复合材料夹芯结构褶皱增强理论和有限元方法

张森林; 吴振; 任晓辉

doi:10.13801/j.cnki.fhclxb.20221110.002

复合材料夹芯结构褶皱增强理论和有限元方法

doi: 10.13801/j.cnki.fhclxb.20221110.002

1.
西北工业大学　航空学院，西安 710072
2.
西安航空学院　机械工程学院，西安 710065

基金项目: 国家自然科学基金(12172295)

详细信息

通讯作者:
吴振，博士，教授，博士生导师，研究方向为复合材料结构力学　E-mail: wuzhenhk@nwpu.edu.cn

中图分类号: TB333
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出版历程
- 收稿日期: 2022-09-22
- 修回日期: 2022-10-19
- 录用日期: 2022-11-02
- 网络出版日期: 2022-11-11
- 刊出日期: 2023-08-15

Enhanced theory and finite element method for wrinkling analysis of composite sandwich structure

1.
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China
2.
School of Mechanical Engineering, Xi'an Aeronautical University, Xi'an 710065, China

Funds: National Natural Science Foundation of China (12172295)

摘要

摘要: 复合材料软核夹芯结构承受面内载荷，面板可能出现褶皱。一旦面板出现褶皱，夹芯结构将失去承载能力。因此，需要发展准确的理论模型预测软核夹芯结构褶皱行为。夹芯结构褶皱是典型三维(3D)问题，鲜有高阶模型能准确预测此类问题。为此，提出考虑局部形变和三维效应的增强型高阶模型。基于此理论，推导了梁单元公式，并分析了不同边界条件复合材料夹芯结构的起皱行为。通过与准三维弹性解和三维有限元解对比，提出方法的准确性得到验证。为了提高夹芯结构抗起皱能力，尝试使用复合材料面板代替金属面板。数值分析结果表明，发展的增强型高阶模型可以准确分析复合材料夹芯结构褶皱行为，并且使用复合材料面板可有效提升夹芯结构抗起皱能力。
- 复合材料 /
- 夹芯结构 /
- 增强型高阶理论 /
- 褶皱 /
- 梁单元
Abstract: Panels wrinkling behaviors may occur when composite soft-core sandwich structures subjected to coplanar compression loads. Once the panels wrinkling appears, the sandwich structures will lose its load-bearing capacity. Therefore, it is necessary to develop an accurate model to predict the wrinkling behaviors of soft-core sandwich structures. Sandwich structure wrinkling is a typical three-dimensional (3D) problem, and few high-order models can accurately predict such issues. Therefore, this paper proposed an enhanced higher-order model including the local deformation and the 3D effects. Based on the proposed theory, the beam element formulation was derived, and the wrinkling behaviors of sandwich structures with different boundary conditions were analyzed. By comparing with the quasi-3D elasticity solution and the 3D finite element results, accuracy of the proposed method has been verified. In order to improve the capability of sandwich structures resisting the wrinkling deformation, this work attempted to use composite face sheets instead of metal panel in the sandwich structure. Numerical results show that the developed enhanced high-order model can accurately predict the wrinkling behaviors of the composite sandwich structures, and the use of composite panels can effectively resist the wrinkling behaviors of sandwich structures.
- composite /
- sandwich structures /
- enhanced higher-order theory /
- wrinkling /
- beam element

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图 1 三层夹芯梁截面

t_c—Thickness of the core layer; t_f—Thickness of the panel layer

Figure 1. Three-layer sandwich beam section

下载: 全尺寸图片幻灯片

图 2 构建的高阶单元收敛率

BE18—Enhanced higher-order model; 3D-FEM—Three-dimensional finite element method

Figure 2. Convergence rate of constructed higher-order elements

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图 3 三层铝面板夹芯梁屈曲和褶皱载荷(芯材与面板厚度之比t_c/t_f =50，夹芯梁长厚比a/h=2)

Figure 3. Buckling and wrinkling loads for three-layer sandwich beam with aluminum face sheets (Ratio of core thickness to panel thickness is t_c/t_f=50, ratio of length to thickness is a/h=2)

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图 4 使用当前模型和3D有限元模型(3D-FEM)计算得到的三层铝面板夹芯梁屈曲行为的位移模态

Figure 4. Displacement modes for buckling behaviors of a three-layer aluminum panel sandwich beam calculated by using the current model and 3D finite element method (3D-FEM)

m—Number of half waves

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图 5 使用当前模型和3D-FEM计算得到的三层铝面板夹芯梁褶皱行为的位移模态

Figure 5. Displacement modes for wrinkling behaviors of a three-layer aluminum panel sandwich beam calculated by using the current model and 3D-FEM

下载: 全尺寸图片幻灯片

图 6 材料参数和几何参数对三层铝面板夹芯梁屈曲和褶皱载荷影响

Figure 6. Influence of material properties and geometric parameters on buckling and wrinkling loads of three-layer sandwich beam with aluminum face sheets

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图 7 几何参数对三层铝面板夹芯梁屈曲和褶皱载荷影响

Figure 7. Influence of geometric parameters on buckling and wrinkling loads of three-layer sandwich beam with aluminum face sheets

下载: 全尺寸图片幻灯片

表 1 3D有限元边界条件

Table 1. Boundary condition for 3D finite element

x=0	x=a	y=0	y=1
U2=U3=UR3=0	U3=UR3=0	U2=0	U2=0
Notes: a—Length of the sandwich beam; U2, U3, UR3—Translational and rotational degrees of freedom in ABAQUS, respectively.

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表 2 三层铝面板夹芯梁屈曲载荷

Table 2. Buckling load of three-layer sandwich beam with aluminum panels

t_c/t_f	a/h	3D-FEM (270000 elements)	BE18 (64 elements)	HYF11^[20]	HYF21^[20]	HOST^[21]	Allen^[22]
5	2	6.6111	6.7131(1.54)	6.2220(5.89)	37.551(468.00)	37.238(463.26)	6.3544(3.88)
	5	14.7065	14.838(0.89)	14.320(2.63)	159.0500(981.49)	159.3200(983.33)	14.385(2.19)
	10	41.6580	41.8190(0.39)	41.0840(1.38)	329.6300(691.28)	321.2600(671.18)	41.1150(1.30)
25	2	1.5342	1.5600(1.68)	1.5299(0.28)	2.3207(51.26)	2.3112(50.64)	1.5923(3.79)
	5	9.0749	9.1046(0.33)	9.0314(0.48)	13.1300(44.68)	13.1130(44.50)	9.0971(0.24)
	10	31.6490	31.6550(0.02)	31.0960(1.75)	42.4330(34.07)	42.4360(34.08)	31.1590(1.55)
50	2	1.4432	1.4640(1.44)	1.4419(0.09)	1.8335(27.04)	1.8301(26.81)	1.5074(4.45)
	5	8.5657	8.6504(0.99)	8.5553(0.12)	10.3110(20.38)	10.3010(20.26)	8.6191(0.62)
	10	27.5850	27.5220(0.23)	26.7620 (2.98)	30.7460(11.46)	30.7690(11.54)	26.8490(2.67)
Notes: t_c/t_f—Core and panel thickness ratio; a/h—Span thickness ratio of sandwich beam; BE18—Present model; HYF11—Quasi-3D model; HYF21 and HOST—Higher-order models; Allen represents the model proposed by Allen.

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表 3 三层铝面板夹芯梁褶皱载荷

Table 3. Wrinkling loads of three-layer sandwich beam with aluminum panels

t_c/t_f	a/h	3D-FEM ( 270000 elements)	BE18 (480 elements)	HYF11^[20]	HYF21^[20]	Allen^[22]
50	2	0.7311 (5)	0.7632 (5)	0.7073 (6)	0.8074	1.3020 (9)
	5	4.5097 (13)	4.7147 (14)	4.3583 (14)	5.0048	8.1376 (23)
	10	18.0910 (27)	18.8830 (27)	17.4330 (28)	20.0190	–
100	2	0.2610 (9)	0.2845 (9)	0.2517 (9)	0.3121	0.6638(9)
	5	1.6318 (22)	1.7768 (22)	1.5736 (23)	1.9480	4.1486 (22)
	10	6.5273 (44)	7.1612 (43)	6.2921 (45)	7.7921	16.594 (45)
Note: Numbers in brackets represent half-wave numbers.

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表 4 三层复合材料夹芯梁屈曲载荷

Table 4. Buckling load of three-layer composite sandwich beam

t_c/t_f	a/h	3D-FEM (270000 elements)	BE18 (240 elements)	BHSDT^[24]	RHSDT^[25]
25	2	11.301	11.457	14.951	15.525
	5	64.288	64.441	85.873	89.282
	10	239.100	239.200	313.650	325.220
50	2	10.016	10.135	13.442	12.360
	5	61.853	61.978	80.805	73.963
	10	222.560	222.510	280.980	259.830
Notes: BHSDT—Higher order model proposed by Babu et al^[24]; RHSDT—Higher-order model proposed by Reddy^[25].

下载: 导出CSV

表 5 三层复合材料夹芯梁褶皱载荷

Table 5. Wrinkling load of three-layer composite sandwich beam

t_c/t_f	a/h	SS		CC
t_c/t_f	a/h	3D-FEM (270000 elements)	BE18 (480 elements)	3D-FEM (270000 elements)	BE18 (480 elements)
50	2	7.5768 (4)	8.0174 (4)	8.0246 (4)	8.5964 (4)
	5	46.4130 (11)	49.2650 (11)	47.1010 (11)	50.0860 (11)
	10	185.7200 (22)	197.4900 (22)	186.4300 (21)	198.3100 (21)
100	2	2.7004 (7)	2.8531 (7)	2.7806 (7)	2.9505 (7)
	5	16.8350 (18)	17.8290 (18)	16.9290 (18)	17.9370 (18)
	10	7.3330 (36)	1.7410 (36)	7.4410 (36)	1.8490 (36)
Notes: SS—Simply supported boundary conditions; CC—Clamped supported boundary conditions; Numbers in brackets represent half-wave numbers.

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