangdong: South China University of Technology, 2020.
[17] S. Ghannadpour, M. Mahmoudi, K.H. Nedjad, Structural behavior of 3D-printed sandwich beams with strut-based lattice core: Experimental and numerical study, Composite Structures, 281 (2022) 115113.
[18] 魏鹏,范海坚,李雪平,等. 基于参数化水平集方法的微结构拓扑优化设计[J]. 计算力学学报,2021,38(4):471-478.
Wei Peng, Fan Haijian, Li Xueping, et al. Topology optimization design of microstructure based on parametric level set method [J]. Journal of Computational Mechanics, 2021,38(4):471-478.
[19] Zhang Yan, Xiao Mi, Li Hao, Gao Liang*. Topology optimization of material microstructures using energy-based homogenization method under specified initial material layout[J]. Journal of Mechanical Science and Technology, 2019, 33(2):677-693.
[20] 冯帅,毛保全,王之千,等. 基于自适应混合近似模型的顶置武器站多柔体系统动力学优化研究[J]. 振动与冲击,2020,39(12):206-212.
Feng Shuai, Mao Baoquan, Wang Zhiqian, et al. Dynamic optimization of multibody system of overhead weapon station based on adaptive hybrid approximation model [J]. Vibration and Shock, 2020,39(12):206-212.
[21] 杨丽丽,孔祥龙,李文龙,等. 基于高保真度代理模型的卫星结构优化[J]. 振动与冲击,2021,40(23):208-215,222.
Yang Lili, Kong Xianglong, Li Wenlong, et al. Satellite Structure Optimization Based on High Fidelity Proxy Model [J]. Vibration and Shock, 2021,40(23):208-215,222.
[22] Kitayama S, Arakawa M, Yamazaki K. Sequential approximate optimization using radial basis function network for engineering optimization[J]. Optimization and Engineering, 2011, 12(4): 535-557.