基于弹性边界的多墙式盒段结构复合材料壁板屈曲分析方法

赵北; 熊斯浚; 陈亮; 王成波; 李锐

doi:10.21656/1000-0887.440283

基于弹性边界的多墙式盒段结构复合材料壁板屈曲分析方法

doi: 10.21656/1000-0887.440283

赵北^{1, 2,},
熊斯浚^{1, 3,},
陈亮^{3, 4,},
王成波^{3, 4,},
李锐^{1, 4, ,}

1.
大连理工大学工程力学系工业装备结构分析优化与CAE软件全国重点实验室，辽宁大连 116024
2.
中国航空工业集团公司成都飞机设计研究所强度部，成都 610091
3.
中国航空工业集团公司沈阳飞机设计研究所综合强度部，沈阳 110035
4.
辽宁省飞行器结构强度数字孪生重点实验室，沈阳 110035

(我刊编委李锐来稿)

基金项目:

国家自然科学基金 12372067

国家自然科学基金 12022209

详细信息

作者简介:
赵北(1998—)，男，助理工程师(E-mail: zhaobei1998@163.com)

熊斯浚(1994—)，男，工程师(E-mail: xiongsijun@mail.dlut.edu.cn)

陈亮(1977—)，男，研究员(E-mail: liangchen110035@163.com)

王成波(1977—)，男，正高级工程师(E-mail: chengbowang110035@163.com)

通讯作者:
李锐(1985—)，男，教授，博士，博士生导师(通讯作者. E-mail: ruili@dlut.edu.cn)

中图分类号: O343.9
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- 文章访问数: 87
- HTML全文浏览量: 24
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- 被引次数: 0
出版历程
- 收稿日期: 2023-09-20
- 修回日期: 2024-05-27
- 刊出日期: 2024-09-01

A Buckling Analysis Method for Composite Panels in Multiweb Box Structures Based on Elastic Boundaries

ZHAO Bei^{1, 2
,},
XIONG Sijun^{1, 3
,},
CHEN Liang^{3, 4
,},
WANG Chengbo^{3, 4
,},
LI Rui^{1, 4
, ,}

1.
State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China
2.
Department of Strength, AVIC Chengdu Aircraft Design and Research Institute, Chengdu 610091, P.R.China
3.
Department of Strength, AVIC Shenyang Aircraft Design and Research Institute, Shenyang 110035, P.R.China
4.
Key Laboratory of Digital Twin for Aircraft Structural Strength, Liaoning Province, Shenyang 110035, P.R.China

(Contributed by LI Rui, M.AMM Editorial Board)

摘要

摘要: 机翼中的多墙式盒段结构是飞机结构设计的重点关注区域之一. 盒段结构主要由蒙皮以及支撑件组合而成，其中蒙皮被支撑件近似分隔为多个矩形壁板. 在飞机服役过程中，机翼主要承受弯曲、扭转或者弯扭耦合载荷等作用，导致盒段结构中矩形壁板容易产生失稳. 在传统复合材料壁板屈曲分析中，往往将边界简化为固支或简支，所得结果与试验差距较大，而采用有限元方法进行全面模拟往往效率较低. 针对上述问题，该文提出了一种结合单胞模型以及微分求积法的复合材料壁板快速屈曲分析方法. 首先，建立了单胞模型计算矩形壁板的弹性边界刚度系数；然后，通过微分求积法求解控制方程，获得了壁板的屈曲载荷；最后，计算了不同类型盒段结构中复合材料壁板的屈曲载荷，并与有限元结果进行对比，验证了该文屈曲分析方法的准确性.
- 复合材料壁板 /
- 弹性边界 /
- 屈曲 /
- 微分求积法
Abstract: The multiweb box structures in the wings are paid special attention in aircrafts' structural design. The multiweb box is mainly composed of skins and stiffeners. The skins are approximately divided into many rectangular panels by stiffeners. During the service of an aircraft, the wing majorly bears bending, torsion, and bending-torsion coupling loads, etc., so the panels in box structures are susceptible to instability. In traditional buckling analysis of composite panels, the boundary conditions were typically simplified as either clamped or simply supported boundaries, with significant deviations from experimental results. On the other hand, comprehensive simulations with the finite element method are generally inefficient. Aimed at the above issues, a rapid buckling analysis method combining the unit cell model with the differential quadrature method for composite panels was proposed. Firstly, the unit cell model was established to calculate the stiffness coefficients of elastic boundaries of rectangular panels. The governing equations were then solved with the differential quadrature method to obtain the buckling loads on the panels. Finally, the buckling loads on composite panels in different types of box structures were calculated and compared to the results obtained with the finite element method to verify the accuracy of the presented buckling analysis method.
- composite panel /
- elastic boundary /
- buckling /
- differential quadrature method
edited-by

edited-by
注释:

1) (我刊编委李锐来稿)

HTML全文

图 1 微分求积法的收敛性分析

Figure 1. Convergence study of the differential quadrature method

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图 2 弹性边界示意图

Figure 2. Schematic of elastic boundaries

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图 3 复合材料层合板屈曲载荷与边界条件的关系

Figure 3. Buckling loads on composite laminates vs. the boundary conditions

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图 4 单胞模型

Figure 4. The unit cell model

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图 5 边界与弯矩载荷

Figure 5. Boundaries and bending moment loads

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图 6 层合板各单层z坐标

Figure 6. Z-coordinates of each layer of the laminate

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图 7 基于弹性边界的多墙式盒段结构复合材料壁板屈曲分析流程

Figure 7. Process of buckling analysis on composite panels for multiweb box structures based on elastic boundaries

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图 8 1号盒段模型

Figure 8. Box model 1

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图 9 1号盒段模型

Figure 9. Box model 1

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图 10 求解矩形壁板弹性边界刚度系数的单胞模型

Figure 10. The unit cell model for calculating the stiffness coefficients of elastic boundaries of the rectangular panel

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图 11 2号盒段模型

Figure 11. Box model 2

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图 12 3号盒段模型

Figure 12. Box model 3

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图 13 4号盒段模型

Figure 13. Box model 4

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图 14 弯剪工况下四种类型盒段结构复合材料壁板在不同边界条件下的屈曲载荷

Figure 14. Buckling loads on composite panels in 4 types of box structures with different boundary conditions under bending and shearing

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图 15 单轴压工况

Figure 15. The uniaxial compression condition

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图 16 单轴压工况下四种盒段结构复合材料壁板在不同边界条件下的屈曲载荷

Figure 16. Buckling loads on composite panels in 4 box structures with different boundary conditions under uniaxial compression

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表 1 常用节点分布公式

Table 1. Commonly used formulas of node distribution

number	formula
1	$x_i=2 \frac{i-1}{N}-1, x_1=-1, x_{N+1}=1$
2	$x_i=\frac{1}{2}-\frac{1}{2} \cos \left[\frac{(i-1) \pi}{N}\right]$
3	$x_i=\frac{1}{2}+\frac{1}{2} \cos \left[\frac{(N+1-i) \pi}{N}\right]$
4	$x_i=\cos \left[\frac{(N+1-i) \pi}{N}\right]$
5	$x_i=-\frac{1}{2} \cos \left[\frac{(i-1) \pi}{N}\right]$

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表 2 正交各向异性单层板无量纲屈曲载荷N_cr的收敛性分析

Table 2. Dimensionless buckling loads on the orthotropic single-layer plate

N	dimensionless buckling load N_cr
N	clamped boundary	simply supported boundary
5	11.175	4.479 2
6	12.321	4.498 9
7	12.428	4.500 0
8	12.487	4.500 0
9	12.403	4.500 0
10	12.448	4.500 0
20	12.449	4.500 0
50	12.449	4.500 0

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表 3 弹性边界下正交各向异性单层板的无量纲屈曲载荷N_cr

Table 3. Dimensionless buckling loads N_cr on the orthotropic single-layer plate under elastic boundaries

η	R	ref. [27]	present
0.5	0.1	6.436 1	6.436 1
	0.3	7.537 4	7.537 4
	0.5	9.073 5	9.073 5
	0.7	11.147	11.147
1	0.1	4.827 1	4.827 1
	0.3	5.654 8	5.654 8
	0.5	6.820 4	6.820 4
	0.7	8.511 6	8.511 6
2	0.1	3.218 1	3.218 1
	0.3	3.769 9	3.769 9
	0.5	4.548 4	4.548 4
	0.7	5.688 3	5.688 3

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表 4 T300/976的材料参数

Table 4. Material parameters of T300/976

material parameter	E₁₁/MPa	E₂₂/MPa	G₁₂/MPa	G₁₃/MPa	G₂₃/MPa	υ₁₂
value	156 500	13 000	6 960	6 960	3 450	0.23

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表 5 单轴压工况下复合材料层合板的无量纲屈曲载荷N_cr

Table 5. Dimensionless buckling loads N_cr on composite laminates under uniaxial compression

R	N_cr		error ε/%
R	FEM	present	error ε/%
0.000 01	22.110	22.288	0.80
0.1	22.802	22.987	0.81
0.2	23.599	23.792	0.82
0.3	24.530	24.729	0.81
0.4	25.632	25.836	0.79
0.5	26.964	27.170	0.76
0.6	28.616	28.821	0.72
0.7	30.756	30.959	0.66
0.8	33.743	33.945	0.60
0.9	38.428	38.645	0.56
0.999 99	47.122	47.422	0.64

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表 6 双轴压工况下复合材料层合板的无量纲屈曲载荷N_cr

Table 6. Dimensionless buckling loads N_cr on composite laminates under biaxial compression

R	N_cr		error ε/%
R	FEM	present	error ε/%
0.000 01	9.942 7	9.970 2	0.28
0.1	10.457	10.491	0.33
0.2	11.071	11.113	0.38
0.3	11.816	11.867	0.43
0.4	12.650	12.744	0.74
0.5	13.642	13.743	0.74
0.6	14.932	15.039	0.71
0.7	16.690	16.804	0.68
0.8	19.259	19.380	0.63
0.9	23.406	23.532	0.54
0.999 99	30.298	30.423	0.41

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表 7 不同边界下复合材料层合板的屈曲载荷

Table 7. Buckling loads on composite laminates under different boundary conditions

simply supported boundary N_cr/N	clamped boundary N_cr/N	elastic boundary N_cr/N
simply supported boundary N_cr/N	clamped boundary N_cr/N	R=0.3	R=0.4	R=0.5	R=0.6	R=0.7
61.42	130.68	71.96	76.88	82.85	89.91	96.12

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表 8 不同边界下模型1壁板的屈曲载荷

Table 8. Buckling loads on the panel in box model 1 under different boundary conditions

	FEM	boundary conditions
	FEM	simply supported boundary	clamped boundary	elastic boundary
the buckling load N_cr/N	8 763	3 261	11 776	8 723
error ε/%	-	-62.79	34.38	-0.46

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表 9 不同边界下模型2壁板的屈曲载荷

Table 9. Buckling loads on the panel in box model 2 under different boundary conditions

	FEM	boundary conditions
	FEM	simply supported boundary	clamped boundary	elastic boundary
the buckling load N_cr/N	3 854	1 975	4 685	3 950
error ε/%	-	-48.75	21.55	2.50

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表 10 不同边界下模型3壁板的屈曲载荷

Table 10. Buckling loads on the panel in box model 3 under different boundary conditions

	FEM	boundary condition
	FEM	simply supported boundary	clamped boundary	elastic boundary
the buckling load N_cr/N	1 477	740	1 724	1 492
error ε/%	-	-49.87	16.70	1.03

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表 11 不同边界下模型4壁板的屈曲载荷

Table 11. Buckling loads on the panel in box model 4 under different boundary conditions

	FEM	boundary condition
	FEM	simply supported boundary	clamped boundary	elastic boundary
the buckling load N_cr/N	2 663	1 160	3 203	2 764
error ε/%	-	-56.43	20.28	3.82

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表 12 单轴压工况下四种盒段模型中矩形壁板在不同边界下的屈曲载荷

Table 12. Buckling loads on rectangular panels in 4 box models with different boundary conditions under uniaxial compression

box models	FEM N_cr/N	elastic boundary N_cr/N	error ε/%	simply supported boundary N_cr/N	error ε/%	clamped boundary N_cr/N	error ε/%
model 1	55 545	51 690	-6.94	21 166	-61.89	67 471	21.47
model 2	36 460	35 986	-1.30	17 994	-50.65	42 783	17.34
model 3	24 664	24 396	-1.09	12 929	-47.58	27 861	12.96
model 4	64 470	69 312	7.51	34 543	-46.42	81 996	27.18

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