圆柱壳三次非均匀有理B样条曲线变角度铺放轨迹设计及屈曲特性

曹忠亮; 林国军; 董明军; 韩振华; 曹清林

doi:10.13801/j.cnki.fhclxb.20210622.003

圆柱壳三次非均匀有理B样条曲线变角度铺放轨迹设计及屈曲特性

doi: 10.13801/j.cnki.fhclxb.20210622.003

曹忠亮^{1, 2, ,},
林国军^2,,
董明军^1,,
韩振华^1,,
曹清林^1,

1.
江苏理工学院　机械工程学院，常州 213000
2.
齐齐哈尔大学　机电工程学院，齐齐哈尔 161001

基金项目: 国家自然科学基金(51705266)

详细信息

通讯作者:
曹忠亮，博士，副教授，硕士生导师，研究方向为复合材料铺放成型工艺、变角度轨迹规划　E-mail：caoliang-8302@163.com

中图分类号: TB330.1
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出版历程
- 收稿日期: 2021-05-19
- 修回日期: 2021-06-15
- 录用日期: 2021-06-16
- 网络出版日期: 2021-06-22
- 刊出日期: 2022-06-01

Variable angle placement trajectory design of non-uniform rational B-splines curve and buckling property of cylindrical shell

CAO Zhongliang^{1, 2
, ,},
LIN Guojun^2
,,
DONG Mingjun^1
,,
HAN Zhenhua^1
,,
CAO Qinglin^1
,

1.
School of Mechanical Engineering, Jiangsu University of Technology, Changzhou 213000, China
2.
School of Mechatronics Engineering, Qiqihar University, Qiqihar 161001, China

摘要

摘要: 基于三次非均匀有理B样条(NURBS)曲线，开展纤维变角度圆柱壳设计及其屈曲特性研究。首先，以三次NURBS曲线定义纤维变角度铺放参考轨迹，确定了变角度铺层的表示方式。其次，以纤维变角度铺层±<25(0.4)(0.8)75>和±<65(0.4)(0.8)10>为例，展示了三次NURBS曲线轴向平移铺层和周向平移铺层在圆柱壳上的纤维角度分布情况。然后，用纤维变角度铺层代替定刚度圆柱壳中的±45°铺层，对变刚度圆柱壳进行线性屈曲分析，对轴向平移圆柱壳、周向平移圆柱壳和定刚度圆柱壳进行对比。最后，在曲率半径约束下，研究权因子对圆柱壳屈曲性能的影响。结果表明：周向平移圆柱壳有着更好的屈曲性能；在曲率半径约束下，通过确定起始角、终止角和控制点参数得到屈曲性能优异的变刚度圆柱壳，而改变权因子能使变刚度圆柱壳的屈曲载荷再次提高。
- 三次非均匀有理B样条(NURBS)曲线 /
- 圆柱壳 /
- 变角度 /
- 轨迹规划 /
- 屈曲特性
Abstract: Based on cubic non-uniform rational B-splines (NURBS) curve, the design and bucking property of cylindrical shell produced by fiber variable angle placement were studied. Firstly, the reference trajectory of fiber variable angle placement was defined by cubic NURBS curve, and the parameterized expression of fiber variable angle placement was determine. Secondly, taking the fiber variable angle placements ±<25(0.4)(0.8)75> and ±<65(0.4)(0.8)10> as examples, the fiber angle distributions of the axial and circumferential shift placements of the cubic NURBS curve on the cylindrical shell were demonstrated. Then, the ±45° placement of constant stiffness cylindrical shell was replaced by the fiber variable angle placements. The linear buckling analysis of the variable stiffness cylindrical shell was carried out, and the axial translation cylindrical shell, circumferential translation cylindrical shell and constant stiffness cylindrical shell were compared. Finally, the influence of weight factors on the buckling property was studied under the constraint of curvature radius. The results show that the circumferential translation cylindrical shell has better buckling performance. Under the constraint of curvature radius, the variable stiffness cylindrical shell with excellent buckling performance can be obtained by determining initial angle, termination angle and control point parameter, and the buckling load of the variable stiffness cylindrical shell can be increased again by changing the weight factor.
- non-uniform rational B-splines (NURBS) curve /
- cylindrical shell /
- variable angle /
- trajectory planning /
- bucking property

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图 1 三次非均匀有理B样条(NURBS)曲线

Figure 1. Cubic non-uniform rational B-splines (NURBS) curve

β₁—Position parameter of P₁; α₀—Angle of P₀; P₁, P₂, P₃, P₀—Control point; h—Distance between P₁ and P₂ along the x-axis; β₂—Position parameter of P₂; α₁—Angle of P₃

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图 2 NURBS曲线随权因子ω变化(ω₁<ω₂<ω₃)

Figure 2. NURBS curve varies with weight factor ω (ω₁<ω₂<ω₃)

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图 3 圆柱壳展开面

Figure 3. Development surface of cylindrical shell

L—Length; H—Hight

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图 4 圆柱壳三维示意图

Figure 4. Three-dimensional diagram of cylindrical shell

θ—Angle between the plane formed by the current calculation point and z-axis and the oxz plane; C—Circumference; r—Radius

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图 5 复合材料圆柱壳±<25(0.4)(0.8)75>铺层示意图

Figure 5. Diagram of composite cylindrical shell ±<25(0.4)(0.8)75> layer

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图 6 复合材料圆柱壳±<65(0.4)(0.8)10>铺层示意图

Figure 6. Diagram of composite cylindrical shell ±<65(0.4)(0.8)10> layer

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图 7 变刚度圆柱壳模型载荷及边界条件

Figure 7. Loading and boundary conditions of variable stiffness cylindrical shell

M_z—Torque load for rotation around the z-axis; F—Axial compression load along the z-axis; U_R_z—Degrees of freedom to rotate around the z-axis; U_z—Degree of freedom to translate along the z-axis

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图 8 含±<25(0.6)(0.8)75>铺层的变刚度(VS)圆柱壳分析模型

Figure 8. Variable stiffness (VS) cylindrical shell analysis model with ±<25(0.6)(0.8)75> layer

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图 9 圆柱壳的一阶屈曲模态(R≥650 mm)

Figure 9. The first order buckling mode of cylindrical shell (R≥650 mm)

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表 1 圆柱壳的铺层结构

Table 1. Laminate structure of cylindrical shell

Name	Layer structure
CS	[±45/0/90]_2s
VSC	[±φ/0/90]_2s
VSA	[±φ/0/90]_2s
Notes: CS—Constant stiffness; VSC—Variable stiffness circumferential translation; VSA—Variable stiffness axial translation.

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表 3 定刚度(CS)圆柱壳线性屈曲分析结果

Table 3. Linear buckling results of constant stiffness (CS) cylindrical shel

Load type	Buckling load coefficient
Axial compression load	1515
Torque load	83892

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表 4 扭矩载荷下的变刚度(VS)圆柱壳线性屈曲分析结果

Table 4. Linear buckling results of variable stiffness (VS) cylindrical shell under torque load

Variable stiffness layer	Curvature radius R/mm	Buckling load coefficient of VSC	Buckling load coefficient of VSA
<25(0.1)(0.8)75>	≥700	97430	75501
<25(0.2)(0.8)75>		97895	75407
<25(0.3)(0.8)75>		98324	75414
<25(0.4)(0.8)75>		98748	75524
<25(0.4)(0.9)75>		95811	78504
<25(0.5)(0.8)75>		99179	75763
<25(0.5)(0.9)75>		96501	78160
<25(0.6)(0.8)75>		99621	76165
<25(0.6)(0.9)75>		97188	77939
<25(0.7)(0.9)75>		97868	77888
<25(0.8)(0.9)75>		98533	78058

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表 5 轴压载荷下的VS圆柱壳线性屈曲分析结果

Table 5. Linear buckling results of VS cylindrical shell under axial compression load

Variable stiffness layer	Curvature radius R/mm	Buckling load coefficient of VSC	Buckling load coefficient of VSA
<65(0.1)(0.2)10>	≥700	1558	1316.8
<65(0.1)(0.3)10>		1565.2	1343.5
<65(0.1)(0.4)10>		1571.9	1363.1
<65(0.1)(0.5)10>		1577.4	1375.9
<65(0.2)(0.3)10>		1598.9	1354.9
<65(0.2)(0.4)10>		1598.7	1367.8
<65(0.2)(0.5)10>		1596.6	1374
<65(0.2)(0.6)10>		1591.9	1375.4
<65(0.2)(0.9)10>		1553.4	1367.7
<65(0.3)(0.4)10>		1642.7	1378.1
<65(0.3)(0.5)10>		1631.6	1380.6
<65(0.3)(0.6)10>		1617.8	1379.1
<65(0.3)(0.7)10>		1601.8	1375.1
<65(0.4)(0.6)10>		1671.6	1390.9
<65(0.4)(0.7)10>		1647.4	1386
<65(0.4)(0.8)10>		1623	1380.1

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表 2 T300碳纤维增强环氧树脂复合材料参数

Table 2. Parameters of T300 carbon fiber reinforced epoxy composite materials

E₁/MPa	E₂/MPa	v₁₂	G₁₂/MPa	G₁₃/MPa	G₂₃/MPa
121000	8600	0.3	5100	5100	3100
Notes: E₁, E₂—Elastic modulus; G₁₂, G₁₃, G₂₃—Shear modulus of elasticity; v₁₂—Poisson's ratio.

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