基于映射的梯度点阵结构设计方法

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振动与冲击 ›› 2020, Vol. 39 ›› Issue (20) : 74-81.

论文

基于映射的梯度点阵结构设计方法

蔡金虎1，王春洁1,2

作者信息 +

A graded lattice structure design method based on mapping process

CAI Jinhu1，WANG Chunjie1,2

Author information +

文章历史 +

摘要

点阵结构因具有高比强度、高比刚度的性能优势而在航空、航天等领域具有广阔的应用前景。梯度点阵结构相比于传统的均匀点阵结构具有更优的力学性能，因此，本文提出了一种基于密度与应力映射的梯度点阵结构设计方法。该方法对结构进行拓扑优化以获取结构的单元相对密度与应力分布信息，并建立单元相对密度、应力与胞元支柱截面尺寸之间的映射函数关系以确定其尺寸。采用反距离加权法对单元相对密度与应力进行过滤，将材料分布在结构的主要传力路径上，并提出了在结构质量不变条件下的胞元支柱尺寸控制方法。本文所提方法建立不同体积与胞元密度的点阵结构只需进行一次拓扑优化设计，并且该方法可应用于较复杂结构的点阵化设计，提升了点阵结构设计的效率。本文所提方法已通过数值算例验证了其可行性与有效性，可推广到相关结构的轻量化设计中。

Abstract

A lattice structure has broad application prospects in aviation and aerospace due to its high specific strength and stiffness. A graded lattice structure may have better mechanical performance than uniform lattice structure. Therefore, a graded lattice structure design method based on density and stress mapping was proposed in this work. The topology optimization method was utilized to obtain the element relative density and stress values, which were used to determine the strut thickness based on an established mapping function between the values and the strut thickness. The inverse distance weighting method was used to filter the relative density and stress to distribute more material on the force path, and the strut minimum dimension control method was proposed under the condition that the structure mass remains unchanged. The design of lattice structure with different volumes are based on the only once topology optimization results, which can significantly improve the design efficiency. The proposed method can be used for structures with complex geometry because the unit cells are established based on the finite elements. The feasibility and effectiveness of the proposed method were verified by a case study, which proves that the proposed method can be extended to the lightweight design of related structures.

导出引用

蔡金虎1，王春洁1,2. 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 Jinhu1，WANG Chunjie1,2. A graded lattice structure design method based on mapping process[J]. Journal of Vibration and Shock, 2020, 39(20): 74-81

参考文献

[1]. 郭锐, 南博华, 周昊, 等. 点阵金属夹层结构抗侵彻实验研究[J]. 振动与冲击, 2016, 35(24): 45-50.
Rui G , Bohua N , Hao Z , et al. Experiment assessment of the ballistic response of a hybrid-cored sandwich structure[J]. Journal of Vibration and Shock, 2016, 35(24):45-50.
[2]. 朱凌雪, 王同银, 朱晓磊. 基于梯度化因子功能梯度点阵夹层结构优化设计[J]. 振动与冲击, 2018, 37(23):106-111+118.
Lingxue Z , Tongyin W , Xiaolei Z , et al. Optimization design of a functionally graded lattice sandwich structure based on gradient factor[J]. Journal of Vibration and Shock, 2018, 37(23):106-111+118.
[3]. 姜世杰, Siyajeu Y , 孙宁宁, 等. 振动利用对FDM薄板机械性能的影响研究[J]. 振动与冲击, 2019, 38(9):22-26.
IANG Shijie, SIYAJEU Yannick, SUN Ningning, et al. Effects of vibration application on mechanical performances of FDM sheets[J]. Journal of Vibration and Shock, 2019, 38(9):22-26.
[4]. 李修峰, 高令飞, 王伟, 等. 一种面向增材制造技术的桁架式支架结构设计方法[J]. 宇航学报, 2017, 38(7): 751-757.
Li X F, Gao L F, Wang W, et al. An Additive Manufacturing Oriented Structural Design Method for Trussed Bracket[J]. Yuhang Xuebao/journal of Astronautics, 2017, 38(7):751-757.
[5]. Gorguluarslan R M, Gandhi U N, Mandapati R, et al. Design and fabrication of periodic lattice-based cellular structures[J]. Computer-Aided Design and Applications, 2016, 13(1): 50-62.
[6]. 陈婷婷, 刘杰, 谭栋国, 等. 金字塔型空心点阵结构的隔声特性研究[J]. 振动与冲击, 2017(23):209-215.
Tingting C , Jie L , Dongguo T , et al. Sound insulation performance of pyramidal hollow lattice structures[J]. Journal of Vibration and Shock, 2017(23): 209-215.
[7]. Brackett D, Panesar A, Aremu A, et al. Adaptive mesh decomposition strategies for topology optimization for multi-functional additive manufacture[C]// World Congress on Computational Mechanics. 2014.
[8]. Chen Y. A mesh-based geometric modeling method for general structures[C]//ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2006: 269-281.
[9]. Wang Y, Jing S, Liu Y, et al. Generative design method for lattice structure with hollow struts of variable wall thickness[J]. Advances in Mechanical Engineering, 2018, 10(3): 1687814017752482.
[10]. Tang Y, Kurtz A, Zhao Y F. Bidirectional Evolutionary Structural Optimization (BESO) based design method for lattice structure to be fabricated by additive manufacturing[J]. Computer-Aided Design, 2015, 69: 91-101.
[11]. Terriault P, Brailovski V. Modeling and simulation of large, conformal, porosity-graded and lightweight lattice structures made by additive manufacturing[J]. Finite Elements in Analysis and Design, 2018, 138: 1-11.
[12]. Liu K, Tovar A. An efficient 3D topology optimization code written in Matlab[J]. Structural and Multidisciplinary Optimization, 2014, 50(6): 1175-1196.
[13]. Andreassen E, Clausen A, Schevenels M, et al. Efficient topology optimization in MATLAB using 88 lines of code[J]. Structural and Multidisciplinary Optimization, 2011, 43(1): 1-16.
[14]. 窦松然, 桂洪斌, 李承豪, 等. 圆柱壳振动控制中的约束阻尼拓扑优化研究[J]. 振动与冲击, 2015, 34(22):149-153.
Song-Ran D , Hong-Bin G , Cheng-Hao L I , et al. Topological optimization for constrained damping in vibration control of cylindrical shell[J]. Journal of Vibration and Shock, 2015, 34(22): 149-153.
[15]. Smith M, Guan Z, Cantwell W J. Finite element modelling of the compressive response of lattice structures manufactured using the selective laser melting technique[J]. International Journal of Mechanical Sciences, 2013, 67(1):28-4.
[16]. 赵建峰, 马智勇, 谢德巧, 等. 金属增材制造技术[J]. 南京航空航天大学学报, 2014, 46(5): 675-683.
Zhao J, Ma Z, Xie D, et al. Metal Additive Manufacturing Technique[J]. Journal of Nanjing University of Aeronautics & Astronautics, 2014, 46(5): 675-683.
[17]. Tang Y, Dong G, Zhou Q, et al. Lattice structure design and optimization with additive manufacturing constraints[J]. IEEE Transactions on Automation Science and Engineering, 2017 (99): 1-17.
[18]. 吕丁. 基于泡沫铝的缓冲吸能结构设计研究[D]. 2017.
[19]. 李萌, 刘荣强, 罗昌杰, et al. 铝蜂窝串联缓冲结构静态压缩仿真与试验研究[J]. 振动与冲击, 2013, 32(9):50-56.
Li M, Liu R, Luo C, et al. Numerical and experimental analyses on series aluminum honeycomb structures under quasi-static load[J]. Journal of Vibration and Shock, 2013, 32(9): 50-56.