Sectionalization-based reinforcement optimization of composite-wound case dome through multi-island genetic algorithm
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摘要: 针对Ф150 mm非等极孔复合材料缠绕壳体，开展了水压爆破试验研究，并通过建立基于三维Hashin失效准则的壳体精细化渐进损伤有限元模型，对壳体复合材料失效模式、爆破位置以及爆破压强进行了准确预测，以验证有限元模型的可靠性。以此为基础，根据壳体封头应力分布状态，建立了基于多岛遗传算法的封头分区补强优化模型，对补强层数和补强角度进行优化，揭示了不同分区补强角度及其耦合作用对封头纤维应力的影响机制，继而获得不同分区最优的补强角度及补强层数，并通过分区补强试验进行验证。结果表明，封头赤道圆至金属接头肩部区域补强角度对纤维应力的影响更为显著，宜采用小角度进行补强；而接头肩部至极孔范围内需采用较大角度分别对轴向和环向进行补强。通过分区补强水压爆破试验结果可知，壳体爆压提高了37.5%，壳体特性系数提高16.6%，说明该优化模型是准确且可靠的。Abstract: The hydrostatic tests for the Ф1
50 mm composite-wound cases with unequal poler openings were carried out. In order to precisely predict the failure modes, burst position and the burst pressure of the composite cases, the progressive damage model based on the 3D Hashin failure criteria was established and its reliability was evaluated by experimental results. Based on the finite element model, the sectionalization-based reinforcement optimization model through multi-island genetic algorithm was established to optimize the reinforcing layers and angles according to the stress distribution on domes. The influence mechanism of the reinforcing angles in different subareas and its coupling effect on the fiber stress were revealed and then the optimal reinforcing angles and layers were obtained. In addition, the subareaalization-based reinforcement test was implemented to validate the optimization model. The results of the numerical model show that the reinforcing angle from the equator of the dome to the shoulder of the metal boss has a more significant effect on the fiber stress and the relative small angle should be employed to reinforce domes; however, the relative large reinforcing angle in the subarea ranging from the poler openings to the shoulder of the boss should be applied to reinforce the axial and circumferential directions. The results of hydraulic burst test of the reinforcing case show that the burst pressure and the performance factor increase by 37.5% and 16.6%, respectively, compared with that of composite case without reinforcement, which indicates that the optimization model is accurate and reliable. -
图 2 未补强复合材料壳体水压爆破试验
Figure 2. Hydrostatic burst tests of composite cases without reinforcement
图 5 复合材料壳体有限元载荷及边界条件
Figure 5. Load and boundary conditions of the composite case finite element model
图 6 未补强复合材料壳体渐进损伤结果
Figure 6. Progressive damage results of the composite case without dome reinforcement ((a) Matrix failure; (b) Delamination failure; (c) Fiber failure; (d) Internal pressure-displacement curves of the dome (Composite case bursts in the dome by 17.9 MPa))
图 7 复合材料壳体螺旋层纤维应力分布及封头分区
Figure 7. Fiber stress distribution on helical layers and subareas of domes of the composite case
图 8 基于多岛遗传算法的分区补强优化流程
Figure 8. Flow chart of sectionalization-based reinforcement optimization based on the multi-island genetic algorithm
图 9 采用3层补强层的复合材料壳体优化结果
Figure 9. Optimization results of the composite case with three dome reinforcement layers
图 10 采用4层补强层的复合材料壳体优化结果
Figure 10. Optimization results of the composite case with four dome reinforcement layers
图 11 采用5层补强层的复合材料壳体优化结果
Figure 11. Optimization results of the composite case with five dome reinforcement layers
图 12 采用6层补强层的复合材料壳体优化结果
Figure 12. Optimization results of the composite case with five dome reinforcement layers
图 13 复合材料壳体不同分区补强角度及最大纤维应力随补强层变化
Figure 13. Reinforcement angles and maximum fiber stress variable with reinforcement layersof the composite case
图 14 复合材料壳体A、B区补强角度与在最大纤维应力的之间的相关系数随补强层数变化关系
Figure 14. Correlation coefficients between reinforcement angles in subarea A and B and the maximum fiber stress variable reinforcement layers of the composite case
图 15 分区补强壳体渐进损伤分析
Figure 15. Progressive damage analysis of the composite case with sectionalization-based reinforcement ((a) Matrix failure; (b) Delamination failure; (c) Fiber failure; (d) Internal pressure-displacement curve of burst location in cylindrical part by 26.2MPa)
图 16 复合材料壳体补强层铺贴示意图
Figure 16. Schematic diagram of reinforcement layers laid on domes of the composite case
图 17 复合材料壳体封头补强角度变化
Figure 17. Variation of reinforcement angle on domes of composite case
图 18 复合材料壳体分区补强工艺及水压爆破试验
Figure 18. Sectionalization-based reinforcement experiment and the hydrostatic test of the composite case
图 19 复合材料壳体数值仿真与补强试验载荷-位移结果对比
Figure 19. Comparison of pressure-displacement curves obtained respectively by simulations and the reinforcement experiment for composite case
表 1 复合材料壳体水压爆破试验结果
Table 1. Results of hydrostatic burst tests of composite cases
1# 2# 3# Average value Burst pressure P/MPa 17.5 17.0 18.0 17.5 Performance factor PV/W/km 26.5 25.8 27.3 26.5 Notes: V—Volume; W—Mass of composite materials. 
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表 2 内衬和金属接头材料属性
Table 2. Mechanical properties of liner and metal boss
Parameter Liner Metal boss Elasticity modulus E/GPa 0.9 196 Poisson’s ratio µ 0.4 0.3
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表 3 T700碳纤维/环氧树脂复合材料力学性能参数
Table 3. Mechanical properties of T700 carbon fiber/epoxy composite
Parameter Value Extensional modulus in1- direction E11/GPa 140 Extensional modulus in 2- direction E22/GPa 9.68 Extensional modulus in 3- direction E33/GPa 9.98 Shear modulus G12/GPa 3.92 Shear modulus G23/GPa 2.92 Shear modulus G13/GPa 3.92 Poisson’s ratio μ12 0.32 Poisson’s ratio μ23 0.43 Poisson’s ratio μ13 0.32 Longitudinal tensile strength Xt/MPa 2250 Longitudinal compressive strength Xc/MPa 1250 Transverse tensile strength in Yt/MPa 49 Transverse compressive Yc/MPa 180 Shear strength S/MPa 61
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表 4 复合材料壳体封头分区尺寸
Table 4. Subarea dimensions of domes of the composite case
Dome reinforcement information Subarea A Subarea B Back dome Subarea a1+
Subarea l1Subarea b1+
Subarea l1Front dome Subarea a2+
Subarea l2Subarea b2+
Subarea l2Range of
subareas/mmBack dome 0-22 15-36 Front dome 0-24 17-36 Width of
subareas/mmBack dome 26 53 Front dome 29 50
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表 5 复合材料壳体补强角度变化后纤维应力轴向分力对比
Table 5. Comparison of the axial component of fiber stress after reinforcement angle changing of composite case
Parameter Original reinforcement angle Maximum reinforcement angle after change Subarea A Subarea B Subarea A Subarea B Reinforcement angle/(°) α=3 α=37 α1=10.5 α1=40 α2=34 Axial component of fiber stress ($ F\cos \alpha$) 0.9986F 0.7986F 0.9833F 0.766F 0.829F Error/% − − −1.5 −4.1 3.8 Notes: F—Stress in fiber direction; α—Reinforcement angle; α1 and α2—Maximum and minimum reinforcement angle, respectively.
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