Design and mechanical analysis of a novel chiral honeycomb structure
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摘要: 当前手性蜂窝结构的研究除了关注结构本身所用材料以外，通过改变单元内部拓扑组合以提升力学性能成为绝大部分研究的重点，而大部分现有的手性蜂窝结构中都存在既会带来更大的结构刚度、同时也会增加整体结构重量的刚性大中心节点。针对现状，本文提出了一种易变形、延展性好的新型四手性细胞结构，通过能量法理论推导了梁结构力学性能的数值解，并用有限元方法进行了数值验证。通过参数分析，讨论了该结构的力学性能。结果表明：该负泊松比结构具有优异的力学表现，等效弹性模量低至10−6，且拥有最低为−5.5的大拉剪耦合系数范围。其等效弹性模量最低仅有V型梁结构的10%，等效剪切模量低于ATCS结构2个数量级；力学性能调节范围也接近于ATCS的1.5至2倍。作为一种新型手性结构，更低的等效弹性模量与范围更广的拉剪耦合系数在航空航天、船舶、医疗等领域有着巨大的应用潜力。Abstract: The current research on chiral honeycomb structures not only focuses on the materials used for the structure itself but also emphasizes improving mechanical performance by altering the internal topological arrangements of the units. Most existing chiral honeycomb structures feature rigid central nodes that increase both structural stiffness and overall weight. Addressing this situation, this paper proposed a novel tetra-chiral cell structure characterized by easy deformability and good extensibility. Theoretical deductions of beam structure mechanics using energy methods were presented, along with numerical validations using finite element analysis. Through parameter analysis, the mechanical performance of this structure was discussed. Results indicate that this structure, with a negative Poisson's ratio, demonstrates excellent mechanical properties. It exhibits an equivalent elastic modulus as low as 10−6 and a large range of shear coupling coefficients as low as −5.5. The equivalent elastic modulus is only 10% of that of a V-beam structure, and the equivalent shear modulus is lower by two orders of magnitude compared to an ATCS structure. The range of mechanical performance adjustment is also approximately 1.5 to 2 times that of the ATCS structure. As a new type of chiral structure, its lower equivalent elastic modulus and wider range of shear coupling coefficients present significant potential applications in aerospace, maritime, medical, and other fields.
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图 2 新型手性结构整体构型及单元构型受拉伸载荷的受力分析
Figure 2. Force analysis of the overall configuration and the unit cell of the novel chiral structure under tensile load
图 5 新型手性结构整体构型以及单元构型受剪切载荷的受力分析
Figure 5. Force analysis of the overall configuration and the unit cell of the novel chiral structure under shear load
图 7 新型手性蜂窝结构变形图：(a)拉伸；(b)剪切
Figure 7. Deformation diagram of the novel chiral honeycomb structure:(a) Tension; (b) Shear
图 8 不同网格尺寸下新型手性蜂窝结构等效弹性模量的有限元仿真结果
Figure 8. Finite element simulation results of the effective elastic modulus of novel chiral honeycomb structures at different mesh sizes
图 9 传统四手性蜂窝结构anti-tetra-chiral structures (ATCS)有限元模型
Figure 9. Finite element model of anti-tetra-chiral structures (ATCS)
图 11 不同参数ζ、ξ下新型手性蜂窝结构等效弹性模量的理论预测、有限元仿真结果
Figure 11. Theoretical prediction and finite element simulation results of equivalent elastic modulus of novel chiral honeycomb structures under different parameters ζ and ξ
图 12 不同参数ζ、ξ下新型手性蜂窝结构拉剪耦合系数的理论预测、有限元仿真结果
Figure 12. Theoretical predictions and finite element simulation results of the tension-shear coupling coefficient of novel chiral honeycomb structures under different parameters ζ and ξ
图 13 不同参数ζ、ξ下新型手性蜂窝结构等效剪切模量的理论预测、有限元仿真结果
Figure 13. Theoretical predictions and finite element simulation results of the equivalent shear modulus of novel chiral honeycomb structures under different parameters ζ and ξ
图 14 不同参数ζ、ξ下新型手性蜂窝结构剪拉耦合系数的理论预测、有限元仿真结果
Figure 14. Theoretical prediction and finite element simulation results of shear-tension coupling coefficient of novel chiral honeycomb structures under different parameters ζ and ξ
图 15 V型蜂窝单元(VS)(a)和anti-tetra-chiral structures (ATCS)(b)单元
Figure 15. Unit cells of the V-shaped honeycomb (VS) (a) and anti-tetra-chiral structures (ATCS)(b)
图 16 三种结构等效弹性模量的理论预测结果
Figure 16. Theoretical prediction results of equivalent elastic moduli of three structures
图 17 三种结构拉剪耦合效应的理论预测结果
Figure 17. Theoretical prediction results of tension-shear coupling effects of three structures
图 18 三种结构等效剪切模量的理论预测结果
Figure 18. Theoretical prediction results of equivalent shear moduli of three structures
图 19 三种结构剪拉耦合效应的理论预测结果
Figure 19. Theoretical prediction of shear-tension coupling effects of three structures
表 1 有限元仿真载荷与边界条件
Table 1. Load and boundary conditions used in the finite element simulation
Conditions Tensile load in the X direction Shear load Load condition $ {U_x}(A) = \dfrac{{ - {\varepsilon _x}}}{2} \times H $
$ {U_x}(B) = \dfrac{{{\varepsilon _x}}}{2} \times H $
$ {U_y}(O) = 0 $$ {U_x}(C) = \dfrac{{ - {\varepsilon _x}}}{2} \times H $
$ {U_x}(D) = \dfrac{{{\varepsilon _x}}}{2} \times H $
$ {U_y}(O) = 0 $z-direction SYMM Periodic condition $ {U_x}(C) = {U_x}(D) $
$ {U_y}(C) = {U_y}(D) $
$ {\theta _{\textit{z}}}(A) = {\theta _{\textit{z}}}(B) $
$ {\theta _{\textit{z}}}(C) = {\theta _{\textit{z}}}(D) $$ {U_y}(A) = {U_y}(B) $
$ {\theta _{\textit{z}}}(A) = {\theta _{\textit{z}}}(B) $
$ {\theta _{\textit{z}}}(C) = {\theta _{\textit{z}}}(D) $
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