Equivalent stiffness calculation based on refined analytical model of composite laminated box beam
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摘要: 提出了基于复合材料层合箱梁改进解析模型的等效刚度计算方法。在考虑三维应变效应的同时用复合材料单层的二维折算模量分量来表示三维折算模量分量,简化了复合材料层合箱梁等效刚度系数的计算,得到了由梁横截面几何尺寸和层合板刚度系数表达的等效抗弯刚度和等效抗扭刚度的解析式。该解析式适用于环向刚度一致的复合材料层合箱梁,并充分考虑了弯曲-剪切耦合和扭转-拉伸耦合效应对等效刚度的影响。通过三点弯试验和扭转试验,验证了解析式的正确性;通过与分层等效叠加法、有限元法进行对比,分析了解析式的计算精度。结合经典层合板理论,研究了铺层方式对等效刚度产生的影响及原因,预测了不同铺层复合材料层合箱梁等效刚度的变化规律。Abstract: An equivalent stiffness calculation method based on refined analytical model of composite laminated box beam was proposed. Considering the three-dimensional strain effect, the two-dimensional reduced modulus component of the composite single layer was used to represent the three-dimensional reduced modulus component, which simplified the calculation of the equivalent stiffness coefficient of the composite laminated box beam, and the analytic formulas of equivalent bending stiffness and equivalent torsional stiffness characterized by the cross-section geometry of the beam and the stiffness coefficient of the laminate were obtained. The analytical formulas are suitable for composite laminated box beam with circumferentially uniform stiffness, and fully consider the effects of bending-shear coupling and torsion-tensile coupling on equivalent stiffness. Through the three-point bending test and the torsion test, the correctness of the analytical formula is verified. By comparing with the layered equivalent superposition method and the finite element method, the analytical precision of the analytical formula is analyzed. Combined with the classical laminated plate theory, the influence of the lamination method on the equivalent stiffness and its causes were studied, and the variation law of the equivalent stiffness of the laminated composite beams with different lay-ups was predicted.
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表 2 复合材料矩形截面管铺层参数和几何尺寸
Table 2. Layup parameters and geometric dimensions of composite rectangular section tube
Group Specimen Lay-ups b/mm h/mm T/mm L/mm B BCS1 [30]6 20 20 1.00 200 BCS2 [0/90]3 20 20 0.98 200 BCS4 [30/−30/30]s 20 20 1.01 200 BCS5 [02/±30/±60] 20 20 1.02 200 T TCS1 [30]6 20 20 1.00 200 TCS3 [04/±45] 20 20 0.99 200 TCS4 [30/−30/30]s 20 20 1.01 200 TCS5 [02/±30/±60] 20 20 1.02 200 Notes: In BCS1 and TCS1, B represents the bending test, T represents the torsion test, CS represents the carbon fiber reinforced resin composite square tube, and 1 is the specimen number; b—Width of the section; h—Height of the section; T—Wall thickness; L—Length of the tube. 表 1 T300/QY8911材料力学性能参数
Table 1. Mechanical properties parameters of T300/QY8911
Material property Value E1/GPa 135 E2=E3/GPa 8.8 G12=G13/GPa 4.47 G23/GPa 3.0 v12=v13 0.33 v23 0.33 表 3 T300/QY8911矩形截面管等效抗弯刚度理论值与试验值对比
Table 3. Comparisons between theoretical and experimental values of equivalent bending stiffness for T300/QY8911 rectangular section tube
No. Experiment/Theory Bending stiffness/(N·mm2) Error/% BCS1 Experiment 54 580 205 − <Kx> 45 536 750 −16.6 Kx 58 547 250 7.3 BCS2 Experiment 162 759 101 − <Kx> 169 383 531 4.1 Kx 168 580 503 3.6 BCS4 Experiment 74 004 918 − <Kx> 45 536 750 −38.5 Kx 78 930 367 6.7 BCS5 Experiment 139 189 698 − <Kx> 125 002 347 −10.2 Kx 143 815 866 3.3 Note: <Kx> and Kx are bending stiffnesses calculated by Eqs.(19) and Eqs.(12),respectively. 表 4 T300/QY8911矩形截面管等效抗扭刚度理论值与试验值对比
Table 4. Comparisons between theoretical and experimental values of equivalent torsional stiffness for T300/QY8911 rectangular section tube
No. Experiment/Theory Torsional stiffness/(N·mm2) Error/% TCS1 Experiment 44 087 964 - <Kz> 106 484 765 141.53 Kz 45 815 345 3.92 TCS3 Experiment 92 078 987 - <Kz> 108 910 048 18.28 Kz 96 489 393 4.78 TCS4 Experiment 159 784 264 - <Kz> 165 162 237 3.36 Kz 165 162 237 3.36 TCS5 Experiment 126 678 364 - <Kz> 144 476 626 14.04 Kz 129 924 277 2.56 Note: <Kz> and Kz are torsional stiffnesses calculated by Eqs.(20) and Eqs.(13),respectively. 表 5 复合材料的层合箱梁5种铺层方式
Table 5. Five kinds of lay-up methods for composite laminated box beam
No. Lay-ups CRL1 [0/(±θ/04)4]s CRL2 [90/(04/±θ)4]s CRL3 [0/(904/±θ)4]s CRL4 [90/(±45)11/±θ]s CRL5 [90/(±45/±θ)4]s -
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