Load distribution law in multi-bolts connected composite structure
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摘要: 针对复合材料多排钉连接结构实际强度破坏极限和破坏模式与传统工程算法不一致的问题，本文以光纤螺栓试验手段为基础，开展了复合材料连接结构钉载分配规律的研究。主要研究了钉载不对称、装配顺序、装配间隙等工艺特征对钉载分配的影响，同时建立了高精度有限元模型进行对比研究。研究结果表明：多排钉连接结构钉载不对称时会加剧钉载的不均匀分配；装配顺序对钉载分配存在影响，在装配螺栓时最后安装最外侧螺栓，可以有效降低钉载分布差异；连接结构存在一致装配间隙时的钉载分配与无间隙情况的载荷分配结果一致。同时，本文发现通过试验手段测得关键螺栓的钉载占比最大比有限元结果高出10%，因此工程算法需要根据装配间隙等制造和工艺特征进行修正。Abstract: To address the issue of inconsistencies between the actual strength and failure mode of composite multi-row nail connection structures and traditional engineering algorithms, this study investigated nail load distribution patterns in composite connection structures based on fibre optic bolt testing techniques. The study primarily examines the effect of process characteristics such as nail load asymmetry, assembly sequence and assembly clearance on nail load distribution, while also establishing a high-precision finite element model for comparative study. The results indicate that asymmetric nail loading in a multi-row nail connection structure exacerbates uneven nail load distribution. Assembly sequence affects nail load distribution, and installing the outermost bolt last during bolt assembly can effectively reduce differences in nail load distribution. Nail load distribution in structures with uniform assembly clearance is consistent with load distribution in structures with no clearance. Additionally, the study finds that the proportion of critical bolt nail loads measured through testing is over 10% higher than the finite element results, suggesting that engineering algorithms need to be modified based on manufacturing and process characteristics such as assembly clearance.
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图 2 光纤螺栓工作方式：(a) 光纤螺栓实物图；(b) 解调仪；(c) 软件解调界面
Figure 2. Working mode of optical fiber bolt: (a) Physical diagram of optical fiber bolt; (b) Demodulation instrument; (c) Softwaredemodulation interface
图 3 6排2列标准试验件尺寸
Figure 3. Six rows and two rows of standard test pieces
a—Thickness of the composite plate; b—Thickness of the metal plate; $\phi $—Bolt diameter
图 6 1#、2#光纤螺栓剪力系数标定结果
Figure 6. Calibration results of 1#, 2# fiber optic bolt shear coefficient
R2—Coefficient of determination
图 7 钉载不对称验证三维有限元模型
Figure 7. 3D finite element model of nail load asymmetry
Px—Force in x direction
图 8 装配间隙验证三维有限元模型
Figure 8. 3D finite element model of assembly gap verification
U2, UR1, UR3—Displacement in the Y direction, rotation in the X direction and Z direction
图 9 复合材料连接结构接触属性主从面示意图
Figure 9. Schematic diagram of master/slave surfaces of contact properties of composite connected structures
图 10 EC试验件钉载不对称验证试验工装示意图
Figure 10. Tooling diagram of EC test piece nail load asymmetrical verification test
图 11 EC有限元模型铝板位移云图
Figure 11. Displacement cloud of EC finite element model aluminum plate
U—Deformation displacement (mm)
图 12 AS试验件4种装配顺序的钉载分配试验结果
Figure 12. Results of nail load distribution test of four assembly sequences of AS test pieces
图 13 AG、EC试验与有限元钉载分配结果
Figure 13. Nailing distribution results of AG and EC test and finite element
表 1 3种试验件尺寸参数
Table 1. Size parameters of three test pieces
Specimen Assembly tolerance/mm b/mm a/mm Ply method Number of pieces EC 0 4 7 1 5 AG 0.1 4 7 1 5 AS 0 3.5 3 2 1 Notes: EC test pieces are used for nail-loading asymmetry studies, and for comparison with AG test pieces to study the influence of assembly clearance on nail-loading distribution, and AS test pieces are used for assembly sequence studies. 
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表 2 复合材料铺层方式
Table 2. Composite material lay-up mode
Ply method Thickness/mm Ply angle 1 7 [45/−45/0/−45/45/90/0/0/
90/45/−45/0/−45/45]2S2 3 [45/−45/0/−45/0/45/0/−45/
90/45/90/0]S
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Parameter Value Parameter Value $ {E}_{1}/\mathrm{G}\mathrm{P}\mathrm{a} $ 157 $ {X}_{\mathrm{T}}/\mathrm{M}\mathrm{P}\mathrm{a} $ 2630 $ {E}_{2}/\mathrm{G}\mathrm{P}\mathrm{a} $ 8.5 $ {X}_{\mathrm{C}}/\mathrm{M}\mathrm{P}\mathrm{a} $ 1480 $ {\mu }_{12} $ 0.35 $ {Y}_{\mathrm{T}}/\mathrm{M}\mathrm{P}\mathrm{a} $ 62 $ {G}_{12}/\mathrm{G}\mathrm{P}\mathrm{a} $ 4.2 $ {Y}_{\mathrm{C}}/\mathrm{M}\mathrm{P}\mathrm{a} $ 213 $ {G}_{13}/\mathrm{G}\mathrm{P}\mathrm{a} $ 4.2 $ {S}_{12}/\mathrm{M}\mathrm{P}\mathrm{a} $ 109 $ {G}_{23}/\mathrm{G}\mathrm{P}\mathrm{a} $ 2.7 $ {S}_{23}/\mathrm{M}\mathrm{P}\mathrm{a} $ 86 Notes: E1, E2—Elasticity modulus in X, Y directions; G12, G13, G23—Shear modulus in X, Y and Z directions; μ12—X-Y planar Poisson's ratio; XT, XC—X-direction tensile and compressive strength; YT, YC—Y-direction tensile and compressive strength; S12, S23—X-Y and Y-Z planar shear strengths.
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表 4 EC试验件无间隙列试验与有限元钉载分配结果
Table 4. Nail load distribution results of EC test piece gapless column test and finite element
Gapless column Test Finite element Asymmetrical bolt load/% Symmetrical bolt loads/% Asymmetrical bolt load/% Symmetrical bolt loads/% Bolt 1 37.5 35.8 32.4 32.0 Bolt 2 16.6 16.8 16.3 15.2 Bolt 3 8.8 9.3 9.0 8.0 Bolt 4 4.3 5.3 7.3 7.2 Bolt 5 5.7 5.5 11.3 12.0 Bolt 6 27.1 27.3 23.7 25.6 Resultant force/kN 17.2 14.9 16.9 15.0 Notes: The EC test piece is loaded and unloaded three times, and the experimental data are the average of the three times data. The table provides information on the bolt load, which represents the coefficient for nail load. The coefficient for nail load is defined as the proportion of the load on a singular bolt to the total load on all bolts.
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表 5 AS试验件4种装配顺序
Table 5. Four assembly sequences for AS test pieces
Case Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 1 Bolt 1 Bolt 2 Bolt 3 Bolt 4 Bolt 5 Bolt 6 2 Bolt 1 Bolt 6 Bolt 2 Bolt 5 Bolt 3 Bolt 4 3 Bolt 3 Bolt 4 Bolt 2 Bolt 5 Bolt 1 Bolt 6 4 Bolt 6 Bolt 5 Bolt 4 Bolt 3 Bolt 2 Bolt 1
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表 6 AS试验件4种装配顺序螺栓载荷标准差结果对比
Table 6. Comparison of standard deviation results of bolt loads for four assembly sequences of AS test pieces
Case Standard deviation/% 1 11.1 2 10.1 3 8.9 4 8.7
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