新型星形负泊松比抗冲击结构设计与入水冲击

doi:10.12382/bgxb.2022.1212

摘要/Abstract

摘要：

针对跨介质飞行器入水过程中受到较大冲击载荷的问题,提出一种基于工程需求的负泊松比抗冲击结构拓扑优化设计方法,通过将弹性模量和泊松比引入拓扑优化设计的目标函数,得到满足抗冲击性能需求的负泊松比星形-四边形蜂窝(Star-quadrangular Honeycomb,SQH)结构。在建立SQH结构理论分析模型的基础上,推导冲击载荷下的平台应力解析公式,并通过数值模拟仿真进行校验。通过与星形-圆环蜂窝(Star-circle Honeycomb,SCH)等多种负泊松比结构的比吸能进行对比,得到SQH结构在低速、中速、高速冲击下的比吸能分别高于SCH结构28.74%、45.2%、7.03%。通过流固耦合仿真分析,对所设计的SQH夹层结构进行入水冲击降载研究,进一步讨论SQH夹层结构主要尺寸参数对入水冲击特性的影响。研究结果表明,在尺寸允许范围内,SQH单元倾角和单元壁厚的增大均使得结构产生的加速度峰值减小,动能转化为结构的变形能也减小,验证了用于工程需求的负泊松比结构拓扑优化设计的有效性。

关键词: 跨介质飞行器, 负泊松比, 拓扑优化, 冲击吸能, 平台应力

Abstract:

To solve the problem that the trans-media flight vehicle will be subjected to large impact load in the process of entering water, a topology optimization design method for anti-impact structure with of negative Poisson’s ratio based on engineering requirements is proposed. A star-quadrangular honeycomb (SQH) structure with negative Poisson’s ratio which meets the requirements of impact resistance is obtained by adding the elastic modulus and Poisson’s ratio into the objective function of topology optimization design. Based on the theoretical analysis model of SQH structure, the analytical formula of plateau stress under impact load is deduced and verified by numerical simulation. Compared with the specific energy absorption of star-circle honeycomb (SCH) and other negative Poisson’s ratio structures, the specific energy absorptions of SQH structure under low-speed, medium-speed and high-speed impact are 28.74%, 45.2% and 7.03% higher than that of SCH structure, respectively. Through the fluid-solid coupling simulation analysis, the designed SQH sandwich structure is studied for load reduction by water- entry impact, and the influence of the main size parameters of SQH sandwich structure on the impact characteristics of water entry is further discussed. The results show that, within the allowable range of size, the increase in the inclination angle and wall thickness of SQH unit will reduce the peak acceleration of the structure and the transformation of kinetic energy into the deformation energy of the structure, which verifies the effectiveness of the negative Poisson’s ratio structure topology optimization design for engineering requirements.

Key words: trans-media flight vehicle, negative Poisson’s ratio, topology optimization, energy absorption, plateau stress

中图分类号:

TJ630.3

金泽华, 刘清洋, 马文朝, 孟军辉. 新型星形负泊松比抗冲击结构设计与入水冲击[J]. 兵工学报, 2024, 45(5): 1497-1513.

JIN Zehua, LIU Qingyang, MA Wenchao, MENG Junhu. Design of Anti-impact Structure with Novel Star-shaped Negative Poisson’s Ratio and Research on Water-entry Impact[J]. Acta Armamentarii, 2024, 45(5): 1497-1513.

图/表 29

图1 负泊松比蜂窝结构面内冲击应力-应变曲线

Fig.1 In-plane impact stress-strain curve of honeycomb structure with negative Poisson’s ratio

图2 负泊松比抗冲击结构拓扑优化

Fig.2 Topology optimization of anti-impact structures with negative Poisson ratio

图3 SQH结构示意图

Fig.3 Schematic diagram of SQH structure

图4 低速冲击下SQH代表单元模式

Fig.4 Collapse mode of SQH cell under low-velocity impact

图5 高速冲击下SQH代表单元压溃模式

Fig.5 Collapse mode of SQH cell under high-velocity impact

图6 SQH结构有限元模型

Fig.6 SQH structure finite element model

表1 铝合金基体材料参数

Table 1 Aluminum alloy matrix material parameters

参数	数值
杨氏模量/GPa	68.2
密度/(kg·m^-3)	2700
屈服应力/MPa	80
泊松比	0.3

图7 SSH验证模型和参考模型的应力-应变曲线对比

Fig.7 Comparison of stress-strain curves of SSH verification and reference models

图8 不同冲击速度下SQH结构变形模式

Fig.8 Deformation modes of SQH structure at different impact velocities

图9 SQH结构在不同冲击速度下的应力-应变曲线

Fig.9 Stress-strain curves of SQH structure at different impact velocities

表2 SQH结构在不同冲击速度下的平台应力

Table 2 Plateau stresses of SQH structure at different impact velocities

冲击速度/ (m·s^-1)	平台应力/MPa		相对误差/%
冲击速度/ (m·s^-1)	理论计算	数值模拟	相对误差/%
1	1.472	1.548	-4.91
5	1.786	1.879	-4.95
70	5.017	5.255	-4.53
80	6.142	6.451	-4.79

图10 SQH结构在不同冲击速度下比吸能-应变曲线

Fig.10 SEA-strain curves of SQH structure at different impact velocities

表3 SQH结构与SCH结构比吸能的比较

Table 3 Comparison of SEAs of SQH structure and SCH structure

冲击速度/ (m·s^-1)	冲击比吸能
冲击速度/ (m·s^-1)	U_M-SQH/ (kJ·kg^-1)	U_M-SCH/ (kJ·kg^-1)	(U_M-SQH-U_M-SCH)/ U_M-SCH/%
1	1.904	1.479	28.74
30	5.666	3.907	45.02
100	12.551	11.727	7.03

表4 SQH与其他负泊松比结构比吸能的比较

Table 4 Comparison of SEAs of SQH structure and other structures with negative Poisson’s ratio

冲击比吸能	U_M-SQH/ (kJ·kg^-1)	U_M-SSH/ (kJ·kg^-1)	U_M-SAH/ (kJ·kg^-1)	U_M-STH/ (kJ·kg^-1)	U_M-RSH/ (kJ·kg^-1)	U_M-SH/ (kJ·kg^-1)	U_M-RH/ (kJ·kg^-1)
低速/(1m·s^-1)	1.904	0.682	0.584	1.104	0.427	0.526	0.233
中速/(30m·s^-1)	5.666	1.508	0.612	1.619	0.560	0.831	0.334
高速/(100m·s^-1)	12.551	10.914	1.690	10.821	4.349	10.146	2.642

表5 空气与水的材料参数

Table 5 Material parameters of air and water

材料	ρ/(kg·m^-3)	动力黏度μ/(Pa·s)
空气	1.29	1.79×10^-5
水	10³	1.01×10^-3

表6 SQH夹层结构单胞尺寸

Table 6 SQH sandwich structure unit cell size

参数	数值
l₁/mm	2.6
l₂/mm	2.0
l₃/mm	3.1
l₄/mm	3.2
t/mm	0.3
α/(°)	45
θ₁/(°)	20
θ₂/(°)	22.5
L₀/mm	9.7
H₀/mm	9.7

图11 SQH夹层结构模型

Fig.11 SQH sandwich structure model

图12 不同网格尺寸下蜂窝结构入水加速度变化曲线

Fig.12 Variation curves of water entry acceleration of honeycomb structure in the case of different grid sizes

图13 蜂窝验证模型和参考模型的上下面板位移对比

Fig.13 Comparison of displacements of upper and lower panels of honeycomb verification model and reference model

图14 SQH夹层结构有限元模型计算域及其网格划分

Fig.14 Computational domain and mesh genertion of finite element model of SQH sandwich structure

图15 SQH夹层结构各入水时刻下应力云图

Fig.15 Stress nephogram of SQH sandwich structure at each water entry time

图16 SQH夹层结构入水冲击特性

Fig.16 Water-entry impact characteristics of SQH structure

图17 SQH夹层结构上下面板变形图

Fig.17 Deformation diagram of upper and lower panels of SQH sandwich structure

图18 不同倾角的SQH夹层结构加速度-时间曲线

Fig.18 Acceleration-time curves of SQH sandwich structures with different concave angles

图19 不同倾角的SQH夹层结构动能-时间曲线

Fig.19 Kinetic energy-time curves of SQH sandwich structures with different concave angles

图20 不同倾角的SQH夹层结构上下面板位移曲线

Fig.20 Displacement curves of upper and lower panels of SQH structure with different concave angles

图21 不同壁厚的SQH夹层结构加速度-时间曲线

Fig.21 Acceleration-time curves of SQH sandwich structures with different wall thicknesses

图22 不同壁厚的SQH夹层结构动能-时间曲线

Fig.22 Kinetic energy-time curves of SQH sandwich structures with different wall thicknesses

图23 不同壁厚的SQH夹层结构上下面板位移曲线

Fig.23 Displacement curves of upper and lower panels of SQH structures with different wall thicknesses

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