基于模态缺陷的变刚度复合材料圆柱壳屈曲特性

doi:10.13229/j.cnki.jdxbgxb20200715

摘要/Abstract

摘要：

研究了基于自动铺丝技术的变刚度复合材料圆柱壳的屈曲性能和缺陷敏感性。基于丝束剪切/重送技术，提出了可以精确模拟圆柱壳面内重叠/间隙区域的简便算法，使有限元模型更加贴近实际制造过程。开展了复合载荷作用下曲线纤维铺层方式对圆柱壳屈曲性能影响的研究，结合Kriging模型和遗传算法，对纤维角度沿环向和轴向线性变化的铺层设计方式进行了优化。最后，利用改进弧长法对不同模态缺陷条件下变刚度复合材料圆柱壳的缺陷敏感性进行了分析。结果表明：在轴压和均匀外压复合作用下，纤维角度沿轴向变化的铺层方式可以有效提高结构的屈曲性能。当带宽为25.4 mm、 $T 0 = 80$ 、 $T 1 = 45$ 时变刚度圆柱壳的屈曲性能最优，较基准构型和常刚度最优构型临界屈曲载荷分别提高了70.9%和34.5%。变刚度圆柱壳的抗缺陷敏感性较基准铺层方式和最优常刚度铺层方式得到了提升。因此，变刚度设计可以使复合载荷作用下的圆柱壳结构在提升结构抗屈曲性能的同时降低对几何缺陷的敏感性。

关键词: 复合材料, 变刚度, 屈曲特性, 模态缺陷, 缺陷敏感性

Abstract:

The buckling performance and imperfection sensitivity of variable stiffness cylindrical shells based on automatic placement technology are studied. Based on the tow shearing/refeeding technology， a simple algorithm that can accurately simulate the overlapping or defect area of the cylindrical shell surface is proposed to make the finite element model closer to the actual structure. A study was conducted on the effect of curved fiber layup on the buckling performance of cylindrical shells under combined loads. Combined with the Kriging model and genetic algorithm， the layup design method， in which the fiber angle changes linearly along the hoop direction and the axial direction， is optimized. The modified arc length method was used to analyze the imperfection sensitivity of composite stiffened cylindrical shells with different mode imperfections. The results show that under the combined action of axial pressure and uniform external pressure， the layering method， in which the fiber angle changes along the axial direction， can effectively improve the buckling performance of the structure. When the bandwidth is 25.4 mm，T₀=80，T₁=45， the buckling performance of the variable stiffness cylindrical shell is optimal， and the critical buckling load is increased by 70.9% and 34.5% compared to the reference configuration and to the constant stiffness optimal configuration. The imperfection sensitivity of the variable stiffness cylindrical shell is also improved compared to the quasi-isotropic layering method and to the optimal constant stiffness layering method. Variable stiffness design can make the cylindrical shell structure under combined load improve the structural buckling resistance and reduce the sensitivity to geometric imperfections.

Key words: composite materials, variable stiffness, buckling performance, mode imperfection, imperfection sensitivity

中图分类号:

TB332

卫宇璇,张明,刘佳,刘硕,路明雨,王洪雨. 基于模态缺陷的变刚度复合材料圆柱壳屈曲特性[J]. 吉林大学学报(工学版), 2022, 52(1): 91-100.

Yu-xuan WEI,Ming ZHANG,Jia LIU,Shuo LIU,Ming-yu LU,Hong-yu WANG. Buckling performance of variable stiffness composite cylindrical shells based on mode imperfections[J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(1): 91-100.

图/表 16

图1

图2

图3

图4

图5

图6

图7

图8

表1

Kriging模型精度验证"

$T 0$ /（ $°$ ）	$T 1$ /（ $°$ ）	带宽50.8 mm				带宽38.1 mm				带宽25.4 mm
$T 0$ /（ $°$ ）	$T 1$ /（ $°$ ）	轴向K	轴向FEA	环向K	环向FEA	轴向K	轴向FEA	环向K	环向FEA	轴向K	轴向FEA	环向K	环向 FEA
20	62	32 130	32 141	34 126	34 185	32 423	32 412	34 514	34 475	33 027	33 038	34 834	34 957
10	17	26 340	26 179	25 858	25 795	26 331	26 209	25 856	25 796	26 339	26 214	25 817	25 801
60	65	42 520	43 565	43 385	43 990	42 668	43 972	43 370	44 635	42 884	44 350	43 472	45 386
74	39	51 044	49 459	40 781	40 401	52 623	51 098	41 456	40 937	55 927	54 227	42 269	41 663
46	15	34 101	34 323	31 592	31 501	34 833	35 074	31 770	31 811	35 430	35 799	32 326	32 148
$e m a x$ /%		3.2		1.4		3.0		2.8		3.3		4.2
$e a v g$ /%		1.4		0.6		1.4		0.9		1.6		1.3
$R 2$		0.99		0.99		0.99		0.99		0.99		0.98

表1

表2

变刚度圆柱壳优化结果"

	带宽50.8 mm		带宽38.1 mm		带宽25.4 mm
	轴向	环向	轴向	环向	轴向	环向
$T 0$ /（ $°$ ）	79	77	80	77	80	77
$T 1$ /（ $°$ ）	47	61	47	62	45	61
$P c r$	53 244	47 716	55 822	48 404	60 280	49 333
$P c r F E A$	52 546	47 293	55 412	47 832	61 806	48 775
$e$ /%	1.3	0.9	0.7	1.2	2.5	1.1

表2

图9

图10

表3

几何缺陷幅值推荐参数"

制造等级		$U n$
Class A	优秀	0.010
Class B	良好	0.016
Class C	普通	0.025

表3

图11

图12

图13

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