基于弯曲刚度比的复合材料帽形加筋板局部屈曲工程修正计算方法

张庆茂; 陈金睿; 孔斌; 白瑞祥; 黄晓笛; 刘文豪

doi:10.13801/j.cnki.fhclxb.20211216.001

基于弯曲刚度比的复合材料帽形加筋板局部屈曲工程修正计算方法

doi: 10.13801/j.cnki.fhclxb.20211216.001

张庆茂^1,,
陈金睿^1, ,,
孔斌^{1, 2},
白瑞祥³,
黄晓笛³,
刘文豪³

1.
中国航空工业集团公司成都飞机设计研究所，成都 610091
2.
南京航空航天大学　机械结构力学及控制国家重点试验室，南京 210016
3.
大连理工大学　工业装备结构分析国家重点试验室，大连 116024

基金项目: 民机科研项目(MJ-2015-F-038)

详细信息

通讯作者:
陈金睿，硕士，工程师，研究方向为复合材料结构设计　E-mail: chenjinrui666@126.com

中图分类号: TB332
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- 被引次数: 0
出版历程
- 收稿日期: 2021-10-08
- 修回日期: 2021-11-15
- 录用日期: 2021-11-26
- 网络出版日期: 2021-12-17
- 刊出日期: 2022-12-01

Local buckling updating engineering method of hat-stiffened composite panel based on flexural stiffness ratio

1.
AVIC Chengdu Aircraft Design and Research Institute, Chengdu 610091, China
2.
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
3.
State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China

摘要

摘要: 为提高复合材料帽形加筋板蒙皮局部屈曲的工程分析方法精度，对典型复合材料帽形加筋板进行了轴压稳定性试验，提出了一种基于弯曲刚度比的复合材料帽形加筋板局部屈曲工程简化分析修正方法，所预测的屈曲载荷与轴压稳定性试验值误差在3%以内。采用有限元方法(FEM)及本文方法对两种构型的带筋条下缘条帽形加筋板进行了对比分析，本文方法与FEM计算误差在10%以内，表明本文提出的修正方法合理有效，满足工程精度要求。采用工程简化分析方法、能量法及本文方法对公开文献的试验数据进行了对比分析，结果表明采用本文方法可将工程简支屈曲分析误差和工程固支屈曲分析误差分别从41.5%、5.3%降低至3.8%，为复合材料帽形加筋板结构初步设计与分析提供了一种新的快速分析思路。
- 帽形加筋壁板 /
- 复合材料 /
- 屈曲 /
- 改进工程算法 /
- 弯曲刚度比
Abstract: In order to improve the accuracy of local buckling engineering method of hat-stiffened composite panel, the stability experiment of typical panels under axial compression was first carried out, and then an updating engineering method for local buckling of hat-stiffened composite panel based on flexural stiffness ratio was proposed. The predicted buckling loads differ less than 3% from experimental results. The buckling analysis of two kinds of hat-stiffened panels with bottom flange was carried out by finite element model (FEM) method and the updating method this paper proposed comparatively. The error of compared results is within 10%, which verifies the reasonableness of the proposed method and satisfies the engineering accuracy. Experimental data recorded in public literature were analyzed by engineering simplified method, energy method and the updating method this paper proposed comparatively. Results show that the error by engineering simply and fixedly supported boundary conditions can be reduced from 41.5% and 5.3% to 3.8% respectively, which provides a new rapid analytical method for preliminary design of hat-stiffened composite panel.
- hat-stiffened panel /
- composites /
- buckling /
- updating method /
- flexural stiffness ratio

HTML全文

图 1 复合材料帽形加筋板试件示意图

Figure 1. Sketch of hat-stiffened composite panel specimens

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图 2 帽形筋条截面尺寸参数

Figure 2. Sectional dimensions of hat stiffener

R—Radius

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图 3 复合材料帽形加筋板轴压试验照片

Figure 3. Photo of test of hat-stiffened composite panel under axial compression

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图 4 试件贴片示意图

Figure 4. Sketch of strain gauge

L—Distance between two horizontal frames; L₁, L₂—Distance between the edge of the glue filling end and the bottom edge of the transverse frame

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图 5 复合材料帽形加筋板试件载荷-应变曲线

Figure 5. Load-strain curves of hat-stiffened composite panel specimens

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图 6 复合材料帽形加筋板有限元(FEM)网格及屈曲模态(以1^#试件为例)

Figure 6. Mesh and buckling mode of finite element model (FEM) of hat-stiffened composite panel (Specimen 1^# for example)

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图 7 正交各向异性矩形平板的轴压K-λ曲线

Figure 7. Axial compression K-λ curves of orthotropic rectangular plates

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图 8 两类帽形加筋板有限元模型示意图

Figure 8. Sketch of finite element models of two kinds of hat-stiffened panels

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图 9 帽形加筋板截面尺寸参数示意图

Figure 9. Cross section of hat-stiffened panel

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图 10 两类帽形加筋板的一阶屈曲模态

Figure 10. First order buckling modes of two kinds of hat-stiffened panels

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图 11 三筋条带横框的复合材料帽形加筋板外形示意图

Figure 11. Sketch of composite hat-stiffened panel with three stiffeners and two frames

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表 1 单层材料参数

Table 1. Lamina material parameters

Material	E₁₁/GPa	E₂₂/GPa	G₁₂/GPa	ν₁₂
X850	162.0	9.1	4.6	0.331
Notes：E₁₁—Elastic modulus in fiber direction; E₂₂—Elastic modulus transverse fiber direction; ν₁₂—Poisson’s ratio; G₁₂—Shear modulus.

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表 2 应变片编码方法

Table 2. Coding method of strain gauge

Coding location	Coding meaning	Coding method
First number	Specimen number	1—Specimen 1^#; 2—Specimen 2^#
Second number	Part type	1—Skin; 2—Stiffener
Third number	Row number of strain gauge	5 rows on skin, 5 rows on stiffeners, 2 rows on 2 frames, counting from up to down respectively
Fourth number	Column number of strain gauge	4 columns on inner skin, 9 columns on outer skin, 5 columns on 5 stiffeners, 4 columns on frame, counting from left to right respectively
Fifth number	Strain gauge on inner skin or outer skin	1—Outer skin; 2—Inner skin
Sixth number	Strain gauge location on stiffener	1—Crown; 2—Left web; 3—Right web; 4—Left bottom flange; 5—Right bottom flange
Seventh number	Strain gauge direction	1—0° direction; 2—45° direction; 3—90° direction

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表 3 复合材料帽形加筋板轴压稳定性试验值与计算值对比

Table 3. Comparison of calculated and experimental values of local buckling load of hat-stiffened composite panel

No.	D	Experimental buckling load /kN	Engineering simplified method/kN		Updating method/kN	Error/%
No.	D	Experimental buckling load /kN	Simply supported	Built-in	Updating method/kN	Simply supported	Built-in	Updating method
1^#	3.501	315	249	383	312	−21.0	21.6	−1.0
2^#	3.456	185	154	244	189	−16.8	31.9	2.2
Note: D—Flexural stiffness ratio.

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表 4 三筋条帽形加筋板有限元模型几何参数

Table 4. Geometric parameters of finite element models of hat-stiffened panels with three stiffeners

Type	a /mm	B /mm	b_c /mm	b_w /mm	b_f /mm	θ/(°)	b_ss /mm
1	300	278	10.4	10.7	16.5	82.9	70
2	590	532	25	33	25	60	103
Notes: a—Length of stiffened panel; B—Width of stiffened panel; b_c—Width of stiffener’s crown; b_w—Width of stiffener’s web; b_f—Width of stiffener’s bottom flange; θ—Angle between stiffener’s web and skin; b_ss—Width of skin adjacent stiffener.

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表 5 三筋条帽形加筋板单层材料参数

Table 5. Lamina material parameters of hat-stiffened panels with three stiffeners

Type	E₁₁/GPa	E₂₂/GPa	G₁₂/ GPa	$ {\nu _{12}} $
1	98	10.8	5.2	0.31
2	154	8.5	4.5	0.35

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表 6 三筋条帽形加筋板有限元模型铺层顺序及铺层厚度

Table 6. Stacking sequence and thickness of finite element models of hat-stiffened panels with three stiffeners

No.	Skin		Crown		Web		Flange
No.	Stacking sequence	Total thickness/ mm	Stacking sequence	Total thickness/ mm	Stacking sequence	Total thickness/ mm	Stacking sequence	Total thickness/ mm
1.1	[45/0/0/−45/90]_s	1	[0₉/−45/45₂/−45₂]_s	2.8	[−45/45₂/−45₂]_s	1	[0₃/−45/45₂/ −45/−45]_s	1.5
1.2	[45/0/−45/90/ 45/−45/0]_s	1.4	[0₉/−45/45₂/−45₂]_s	2.8	[−45/45₂/−45₂]_s	1	[0₃/−45/45₂/ −45/−45]_s	1.5
1.3	[0/90]_3s	1.2	[45/0/90/0/−45/ 0/45/90]_s	1.5	[45/0/90/0/−45/ 0/45/90]_s	1.5	[45/0/90/0/−45/ 0/45/90]_s	1.5
2.1	[45/−45/−45/ 90/45/0]_s	1.2	[45/0/0/−45/90]_s	0.9	[45/0/0/−45/90]_s	0.9	[45/0/0/−45/90]_s	0.9
2.2	[45/−45/90₂/ 45/0/90/0]_s	1.5	[0/45/0/0/−45/45]_s	1.2	[0/45/0/0/−45/45]_s	1.2	[0/45/0/0/−45/45]_s	1.2
2.3	[45/−45/90₂/45/ 0/90/0]_s	1.5	[45/0/0/−45/90]_s	0.9	[45/0/0/−45/90]_s	0.9	[45/0/0/−45/90]_s	0.9

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表 7 两类帽形加筋板轴压稳定性有限元值与计算值对比

Table 7. Comparison of calculated and FEM values of local buckling load of two kinds of hat-stiffened composite panels

No.	D	FEM buckling load/kN	Engineering simplified method/kN		Updating method /kN	Error/%
No.	D	FEM buckling load/kN	Simply supported	Built-in	Updating method /kN	Simply supported	Built-in	Updating method
1.1 1.2 1.3 2.1 2.2 2.3	2.750 4.713 4.842 4.014 4.019 3.815	13.0 38.5 23.9 26.4 52.7 43.2	7.7 15.9 9.4 16.0 28.5 23.1	13.1 29.0 19.1 24.7 46.5 37.7	14.2 38.1 26.0 27.9 54.6 41.2	−40.8 −58.7 −60.7 −39.4 −45.9 −46.5	0.8 −24.7 −20.1 −6.4 −11.8 −12.7	9.2 −1.0 8.8 5.7 3.6 −4.6

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表 8 带横框的三筋条帽形加筋板局部屈曲载荷计算值与试验值对比

Table 8. Comparison of calculated and experimental values of local buckling load of hat-stiffened panels with three stiffeners and two frames

D	Experimental buckling load/kN	Engineering simplified method/kN		Energy method/kN	Updating method/kN	Error/%
D	Experimental buckling load/kN	Simply supported	Built-in	Energy method/kN	Updating method/kN	Simply supported	Built-in	Energy method	Updating method
3.641	245.0	143.3	258	238.2	235.8	−41.5	5.3	−2.8	−3.8

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