FINITE ELEMENT MODEL FOR BUCKLING OF STIFFENED COMPOSITE SANDWICH STRUCTURES BASED ON HIGHER-ORDER THEORY
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摘要:加筋复合材料夹芯结构由于面板与夹芯层的力学性能差异较大, 层间剪切变形明显, 层间剪切应力对结构的屈曲特性影响非常明显. 此外筋条与面板之间横向剪切变形也会显著地影响加筋夹芯结构的屈曲特性. 因此, 需要发展一种能准确计算面板与芯体之间、筋条与板之间横向剪切应力的模型来分析复合材料加筋夹芯结构的屈曲特性. 文章推导了正弦型整体−局部高阶剪切变形理论, 该理论满足面内位移、横向剪切应力连续条件和自由表面条件, 并且未知量个数独立于加筋夹芯板的层数. 基于此理论, 结合离散的Kirchhoff三角形单元(DKT单元)构造了正弦型整体−局部高阶三角形板单元(SGLT), 该单元满足面内位移在厚度方向的锯齿分布和横向剪切应力层间连续性条件, 并通过两个数值算例验证了模型的准确性. 随后评估了金属面板加筋夹芯板和复合材料面板格栅加筋夹芯板在各种几何、材料参数和边界条件下的屈曲特性. 数值分析结果表明, 建立的有限元模型能准确地预测加筋复合材料夹芯结构的屈曲行为. 并且相较于三维有限元模型, 建立的模型具有更高的计算效率.
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关键词:
- 加筋复合材料夹芯结构/
- 横向剪切应力/
- 屈曲特性/
- 格栅加筋夹芯板/
- 三角形单元
Abstract:Due to the large difference in mechanical properties between the faceplates and core, the interlaminar shear deformation of the stiffened composite sandwich structure is obvious, and the interlaminar shear stress has a significant impact on the buckling characteristics of the structure. In addition, the transverse shear deformation between stiffeners and plates will also significantly affect the buckling characteristics of the stiffened sandwich structure. Therefore, it is necessary to develop a mechanical model that can accurately calculate the transverse shear stresses between the faceplates and core and between stiffeners and faceplates to study the buckling characteristics of composite stiffened sandwich structures. Thus the sine type global-local higher-order shear deformation theory is derived. This theory meets the conditions of in-plane displacement, transverse shear stress continuity and free surface conditions, and the number of unknowns is independent of the number of layers of stiffened sandwich plates. Based on the theory, the discrete Kirchhoff triangular element (DKT element) is used to construct the sinusoidal global-local triangular plate element (SGLT), and the accuracy of the model is verified by two numerical examples. Then the buckling characteristics of metal stiffened sandwich plates and composite grid stiffened plates under various geometric, material parameters and boundary conditions are evaluated. The numerical examples show that the established finite element model can accurately predict the buckling behaviors of stiffened sandwich structures. And compared to the three-dimensional (3D) finite element model, the established model has high computational efficiency. -
图 211层复合材料夹芯方板的x-z平面的示意图
Figure 2.x-zsection schematic diagram of eleven-ply composite sandwich plate
图 3玻璃纤维面板帽形加筋夹芯板的示意图
Figure 3.Schematic diagram of hat-stiffened sandwich plate with glass fiber panels
图 4玻璃纤维面板帽形加筋夹芯板的一阶屈曲模态
Figure 4.the first-order mode of hat-stiffened sandwich plate with glass fiber panels
图 5金属面板单侧加筋夹芯板的几何构型
Figure 5.Geometric data of the single stiffened sandwich plate with metal panels
图 6不同模型计算的不同长宽比和宽厚比的临界屈曲载荷
Figure 6.Critical buckling loads under different aspect and width-thickness ratios obtained from various models
图 7固定筋条宽度和高度前提下, 由不同模型计算的临界屈曲载荷
Figure 7.Critical buckling loads obtained from various models when the width and depth of stiffeners fixed
图 8复合材料面板格栅加筋夹芯板的示意图
Figure 8.Schematic diagram of grid-stiffened sandwich plate with composite panels
图 93种边界条件下三维有限元(3D-FEM)与正弦型高阶模型计算的复合材料格栅加筋板的屈曲模态
Figure 9.Displacement modes of the composite grid-stiffened plates obtained by the model 3D-FEM and SGLT under three boundary conditions
表 1模型的边界条件
Table 1.Boundary conditions in present model
Simply-supported (S) Clamped (C) ${v_0} = {w_0} = {v^1_1} = {\theta _y} = \dfrac{ {\partial {w_0} } }{ {\partial y} } = 0$ ${v_0}{\text{ } } = {u^1_1} = {\theta _x} = \dfrac{ {\partial {w_0} } }{ {\partial x} } = 0$ or and ${u_0} = {w_0} = {u^1_1} = {\theta _x} = \dfrac{ {\partial {w_0} } }{ {\partial y} } = 0$ ${w_0} = {v^1_1} = {\theta _y} = \dfrac{ {\partial {w_0} } }{ {\partial y} } = 0$ 
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表 2各种模型计算的11层复合材料夹芯方板的无量纲临界屈曲载荷
Table 2.Normalized critical buckling loads acquired by diverse models for the eleven-ply composite sandwich plate
a/h Models tf/h 0.025 0.050 0.075 0.1 10 exact[23] 2.2081 3.7385 4.8307 5.6721 CFS-LW[24] 2.2639 3.7649 4.8302 5.6255 SGLT 2.2905 3.8330 4.9267 5.7625 IGA[25] 2.3000 3.8560 4.9554 5.7859 IGA[26] 2.2909 3.8335 4.9307 5.7786 SPT[27] 2.3161 3.8846 4.9904 5.8237 RHSDT[28] 2.3054 3.8573 4.9602 5.8111 THSDT[29] 2.3182 3.8824 5.0015 5.8448 KHSDT[30] 2.3121 3.8751 4.9797 5.8178 FSDT 2.2976 3.8908 5.4079 6.6490 20 exact[23] 2.5534 4.6460 6.4401 7.9352 CFS-LW[24] 2.5660 4.6817 6.4428 7.9184 SGLT 2.5579 4.6781 6.4461 7.9386 IGA[25] 2.5619 4.6891 6.4624 7.9554 IGA[26] 2.5591 4.6807 6.4518 7.9520 SPT[27] 2.5757 4.7147 6.4968 7.9959 RHSDT[28] 2.5757 4.7100 6.4913 7.9994 THSDT[29] 2.6780 4.8374 6.6455 8.1693 KHSDT[30] 2.5744 4.7112 6.4922 7.9931 FSDT 2.6555 4.8584 6.7891 8.4964 下载:
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表 3各种模型计算的玻璃纤维面板帽形加筋夹芯板临界屈曲载荷
Table 3.Critical buckling loads (N) acquired by diverse models for the hat stiffened sandwich plate with glass fiber panels
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表 4金属面板加筋夹芯板屈曲载荷的收敛率(b/a= 1,tst/tf= 2)
Table 4.Convergence rate of buckling loads for the stiffened sandwich plate with metal panels (b/a= 1,tst/tf= 2)
Models a/h 5 10 20 3D-FEM
SGLT (240 elements)
SGLT (312 elements)
SGLT (480 elements)
SGLT (800 elements)
SGLT(1152 elements)0.02112
0.01868
0.01886
0.01899
0.01931
0.019320.05527
0.04692
0.04756
0.04808
0.04909
0.049110.18210
0.15173
0.15393
0.15578
0.15931
0.15932下载:
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表 5金属面板加筋夹芯板临界屈曲载荷对比
Table 5.Critical buckling loads for the stiffened sandwich plate with metal panels
b/a a/h 3D-FEM SGLT S4R SPT[27] RHSDT[28] 0.5 5 0.04469 0.04468 0.01452 0.14528 0.17664 10 0.07865 0.07282 0.05277 0.46467 0.57443 20 0.21698 0.19382 0.19380 1.45112 1.72694 1 5 0.02112 0.01931 0.01399 0.11996 0.14885 10 0.05527 0.04909 0.05048 0.36611 0.43620 20 0.18210 0.15931 0.17971 0.82386 0.90770 1.5 5 0.01616 0.01446 0.01367 0.10639 0.13001 10 0.04944 0.04346 0.04846 0.27664 0.31541 20 0.15809 0.13722 0.15813 0.47792 0.50527 2 5 0.01427 0.01266 0.01340 0.09364 0.11188 10 0.04584 0.04009 0.04602 0.20616 0.22708 20 0.13500 0.11651 0.13507 0.30052 0.31117 2.5 5 0.01327 0.01171 0.01310 0.08144 0.09503 10 0.04268 0.03720 0.04320 0.15517 0.16680 20 0.11384 0.09776 0.11369 0.20281 0.20766 下载:
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表 6固定筋条宽度前提下, 金属面板加筋夹芯板临界屈曲载荷(b/a= 1)
Table 6.Critical buckling loads for the stiffened sandwich plate with metal panels when the width of stiffeners fixed (b/a= 1)
hs/tf a/h 3D-FEM SGLT S4R SPT[27] RHSDT[28] 2 5 0.02658 0.02457 0.01556 0.11801 0.14623 10 0.06419 0.05668 0.05854 0.37099 0.44272 20 0.19626 0.18904 0.20910 0.84441 0.93201 3 5 0.03567 0.03958 0.01875 0.12562 0.16211 10 0.07823 0.08205 0.06474 0.36859 0.45369 20 0.21545 0.20988 0.22861 0.79294 0.88304 4 5 0.04838 0.05290 0.02278 0.14942 0.15962 10 0.09643 0.09213 0.07626 0.39321 0.47902 20 0.24334 0.23456 0.24695 0.77341 0.85620 下载:
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表 7固定筋条高度前提下, 金属面板加筋夹芯板临界屈曲载荷对比(b/a= 1)
Table 7.Critical buckling loads for the stiffened sandwich plate with metal panels when the depth of stiffeners fixed (b/a= 1)
tst/tf a/h 3D-FEM SGLT S4R SPT[27] RHSDT[28] 2 5 0.02091 0.01908 0.01404 0.11996 0.14885 10 0.06107 0.05174 0.05563 0.34906 0.42734 20 0.20671 0.19349 0.20147 0.64167 0.71476 3 5 0.022341 0.02012 0.01576 0.12361 0.15392 10 0.06421 0.05669 0.05960 0.36859 0.45369 20 0.21725 0.20354 0.21691 0.67501 0.74678 4 5 0.02348 0.02113 0.01660 0.12781 0.15888 10 0.06702 0.06050 0.06262 0.38704 0.47743 20 0.22671 0.21967 0.23301 0.70405 0.77467 下载:
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表 8不同筋条铺层序列的复合材料格栅加筋板在四边简支边界条件下(SSSS)的前3阶屈曲载荷
Table 8.Buckling loads of first three mode for the composite grid-stiffened plate with various stiffened lay-up under four supported edges (SSSS)
a/h Layers
(X/Y)m= 1 m= 2 m= 3 3D-FEM SGLT 3D-FEM SGLT 3D-FEM SGLT 5 (0°/0°)s 0.51061 0.56992
(11.61)0.87912 0.89460
(1.76)1.28376 1.33718
(4.16)(0°/90°)s 0.47306 0.52839
(11.69)0.86642 0.91369
(5.45)1.10996 1.18809
(7.04)(30°/60°)s 0.43841 0.48872(11.48) 0.63842 0.66204
(3.70)0.99288 1.09667(10.45) (45°/45°)s 0.40250 0.44542(10.66) 0.56123 0.61829(10.17) 0.89816 1.01054(12.51) (90°/0°)s 0.44234 0.49029
(10.83)0.49816 0.53150
(6.69)0.76805 0.78496
(2.20)(90°/90°)s 0.35773 0.40619
(13.55)0.46637 0.52477
(12.52)0.73938 0.80863
(9.36)10 (0°/0°)s 1.21182 1.24706
(2.91)1.32953 1.34096
(0.86)1.93061 1.98763
(2.95)(0°/90°)s 1.05391 1.17401
(11.39)1.29857 1.36911
(5.43)1.92566 2.07335
(7.67)(30°/60°)s 1.03563 1.09172
(5.42)1.15368 1.14767
(0.52)1.37657 1.50243
(9.14)(45°/45°)s 0.96818 1.02261(5.62) 1.05107 1.21091(15.21) 1.27063 1.42167(11.89) (90°/0°)s 0.93238 0.95370
(2.28)1.10387 1.16005
(5.09)1.19905 1.19784
(0.10)(90°/90°)s 0.87974 0.95486
(8.54)0.91353 1.06189
(16.24)1.12642 1.22889
(9.09)20 (0°/0°)s 3.29477 2.96677
(9.95)3.45361 3.43780
(0.45)3.88449 3.54107
(8.84)(0°/90°)s 3.07062 2.99975
(2.31)3.29081 3.32838
(1.14)3.97298 3.56543
(10.25)(30°/60°)s 3.10604 2.73718
(11.87)3.40152 3.03193
(10.86)3.60782 3.41138
(5.44)(45°/45°)s 2.95776 2.84034(3.97) 3.17860 3.22310(1.39) 3.38709 3.53572(4.39) (90°/0°)s 2.92260 2.51364
(13.99)2.97922 2.56561
(13.88)3.27399 2.87182
(12.28)(90°/90°)s 2.82265 2.50446
(11.27)2.85318 2.61268
(8.42)3.13770 2.96936
(5.36)Note: Numbers in brackets are the absolute value of percentage errors from selected elements with respect to 3D-FEM. 下载:
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表 9复合材料格栅加筋板在不同边界条件下临界屈曲载荷
Table 9.Critical buckling loads for the composite grid-stiffened plate under various boundary conditions
Layers Boundary conditions SCSC SFSF 3D-FEM
(256800
elements)SGLT
(1152
elements)THSDT[29]
(1152
elements)KHSDT[30]
(1152
elements)3D-FEM
(256800
elements)SGLT
(1152
element)THSDT[29]
(1152
elements)KHSDT[30]
(1152
elements)[0°/0°] 1.4667 1.5202 7.2374 9.2387 0.6492 0.5741 4.6792 5.8497 [0°/90°] 1.2603 1.3461 6.3949 7.9208 0.6513 0.5908 4.9295 6.1641 [30°/60°] 1.1521 1.2374 6.2984 7.8750 0.5722 0.5107 4.2576 5.2949 [45°/45°] 1.0850 1.1660 6.7362 8.5231 0.5562 0.5388 4.4306 5.5231 [90°/0°] 1.0675 1.1231 6.2803 8.3828 0.5270 0.4658 3.8626 4.7862 [90°/90°] 1.1090 1.0681 5.6764 6.9881 0.5328 0.4759 4.0570 5.0324 下载:
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