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微桁架点阵结构胞元拓扑优化及其变密度设计

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设计满足特定需求的三维有序多孔的微桁架点阵结构,是解决航空航天领域某些构件轻量化问题的方法之一.首先,基于具有惩罚的实体各向同性材料(Solid isotropic microstructure with penalization,SIMP)拓扑优化算法,以最小柔度为目标,在不同载荷边界条件下进行点阵胞元的优化,随后对拓扑优化的点阵胞元进行几何重构.采用三维数值均匀化算法分析胞元在不同相对密度下的弹性矩阵及弹性模量曲面,对比 4 种胞元的各项力学性能;对选择性激光烧结(Selective laser sintering,SLS)增材制造技术制备的试件进行物理试验并对比试验结果,得到不同构型点阵结构胞元的力学性能.最后,以三点弯曲梁为例分析应力分布,并按照应力分布对梁结构进行Octet胞元的变密度点阵结构设计;同时设计均匀点阵结构作为对照,并通过三点弯曲试验对比变密度点阵结构与均匀点阵结构的力学性能.结果表明,优化并重构的4种胞元的三维数值均匀化模拟与压缩试验结果吻合良好;S Star Tet胞元的弹性模量最大,Octet胞元具有最高的剪切模量和较好的各向同性.相较于均匀点阵结构,变密度点阵结构的弯曲刚度和弯曲强度分别提高了162.6%和250.5%.
Topology Optimization and Variable Density Design of Micro-Truss Lattice Structure Cells
One of the methods to solve the lightweight problem of some components in aerospace field is to design the three-dimensional ordered porous micro-truss lattice structure to meet the specific needs.Firstly,based on the solid isotropic microstructure with penalization(SIMP)topology optimization algorithm,the lattice cells are optimized under different load boundary conditions with the goal of minimum flexibility,after which the topology optimized lattice cells are geometrically reconstructed.Then,the elastic matrix and elastic modulus surface of the cells under different relative densities are analyzed by using the three-position numerical homogenization algorithm and the mechanical properties of the four cells are compared as well.Physical experiments are conducted on the specimens manufactured by selective laser sintering(SLS)additive manufacturing technology and the experimental results are compared to obtain the mechanical properties of the lattice structure cells with different configurations.Finally,a three-point curved beam is taken as an example to analyze the stress distribution,and the variable density design for lattice structure of Octet cell of the beam is carried out according to the stress distribution.A uniform lattice structure is designed as the control to be compared with the variable density lattice structure in terms of mechanical properties through the three-point bending experiment.The results show that the homogenization simulation results of the four types of cells after optimization and reconstruction are in good agreement with the compression test results.S Star Tet cell has the largest elastic modulus,while Octet cell has the highest shear modulus and good isotropy.Compared with the uniform lattice structure,the bending stiffness and bending strength of the variable density lattice structure is increased by 162.6%and 250.5%,respectively.

Lattice structureTopology optimizationElastic modulusVariable density designLightweight design

郝博、闫志杰、汪万炯、赵玉欣

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东北大学,沈阳 110819

东北大学秦皇岛分校,秦皇岛 066004

点阵结构 拓扑优化 弹性模量 变密度设计 轻量化设计

2024

航空制造技术
北京航空制造工程研究所

航空制造技术

CSTPCD北大核心
影响因子:0.403
ISSN:1671-833X
年,卷(期):2024.67(19)