碳纤维增强树脂复合材料螺旋加强金属柱壳屈曲特性

左新龙; 唐文献

碳纤维增强树脂复合材料螺旋加强金属柱壳屈曲特性

左新龙^{1, 2, ,},
唐文献³

1.
江苏开放大学　信息工程学院, 南京 210000
2.
江苏科技大学　江苏省船海机械装备先进制造实验室, 镇江 212003
3.
江苏科技大学　机械工程学院, 镇江 212003

基金项目: 国家自然科学基金(52171258)

详细信息

通讯作者:
左新龙，博士，讲师，研究方向为深海耐压结构设计与制造　E-mail: 386716254@qq.com

中图分类号: U674.941
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- 文章访问数: 215
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- 被引次数: 0
出版历程
- 收稿日期: 2023-08-08
- 修回日期: 2023-09-08
- 录用日期: 2023-09-13
- 网络出版日期: 2023-09-25
- 刊出日期: 2024-06-15

Buckling of metallic cylindrical shells stiffened with helical CFRP stripes

ZUO Xinlong^{1, 2
, ,},
TANG Wenxian³

1.
School of Information Technology, Jiangsu Open University, Nanjing 210000, China
2.
Jiangsu Marine Machinery Equipment Advanced Manufacturing Laboratory, Jiangsu University of Science and Technology, Zhenjiang 212003, China
3.
School of Mechanical Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China

Funds: National Natural Science Foundation of China (52171258)

摘要

摘要: 为开展碳纤维增强树脂复合材料螺旋加强金属柱壳屈曲特性理论研究，建立了复合材料螺旋加强金属柱壳的复材层局部包裹面积比与厚度比数学关系，推导了金属内衬复材螺旋缠绕多层耐压壳抗压极限载荷理论模型。其次，开展了线性屈曲及非线性屈曲分析，并与试验结果对比分析。最后，根据推导的理论模型，形成了该类型全尺寸柱壳适用水深图谱。结果表明：插值法分析中数值分析与理论计算值的误差随复合材料包裹面积比增加而减小，最大误差为5.2%，最小误差为0.9%；试验模型中理论计算与数值分析、试验结果误差分别为3.20%、3.46%，三者具有良好一致性；内衬金属层厚度一定时，螺旋包裹适当复合材料带可适应水深范围较广，该应用对水下管路原位加强、深水管再利用等方面提供新思路。
- 碳纤维增强树脂复合材料 /
- 柱壳 /
- 屈曲理论模型 /
- 有限元 /
- 螺旋肋
Abstract: Buckling of metallic cylindrical shells stiffened with helical composite stripes was investigated in the current study. A mathematical relationship between area ratio and thickness ratio of composite layer for externally pressurized metallic cylinder stiffened with helical composite stripes was proposed. An analytical formula for collapse load of such hybrid structure was derived. Numerical analysis and experimental verification were conducted. Furthermore, depth chart for full-scale hybrid cylinder was designed using analytical formulae. The results indicate that the maximum and minimum difference between numerical and theoretical results obtained using interpolation method are 5.2% and 0.9%, respectively. The theoretical, numerical and experimental data for samples agree favorably. The difference between theoretical and numerical results is 3.20%; The difference between theoretical and experimental results is 3.46%. Metallic cylindrical shells stiffened with multiple helical composite stripes is satisfy for a wide range of depths. Composite stripe stiffeners have vast potential for application in installed and reusable tubes.
- CFRP /
- cylindrical shell /
- theoretical model of buckling /
- finite element analysis /
- helical stiffener

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图 1 金属柱壳复合材料加强示意图

Figure 1. Sketch of steel cylinder strengthen with composite

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图 2 复合材料带

Figure 2. Composite stripes

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图 3 复合材料螺旋加强金属柱壳数值模型

Figure 3. Finite-element model of the steel cylinder with helical composite stiffeners

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图 4 柱壳受静水压力

Figure 4. Cylindrical shell under hydrostatic pressure.

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图 5 网格收敛性验证

Figure 5. Convergence of the mesh size of finite element model

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图 6 复合材料螺旋加强金属柱壳屈曲载荷

Figure 6. Linear buckling loads of the steel cylinders with composite helical stiffeners

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图 7 载荷比拟合

Figure 7. Fitting model for ratio of buckling loads

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图 8 系数拟合

Figure 8. Fitting parameters

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图 9 复合材料螺旋加强金属柱壳屈曲载荷值(P_n：数值解；P_t：理论解)

Figure 9. Buckling loads of composite helical stiffened steel cylinders obtained using fitting parameters (P_n：Numerical results；P_t：Analytical results)

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图 10 试验流程：(a)长金属柱壳；(b)试样切割与研磨；(c)无封盖试样；(d)试样；(e)静水压力试验

Figure 10. Experimental flow: (a)Long steel cylinder; (b)Cutting and grinding of hybrid cylinder; (c)Sample without bung; (d)Sample; (e)Sample testing

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图 11 碳纤维增强树脂复合材料螺旋加强金属柱壳静水加压曲线

Figure 11. Pressure–time curves obtained from the hydrostatic test of the fabricated metallic cylindrical shells stiffened with helical CFRP stripes

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图 12 复合材料螺旋加强柱壳水深图谱

Figure 12. Chart design for cylinder stiffened with helical composite stripes

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图 13 复合材料螺旋加强柱壳平衡曲线

Figure 13. Applied pressure versus collapse point displacement for cylinder stiffened with helical composite stripes

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表 1 碳纤维增强树脂复合材料属性

Table 1. Material properties of CFRP composites provided by the manufacturer

Strength /MPa	X_T	1400.09	Young’s modulus /GPa	E₁₁	115
	X_C	580.06		E₂₂	7.7
	Y_T	44.36		G₁₂	3.72
	Y_C	133.03		G₁₃	3.72
	S₁₂	45.04	Poisson’s ratio	v₁₂	0.33
	S₁₃	45.04

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表 2 复合材料螺旋加强与全包裹组合柱壳屈曲载荷值

Table 2. Buckling loads of the hybrid cylinders and steel cylinders with helical stiffeners

Sample	Thickness ratio	P_W-N/ MPa	l/R	Area ratio	P_H-N/ MPa	P_H-N/ P_W-N
1	t_c/t_s=0.2	3.205	0.1	0.111	2.813	0.878
2			0.2	0.222	2.859	0.892
3			0.3	0.333	2.898	0.904
4			0.4	0.444	2.948	0.920
5			0.5	0.555	2.993	0.934
6			0.6	0.666	3.034	0.947
7			0.7	0.777	3.085	0.963
8			0.8	0.888	3.130	0.977
9	t_c/t_s=1.0	7.438	0.1	0.111	3.280	0.441
10			0.2	0.222	3.720	0.500
11			0.3	0.333	4.084	0.549
12			0.4	0.444	4.519	0.608
13			0.5	0.555	4.959	0.667
14			0.6	0.666	5.410	0.727
15			0.7	0.777	5.933	0.798
16			0.8	0.888	6.464	0.869
17	t_c/t_s=1.4	9.934	0.1	0.111	3.683	0.371
18			0.2	0.222	4.410	0.444
19			0.3	0.333	4.985	0.502
20			0.4	0.444	5.626	0.566
21			0.5	0.555	6.089	0.613
22			0.6	0.666	6.503	0.655
23			0.7	0.777	7.048	0.709
24			0.8	0.888	6.610	0.766
Notes: P_W-N—Numerical buckling load of steel cylinder strengthen wholly with composite; P_H-N—Numerical buckling load of steel cylinder with helical stiffeners; t_c—Thickness of composite layer; t_s—Thickness of steel layer; l—Width of composite stripes; R—Outer radius of inner steel layer.

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表 3 拟合系数

Table 3. Fitting parameters

Sample	t_c/t_s	a	b
1	0.2	0.127	0.863
2	1	0.544	0.373
3	1.4	0.493	0.332
Notes: t_c=Thickness of composite layer; t_s=Thickness of steel layer; a, b=Coefficient of linear function.

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表 4 拟合系数求解的螺旋加强载荷值(与全包裹载荷比值)(t_c/t_s=0.6)

Table 4. Buckling loads of helical stiffened cylinders obtained using fitting parameters (ratio of calculated values to one of hybrid cylinders) (t_c/t_s=0.6)

Sample	l/R	Area ratio	P_H-T/P_W-T	P_H-T/MPa	P_H-N/MPa	Difference (%)
1	0.1	0.111	0.597	2.832	2.988	5.2
2	0.2	0.222	0.644	3.055	3.192	4.3
3	0.3	0.333	0.691	3.277	3.365	2.6
4	0.4	0.444	0.737	3.500	3.570	2.0
5	0.5	0.555	0.784	3.722	3.775	1.4
6	0.6	0.666	0.831	3.945	3.981	0.9
7	0.7	0.777	0.878	4.167	4.216	1.2
8	0.8	0.888	0.925	4.390	4.433	1.0
Notes: P_H-T—Theoretical solution for buckling load of steel cylinder with helical stiffeners.

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表 5 碳纤维增强树脂复合材料螺旋加强金属柱壳载荷数值结果\理论值\试验结果

Table 5. Numerical, theoretical and experimental results of the fabricated metallic cylindrical shells stiffened with helical CFRP stripes; the ratio of calculated value to experimental value is indicated in parentheses

Sample	P_test (MPa)	P_non (MPa)	P_CH (MPa)	Difference(%)
HC1	6.018	6.109 (1.015)	5.932 (0.970)	3.46
HC2	6.214	6.094 (0.981)	5.932 (0.970)	3.46
Notes: P_test—Experimental results of the fabricated sample; P_linear—Linear buckling load of steel cylinder strengthen wholly with composite; P_non—Non-linear buckling load of steel cylinder with helical stiffeners; P_CH—Theoretical solution for buckling load of the fabricated sample; Difference (%) = [(6.018+6.214)/2-5.932]/5.932.

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表 6 复材螺旋加强金属柱壳前20阶模态及特征值

Table 6. First 20 linear eigenvalues (MPa) and eigenmodes of cylinder stiffened with helical composite stripes

NO.	1^st	2^nd	3^rd	4^th	5^th	6^th	7^th	8^th	9^th	10^th
P_liner	5.823	5.856	8.028	8.035	9.912	9.912	14.056	14.058	14.266	14.275
Mode
NO.	11^th	12^th	13^th	14^th	15^th	16^th	17^th	18^th	19^th	20^th
P_liner	15.031	15.032	16.630	16.633	19.082	19.086	20.602	20.641	21.861	21.862
Mode
Notes: P_linear—Linear buckling load.

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