Optimization technology for composite flexible skin based on negative Poisson's ratio honeycomb
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摘要: 针对由负泊松比蜂窝夹芯和弹性表皮构成的复合式柔性蒙皮,提出了柔性蒙皮几何参数优化方法。首先,将柔性蒙皮的胞壁长度、胞壁夹角、蜂窝高度、胞壁厚度、表皮厚度等几何参数作为变量,设计了柔性蒙皮结构参数化建模方法;其次,通过均实验设计方法获取样本点,利用参数化方法构建柔性蒙皮结构有限元模型,并通过仿真获取各几何参数组合状态对应的结构性能;然后,基于响应面方法构造柔性蒙皮几何参数与结构性能关系的近似模型,并对近似模型的精度进行了定量评估;最后,以近似模型为基础,以柔性蒙皮几何参数为优化变量,综合考虑面内应变、泊松比、面外挠度、质量等因素,采用加权系数法构造了综合优化目标函数,并采用遗传算法进行优化,得到了柔性蒙皮结构综合性能最优的构型。构建了复合式柔性蒙皮有限元模型,进行优化方法验证,结果显示,优化后的构型与初始构型相比,面内变形能力提升30.73%,面外承载能力提高30%,结构质量减轻22.77%,泊松比降低20.73%。Abstract: The geometric parameter optimization method of flexible skin composed of negative Poisson's ratio honeycomb core and elastic skin was proposed. Firstly, a parameterized modeling method for the flexible skin structure was designed, with geometric parameters such as cell wall length, cell wall Angle, honeycomb height, cell wall thickness and skin thickness. Secondly, the sample points were obtained by uniform experimental design method, the finite element models of flexible skin structure were constructed using the parameterized method, and the structural performance corresponding to various combinations of geometric parameters was obtained through simulation. Then, an approximate model for the relationship between the geometric parameters of the flexible skin and the structural performance was constructed using the response surface method, and the accuracy of the approximate model was quantitatively evaluated. Finally, based on the approximate model, taking the geometric parameters of the flexible skin as optimization variables, and considering the factors such as internal strain, Poisson's ratio, out-of-plane deflection, and mass, a comprehensive optimization objective function was constructed using the weighted coefficient method, and the optimal configuration of the flexible skin structure was obtained by genetic algorithm. A finite element model of the composite flexible skin was constructed to validate the optimization. The results show that compared with the initial configuration, the in-plane deformation capacity is increased by 30.73%, the out-of-plane load capacity is increased by 30%, the structural mass is reduced by 22.77%, and the Poisson’s ratio is reduced by 20.73%.
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表 1 聚二甲基硅氧烷(PDMS)-Nylon6复合材料力学性能
Table 1. Mechanical properties of Polydimethylsiloxane (PDMS)-Nylon6 composite materials
Material Elastic modulus/
MPaPoisson's ratio Density/
($kg \cdot m{m^{ - 3}}$)Nylon6 1.06 0.35 $1.14 \times {10^{ - 6}}$ PDMS 1.8 0.49 $2.33 \times {10^{ - 6}}$ 表 2 PDMS-Nylon6复合材料柔性蒙皮模型边界条件
Table 2. Boundary conditions of the PDMS-Nylon6 composite flexible skin model
Boundary Boundary of in-plane
load conditionsBoundary of out-plane load conditions A ${u_x} = {u_y} = {u_{\textit{z}}} = 0$
${\gamma _x} = {\gamma _y} = {\gamma _z} = 0$${u_x} = {u_y} = {u_{\textit{z}}} = 0$
${\gamma _x} = {\gamma _y} = {\gamma _{\textit{z}}} = 0$B ${F_x}$
${\gamma _x} = {\gamma _y} = {\gamma _{\textit{z}}} = 0$${u_x} = {u_y} = {u_{\textit{z}}} = 0$
${\gamma _x} = {\gamma _y} = {\gamma _{\textit{z}}} = 0$C Free Free D Free Free E Free Free F Free ${P_{\text{n}}} = 0.001{\text{MPa}}$ 表 3 PDMS-Nylon6复合材料柔性蒙皮均匀实验设计
Table 3. Uniform experimental design for PDMS-Nylon6 composite flexible skin
Parameters Levels 1 2 3 4 5 ${L_1}$/mm 4.5 4.75 5 5.25 5.5 ${L_2}$/ mm 6.75 7.125 7.5 7.875 8.25 $\theta $ /(°) 31.5 33.25 35 36.75 38.5 H /mm 1.8 1.9 2 2.1 2.2 t /mm 0.45 0.475 0.5 0.525 0.55 ${t_{\text{f}}}$/ mm 0.9 0.95 1 1.05 1.1 F / N 450 475 500 525 550 Notes: F is the external load. 表 4 PDMS-Nylon6复合材料柔性蒙皮近似模型的评估
Table 4. Evaluation of the approximated model for PDMS-Nylon6 composite flexible skin
${\varepsilon _x}$ μ ω G R 0.9996 0.9999 0.9999 1.0 $\bar e$ 0.99% 0.32% 0.83% 0.05% ${\sigma _e}$ 1.20% 0.24% 0.67% 0.06% Notes: ${\varepsilon _x}$ is the in-plane tensile strain; μ is the Poisson’s ratio; ω is the out-of-plane deflection; G is the structural mass; R is the correlation coefficient; $\bar e$ is the mean of the relative error; ${\sigma _e}$ is the standard deviation of the relative error. 表 5 优化前后PDMS-Nylon6复合材料柔性蒙皮的几何参数对比
Table 5. Comparison of geometric parameters of PDMS-Nylon6 composite flexible skin before and after optimization
Variable Initial value Optimized value ${L_1}$/mm 5 4.5 ${L_2}$/ mm 7.5 7.3164 $\theta $ /(°) 35 38.5 H /mm 2 2.2 t /mm 0.65 0.45 ${t_{\text{f}}}$/ mm 1 0.9 表 6 优化前后PDMS-Nylon6复合材料柔性蒙皮的性能对比
Table 6. Comparison of PDMS-Nylon6 composite flexible skin performance before and after optimization
Variable Initial value Optimized value Percent change ${\varepsilon _x}$ 23.92% 31.27% 30.73% $\mu $ 1.3886 1.1008 -20.73% $\omega $ 1.6% 1.12% -30% G 0.0584 0.0451 -22.77% F(x) 0.3522 0.0740 -78.99% -
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