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反四手性负泊松比蜂窝面外双曲变形研究

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针对反四手性负泊松比蜂窝面外变形快速求解问题,提出了一种利用数值拟合进行快速求解的方法.首先利用有限元分析软件对蜂窝的面外变形进行了求解,把结果数据分为训练数据及验证数据;然后使用最小二乘法对求解结果拟合,针对蜂窝面外变形的特点及量纲分析,构造了一个3参数的拟合方程,得到蜂窝对称轴上的拟合曲线.接着对求解结果及蜂窝尺寸参数进行二次拟合,得到蜂窝尺寸和变形曲线的关系,然后利用该关系对其他尺寸下蜂窝的变形曲线进行预测,并与验证数据进行对比.此后,对两段式非均匀蜂窝的面外变形也进行了仿真求解,利用均匀蜂窝的拟合结果及Logistic函数构造拟合函数进行拟合,并用拟合结果在其他尺寸下蜂窝的变形与验证数据进行对比.结果表明,拟合方程预测结果与仿真结果吻合良好.该数值方法可以运用于反四手性蜂窝变形预测与设计.
Hyperbolic Outer Plane Deformation of Anti-Tetrachiral Negative Poisson's Ratio Honeycomb
For the problem of fast solution of the anti-tetrachiral negative Poisson's ratio honeycomb out-of-face deformation,a fast solution method using numerical fitting is proposed.First,the out-of-plane deformation of the honeycomb was solved by finite element analysis software,and the result data were divided into training data and validation data.Then,the least squares method was used to fit the solution results.According to the characteristics and dimensional analysis of the out-of-plane deformation of the honeycomb,a three-parameter fitting equation was constructed.And the fitting curve on the symmetry axis of the honeycomb was obtained.Next,the fitting parameter results and the size parameters of the honeycomb were fitted again.The relationship between the size and the deformation curve of the honeycomb was obtained.Then,the deformation of the honeycomb under other sizes predicted by using this relationship was compared with the validation data.In addition,the out-of-plane deformation of the two-stage non-uniform honeycomb was also studied.The fitting function was constructed by using the fitting results of the previous uniform honeycomb and the Logistic function.And the fitting results were compared with validation data.The results show that the prediction results of the fitting equation are in good agreement with the simulation results.This numerical method can be applied to the deformation prediction and design of anti-chiral honeycomb.

Negative Poisson's ratioAnti-tetrachiralOuter plane deformationLeast squares methodNumerical fitting

杜林喆、叶长水、高飞宇、孙健、刘彦菊、冷劲松

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哈尔滨工业大学先进复合材料国家重点实验室,哈尔滨 150001

航空工业成都飞机设计研究所,成都 610073

哈尔滨工业大学航天科学与力学系,哈尔滨 150001

负泊松比 反四手性蜂窝 面外变形 最小二乘法 数值拟合

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(1)
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