复合材料加筋壁板轴压屈曲载荷工程估算新方法

张驰; 郑锡涛; 张东健; 刘建平

doi:10.13801/j.cnki.fhclxb.20240402.003

复合材料加筋壁板轴压屈曲载荷工程估算新方法

doi: 10.13801/j.cnki.fhclxb.20240402.003

张驰^{1, 2},
郑锡涛^{2, 3, ,},
张东健^{2, 3},
刘建平⁴

1.
西北工业大学国家卓越工程师学院，西安 710072
2.
西北工业大学航空学院，西安 710072
3.
西北工业大学飞行器复合材料结构研究所，西安 710072
4.
陕西飞机工业有限责任公司，汉中 723000

详细信息

通讯作者:
郑锡涛，博士后，教授，博士生导师，研究方向为复合材料力学行为的宏细观分析、损伤演化与失效分析，三维编织复合材料力学行为的数值仿真与试验验证技术，飞机复合材料结构损伤容限设计与分析　E-mail: zhengxt@nwpu.edu.cn

中图分类号: TB332
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出版历程
- 收稿日期: 2024-01-05
- 修回日期: 2024-02-21
- 录用日期: 2024-03-03
- 网络出版日期: 2024-04-03
- 刊出日期: 2024-09-15

A new engineering method for predicting the axial compression buckling load of composite stiffened panels

ZHANG Chi^{1, 2},
ZHENG Xitao^{2, 3
, ,},
ZHANG Dongjian^{2, 3},
LIU Jianping⁴

1.
School of National Institute of Excellent Engineers, Northwestern Polytechnical University, Xi'an 710072, China
2.
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China
3.
Institute of Aircraft Composite Structrues, Northwestern Polytechnical University, Xi'an 710072, China
4.
Shaanxi Aircraft Industry CO., LTD., AVIC, Hanzhong 723000, China

摘要

摘要: 加筋壁板是飞机机翼、尾翼和机身结构上普遍采用的典型结构形式，当机翼、尾翼结构受气动载荷作用时，机翼上翼面加筋壁板处于受压状态，受压壁板易发生屈曲甚至破坏。本文基于前期复合材料加筋壁板轴压稳定性工程算法研究，并借鉴已在工程上成熟应用的金属加筋壁板轴压稳定性工程方法，提出了一种能够合理预测复合材料加筋壁板轴压屈曲载荷的工程算法。通过选取2类加强筋形式，其中3种Y型及2种J型，共5种复合材料加筋壁板为算例，对5种复合材料加筋壁板的轴压屈曲载荷进行了计算，并开展了有限元数值模拟与试验验证。此工程算法的计算结果与试验值对比，相对误差均在10%以内。与有限元计算结果对比，除一种Y型长桁加筋壁板计算结果在10%，其余构型相对误差均在5%，满足工程要求，证明此种方法的有效性，此种工程算法已经在型号飞机研制中得以应用。此外，发现对加筋壁板长桁缘条的削弱会降低复合材料加筋壁板的屈曲载荷，而Y型加筋壁板削弱中间两长桁，可以使长桁与蒙皮刚度更加匹配，提升Y型长桁加筋壁板的破坏应变水平。
- 复合材料 /
- 加筋壁板 /
- 轴向压缩 /
- 稳定性 /
- 工程计算方法
Abstract: Composite stiffened panel is typical structural form, which is widely used in aircraft wing, tail, and fuselage structures. When suffering aerodynamic loading, such composite stiffened panel on the wing surface of the wing is under compressive pressure, and this pressure could cause such panel to buckle or even failure. In this paper, an engineering method of reasonably predicting the buckling load of composite stiffened panels under axial compression is proposed, according to previous research on the stability engineering method composite stiffened panels under axial compression and stability engineering method of metal stiffened panels under axial compression which has been maturely applied in engineering. Therefore, two kinds of reinforcement composite stiffened panels (i.e., three types of Y type and two types of J type) are considered. The axial buckling load of the example is calculated by using the engineering method proposed in this paper, and the finite element numerical simulation and test verification are carried out. Compared with the experimental results, the relative error of the engineering method is less than 10%. Compared with the finite element calculation results, the relative errors of the other configurations are 5% except for one Y-shaped truss stiffened panel which is 10%, which meets the engineering requirements and proves the effectiveness of this method. This engineering method has been applied in the development of model aircraft. In addition, it is found that the weakening of the stringer edge of the stiffened panel will reduce the buckling load of the composite stiffened panel, and the weakening of the middle two stringers of the Y-stiffened panel can make the stringers more match the stiffness of the skin, and improve the failure strain level of the Y-stiffened panel.
- composite material /
- stiffened panel /
- axial compression /
- stability /
- engineering method

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图 1 J型长桁的典型横截面

Figure 1. A typical cross section of a J-Stringer

t_c—Thickness of upper protrusion; t_w—Web thickness; t_f—Lower flange thickness; t_s—Skin thickness; w_c—Upper protrusion width; w_w—Web width; w_f—Width of the lower protrusion

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图 2 两类壁板原准结构截面形状尺寸示意图(单位：mm)

R—Radius

Figure 2. Schematic diagram of section shapes and dimensions of two baseline panels (Unit: mm)

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图 3 复合材料加筋壁板的有限元模型(FEM)

Figure 3. Finite element model (FEM) of stiffened composite panel

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图 4 复合材料加筋壁板有限元模型边界条件示意图

Figure 4. Boundary conditions for FEM model of stiffened composite panel

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图 5 5种构型壁板载荷-位移曲线

Figure 5. Load-displacement curves of five panel configurations

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图 6 5种构型在屈曲载荷时的位移云图

Figure 6. Displacement nephogram of five configurations under buckling load

U—Displacement; U2—Y-direction displacement

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图 7 试验件加载及支持状态

Figure 7. Test item loading and support status

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图 8 Y型长桁试验件贴片图

Figure 8. Strain gauge arrangement plan of Y-stringer panel

Gauge 1 to 53 pasted back-to-back (101 to 153), gauge 54 to 73 pasted at the center of the two slopes of the Y stringer

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图 9 J型长桁试验件贴片图

Figure 9. Strain gauge arrangement plan of J-stringer panel

Gauge 1 to 51 pasted back-to-back (101 to 151), gauge 52 to 75 pasted at the center of the J stringer web

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图 10 Y-1型壁板轴压破坏模式

Figure 10. Failure mode of panel Y-1

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图 11 Y-1型壁板典型载荷-应变曲线

Figure 11. Typical load-strain curves for panel Y-1

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图 12 Y-2型壁板轴压破坏模式

Figure 12. Failure mode of panel Y-2

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图 13 Y-2型壁板典型载荷-应变曲线

Figure 13. Typical load-strain curves for panel Y-2

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图 14 Y-3型壁板轴压破坏模式

Figure 14. Failure mode of panel Y-3

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图 15 Y-3型壁板典型载荷-应变曲线

Figure 15. Typical load-strain curves for panel Y-3

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图 16 J-1型壁板轴压破坏模式

Figure 16. Failure mode of panel J -1

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图 17 J-1型壁板典型载荷-应变曲线

Figure 17. Typical load-strain curves for panel J-1

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图 18 J-2型壁板轴压破坏模式

Figure 18. Failure mode of panel J-2

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图 19 J-2型壁板典型载荷-应变曲线

Figure 19. Typical load-strain curves for panel J-2

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表 1 复合材料加筋壁板的结构形式及尺寸

Table 1. Structural form and size of stiffened panels

Configuration	Rib spacing, L/mm	Total panel length, l/mm	Stringer spacing, b_s/mm
Y-1	460	600	105
Y-2	460	600	105
Y-3	460	600	105
J-1	460	600	105
J-2	460	600	105

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表 2 Y型壁板铺层参数

Table 2. Lay-ups of Y stringer panels

Part	Lay-up	Total number of layers
Skin	[+45/−45/+45/−45/0/+45/−45/0/$\overline {90} $]_S	17
Y stringer vertical web	[+45/0₃/−45/0₃/90/0₃]_S	24
Other parts of Y stringer	[+45/0₃/−45/0₃/$\overline {90} $]_S	17

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表 3 J型壁板铺层参数

Table 3. Lay-ups of J stringer panels

Part	Lay-up	Total number of layers
Skin	[+45/−45/+45/−45/0/+45/−45/0/$\overline {90} $]_S	17
J stringer	[45/0₃/+45/−45/0₂/+45/0₃/−45/90/+45/0₃/−45/0₂/+45/0₃/−45]	26

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表 4 J-1型复合材料加筋壁板的几何参数

Table 4. Geometric parameters of panel J-1

t_c/mm	t_w/mm	t_f/mm	w_c/mm	w_w/mm
3.25	3.25	5.45	12	26.89
w_f/mm	t_s/mm	w_s/mm	l/mm	n
30	2.2	105	600	4
Notes: t_c—Thickness of upper protrusion; t_w—Web thickness; t_f—Lower flange thickness; t_s—Skin thickness; w_c—Upper protrusion width; w_w—Web width; w_f—Width of the lower protrusion; w_s—Bar spacing; l—Length of reinforcing ribs; n—Number of stringer.

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表 5 Y-1型复合材料加筋壁板的几何参数

Table 5. Geometric parameters of panel Y-1

t_c/mm	t_w/mm	t_f/mm	t_x/mm	w_c/mm	w_w/mm
2.21	3.21	4.42	2.21	10	13.45
w_f/mm	t_s/mm	w_s/mm	l/mm	w_x/mm	n
22	2.21	105	600	19.35	4
Notes: t_x—Inclined web thickness; w_x—Inclined web width.

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表 6 本文工程算法计算得到的加筋壁板屈曲载荷

Table 6. Buckling load of stiffened panel calculated by engineering method in this paper

Configuration	Buckling load/kN
Y-1	600
Y-2	500
Y-3	519
J-1	303
J-2	296

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表 7 5种构型壁板临界屈曲载荷、整体应变水平模拟值

Table 7. Simulation values of critical buckling load and global strain level of five panel configurations

Group	Critical buckling load/kN	Global strain level/10⁻⁶
Y-1	535	5594
Y-2	502	5308
Y-3	533	5477
J-1	318	4242
J-2	281	3983

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表 8 5种复合材料加筋壁板数值模拟屈曲破坏形式

Table 8. Numerical simulation of buckling failure of five panel configurations

Configuration	Buckling failure mode
Y-1	Skin buckles
Y-2	Skin buckles
Y-3	Skin buckles
J-1	Skin between two middle stringer buckles
J-2	Skin between two middle stringer buckles

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表 9 试验加载级差

Table 9. Test load sequence

Testing stage	Loading sequence
Stage 1: Preload	10%-20%-30%
Stage 2: Desig limit load test	10%-20%-30%-40%-50%-55%-60%-65%-67% (Holding load 30 s)
Stage 3: Design ultimate load test	10%-20%-30%-40%-50%-55%-60%-65%-67%-70%-75%-80%-82%-84%-100% (Holding load 3 s)-102%-104%……Specimen failure

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表 10 轴压试验结果汇总

Table 10. Summary of axial compression test results

Configuration	Critical buckling load/kN	Global strain level/10⁻⁶	Destroy load/kN
Y-1 (Protoquasi structure)	550	4800	674
Y-2 (No free flanges)	470	5400	626
Y-3 (Unilateral free flange)	500	5900	708
J-1 (Protoquasi structure)	310	4500	476
J-2 (Free flange weakening)	270	4500	442

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表 11 轴压试验失效形式汇总

Table 11. Summary of failure forms in axial compression tests

Group	Failure mode
Y-1 (Protoquasi structure)	Crippling after skin buckled
Y-2 (No free flanges)	Crippling after skin buckled
Y-3 (Unilateral free flange)	Crippling after skin buckled
J-1 (Protoquasi structure)	Global buckling after skin and two middle stringer buckled simultaneously
J-2 (Free flange weakening)	Global buckling after skin between two middle stringer buckled first

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表 12 本文工程算法与传统理论方法计算屈曲载荷值与试验值对比

Table 12. Buckling load value calculated by the engineering method of this paper and the traditional theoretical method compared with the test value

Configuration	Experimental value/kN	Engineering method of this paper/kN	Relative error/%	Traditional engineering method/kN	Relative error/%
Y-1	550	600	9.09	483	−12.18
Y-2	470	500	6.38	407	−13.40
Y-3	500	519	3.80	449	−10.20
J-1	310	303	−2.26	324	4.51
J-2	270	296	9.63	274	1.48

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表 13 本文工程算法与传统理论方法计算屈曲载荷值与数值模拟值对比

Table 13. Buckling load value calculated by the engineering method of this paper and the traditional theoretical method compared with the numerical simulation value

Group	Value of simulation/kN	Engineering method of this paper/kN	Relative error/%	Traditional engineering method/kN	Relative error/%
Y-1	535	600	10.83	483	−9.72
Y-2	502	500	−0.40	407	−18.92
Y-3	533	519	−2.70	449	−15.76
J-1	318	303	−4.95	324	1.89
J-2	281	296	5.07	274	−2.49

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