In-plane tensile property of deformable honeycomb structure with compliant hinge
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摘要: 提出了一种柔性铰可变形蜂窝结构，该结构由十字形蜂窝和内LET半铰(Half Inside Lamina Emergent Torsional Joint)组成，通过降低结构面内刚度提升变形能力，具有重量轻、面内模量低的特点。通过理论分析研究了柔性铰可变形蜂窝结构的面内等效弹性模量，并进行了仿真和实验验证，分析了几何参数对结构等效弹性模量的影响，最后通过仿真和实验比较了柔性铰可变形蜂窝与十字形蜂窝的面内刚度。结果表明：柔性铰可变形蜂窝的等效弹性模量与十字形蜂窝相比降低了80%以上，具有更优秀的面内变形能力，将可变形蜂窝结构与柔性铰链巧妙结合是一种提升蜂窝结构面内变形能力的有效方式。Abstract: A deformable honeycomb structure with compliant hinge which is composed of the cross-shaped honeycomb and the half inside Lamina Emergent Torsional joint was proposed. By reducing the in-plane stiffness, the deformation ability of the structure is improved, and it has the characteristics of light weight and low in-plane modulus. The in-plane equivalent elastic modulus of the deformable honeycomb structure was studied by theoretical analysis, and simulation and experimental verification were carried out. The influence of geometric parameters on the equivalent elastic modulus of the structure was also analyzed. The in-plane deformation ability of the deformable honeycomb with compliant hinge and the cross-shaped honeycomb were compared through simulation and experiment. The results show that the deformable honeycomb structure with compliant hinge has better in-plane deformable ability. Compared with cross-shaped honeycomb, the equivalent elastic modulus of deformable honeycomb with compliant hinge is reduced by more than 80%. Thus, the combination of compliant hinge and deformable honeycomb structure is an effective way to improve the in-plane deformation ability of honeycomb structure.
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图 1 柔性铰可变形蜂窝几何模型
Figure 1. Geometry model of the deformable honeycomb with compliant hinge
图 2 柔性铰可变形蜂窝单元的几何参数
Figure 2. Geometric parameters of deformable honeycomb with compliant hinge unit cell
l1—Length of the inclined beam; t1—Thickness of the inclined beam; l2—Length of the vertical beam; t2 —Thickness of the vertical beam; θ—Honeycomb angle; d1—Width of connecting element in the inclined beam; h1 —Length of connecting element in the inclined beam; d2—Width of the connecting element in the vertical beam; h2—Length of the connecting element in the vertical beam; d3—Width of torsional hinge
图 3 在x方向加载时柔性铰可变形蜂窝受力分析
Figure 3. Force analysis of deformable honeycomb with compliant hinge loaded in x direction
σx—Equivalent stress along the x-direction; F—Tensile load along the x-direction; M—Bending moment of the cross section; δ—Deflection of the inclined beam; α—Rotation angle of the inclined beam; u—Deflection of the vertical beam
图 4 内LET半铰伪刚体模型
Figure 4. Pseudo-rigid-body model of half inside Lamina Emergent Torsional (LET) joint
kB1 and kB2—Spring constant of connecting elements in the inclined beam and vertical beam, respectively; kT—Spring constant of torsional hinge
图 5 柔性铰可变形蜂窝结构的有限元模型
Figure 5. Finite element model of deformable honeycomb structure with compliant hinge
图 6 不同d1值下柔性铰可变形蜂窝结构等效弹性模量E*随h1的变化规律
Figure 6. Variation law of equivalent elastic modulus E* of the deformable honeycomb structure with compliant hinge with h1 for different d1 values
图 7 不同d3值下柔性铰可变形蜂窝结构等效弹性模量E*随h1的变化规律
Figure 7. Variation law of equivalent elastic modulus E* of the deformable honeycomb structure with compliant hinge with h1 for different d3 values
图 8 不同h2值下柔性铰可变形蜂窝结构等效弹性模量E*随h1的变化规律
Figure 8. Variation law of equivalent elastic modulus E* of the deformable honeycomb structure with compliant hinge with h1 for different h2 values
图 9 不同d2值下柔性铰可变形蜂窝结构等效弹性模量E*随h1的变化规律
Figure 9. Variation law of equivalent elastic modulus E* of the deformable honeycomb structure with compliant hinge with h1 for different d2 values
图 10 柔性铰可变形蜂窝结构实验件模型和单轴拉伸实验
Figure 10. Test specimen model and uniaxial tensile experiment for the deformable honeycomb structure with compliant hinge
图 11 4×8构型的柔性铰可变形蜂窝和十字形蜂窝结构模型
Figure 11. Deformable honeycomb with compliant hinge and the cruciform honeycomb structure models with 4×8 configuration
图 13 十字形蜂窝结构实验件模型和单轴拉伸实验
Figure 13. Test specimen model and uniaxial tensile experiment for the cruciform honeycomb structure
图 14 柔性铰可变形蜂窝和十字形蜂窝的应力-应变关系
Figure 14. Stress-strain relationship of deformable honeycomb with compliant hinge and cruciform honeycomb
L, W and H—Length of the test specimen in the x, y, z direction, respectively; $ \Delta $—Deformation in the x direction
表 1 柔性铰可变形蜂窝结构等效弹性模量E*理论与仿真值的比较
Table 1. Comparison between the theoretical and FEM results of equivalent elastic modulus E*of the deformable honeycomb structure with compliant hinge
Number Parameter of the unit/mm E*/MPa(Theoretical value) E*/MPa(FEM value) Error/% 1 d1=2, d2=2, d3=1h1=7, h2=1 6.20×10−3 6.13×10−3 1.13 2 d1=4, d2=2, d3=1h1=7, h2=1 5.90×10−3 5.83×10−3 1.19 3 d1=6, d2=2, d3=1h1=7, h2=1 5.60×10−3 5.56×10−3 0.71 4 d1=10, d2=2, d3=1h1=4, h2=1 3.90×10−3 3.79×10−3 2.82 5 d1=10, d2=2, d3=1.5h1=4, h2=1 4.80×10−3 4.72×10−3 1.67 6 d1=10, d2=2, d3=2h1=4, h2=1 5.40×10−3 5.49×10−3 1.67 7 d1=10, d2=2, d3=1h1=3, h2=2 3.80×10−3 3.74×10−3 1.58 8 d1=10, d2=2, d3=1h1=3, h2=3 4.10×10−3 4.12×10−3 0.49 9 d1=10, d2=2, d3=1h1=3, h2=4 4.40×10−3 4.49×10−3 2.05 10 d1=10, d2=0.75, d3=1h1=6, h2=1 5.20×10−3 5.05×10−3 2.88 11 d1=10, d2=1.5, d3=1h1=6, h2=1 4.90×10−3 4.87×10−3 0.61 12 d1=10, d2=2.25, d3=1h1=6, h2=1 4.60×10−3 4.75×10−3 3.26 
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表 2 柔性铰可变形蜂窝和十字形蜂窝的结构参数
Table 2. Parameters of the deformable honeycomb with compliant hinge and the cruciform honeycomb
Number Configuration Parameter of the honeycomb unit/mm Parameter of the compliant hinge/mm Parameter of the model/mm 1 4×8 l1= l2=10, t1= t2=0.25, b=25, θ=13° d1=10, d2=2, d3=1h1=12, h2=1 312×186×25 2 5×10 l1= l2=5, t1= t2=0.1, b=10, θ=13° d1=5, d2=1, d3=0.5h1=5, h2=0.5 195×118×10 3 6×8 l1= l2=20, t1= t2=1, b=40, θ=13° d1=20, d2=4, d3=3h1=20, h2=2 624×568×40
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表 3 柔性铰可变形蜂窝结构和十字形蜂窝结构的面内拉伸等效弹性模量E*
Table 3. Equivalent elastic modulus E*of the deformable honeycomb structure with compliant hinge and the cruciform honeycomb
Number Configuration E*/MPa (The deformable honeycomb
with compliant hinge)E*/MPa(The cruciform honeycomb) Difference value/% 1 4×8 0.0064 0.0595 89.2 2 5×10 0.0054 0.0305 82.3 3 6×8 0.0725 0.4515 83.9
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