Stacking sequence optimization of composite stiffened panel considering buckling
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摘要: 提出了一种考虑屈曲的复合材料加筋壁板铺层顺序优化方法。基于复合材料加筋壁板屈曲载荷求解的能量法,系统推导了轴压载荷作用下复合材料加筋壁板蒙皮、筋条局部屈曲载荷的显示表达式,考虑了加筋壁板各板元之间的弹性支持作用及筋条下缘条的影响,引入工程法求解了加筋壁板整体屈曲载荷。基于国产自主结构分析软件HAJIF中的复合材料铺层工程数据库,以铺层参数为中间变量,利用本文提出的复合材料加筋壁板屈曲载荷求解方法,构建了考虑屈曲的复合材料加筋壁板铺层顺序优化设计流程并完成程序实现,将最小二乘法用于最优铺层顺序与工程铺层数据库的匹配。相比于传统有限元计算方法,本文提出的复合材料加筋壁板屈曲载荷求解方法具备较好的求解精度及求解效率。复合材料加筋壁板优化算例表明,采用本文提出的加筋壁板屈曲载荷分析及其优化方法,在结构重量不变的前提下,屈曲载荷提高约17%,且铺层顺序优化结果可直接从铺层工程数据库中提取并用于工程实际。Abstract: A method dealing with stacking sequence optimization of composite stiffened panel considering buckling was proposed. Based on the energy-based method in calculating buckling loads of composite stiffened panels, the explicit formulations in calculating local buckling loads of skin and stiffener of composite stiffened panel were proposed systematically. The influences of each elastic supporting panel element and stiffener’s foot were taken into account during the calculation of the local buckling loads of skin and stiffener. Engineering method was introduced to calculate the global buckling load. Based on the homemade HAJIF’s composite stacking engineering library, the stacking parameters were regarded as design variables and the proposed explicit formulations in calculating buckling loads were used to build an optimization progress of composite stiffened panels’ stacking sequence and its program implementation. The least square method was applied to choose the most closed staking parameter of optimized and engineering-library laminates automatically. A higher accuracy and efficiency of the proposed formulations in calculating the buckling loads of composite stiffened panels was obtained in comparison with the traditional FEA method. The numerical optimization examples of the composite stiffened panel show that the stiffened panel’s buckling load increases by 17% with an almost unchanged weight. And the optimal stacking sequence results can be extracted from the composite stacking engineering library and be used in practical structure directly.
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表 1 帽型加筋壁板单层材料属性
Table 1. Material property of laminate of cap-shape stiffened panel
Property E1/GPa E2/GPa G12/GPa ν12 Value 98 10.78 5.194 0.31 Notes: E1, E2,G12—Elastic constants of the material; ν12—Poisson's ratio. 表 2 帽型加筋壁板基本参数
Table 2. Basic parameters of cap-shape stiffened panel
No. b2/mm b3/mm h/mm bf/mm 1 10 14 16 12 2 10 14 16 13 3 10 14 16 14 4 10 14 16 15 5 10 14 16 16 6 10 14 16 17 7 10 14 16 18 8 10 14 16 19 9 10 14 16 20 表 3 T型加筋壁板单层材料属性
Table 3. Material property of laminate of T-shape stiffened panel
Property E1/GPa E2/GPa G12/GPa ν12 Value 59.2 58 3.77 0.32 表 4 T型加筋壁板基本参数
Table 4. Basic parameters of T-shape stiffened panel
No. b2/mm b3/mm 1 24 18 2 24 20 3 24 22 4 26 18 5 26 20 6 26 22 7 28 18 8 28 20 9 28 22 表 5 Z型加筋壁板单层材料属性
Table 5. Material property of laminate of Z-shape stiffened panel
Property E1/GPa E2/GPa G12/GPa ν12 Value 118 8.11 3.75 0.31 表 6 T型加筋壁板织物及单向带材料属性
Table 6. Woven and unidirectional fabric material property of laminate of Z-shape stiffened panel
Woven property Ex/GPa Ey/GPa Gxy/GPa νxy Value 50 50 4.8 0.3 Unidirectional fabric property E11/GPa E22/GPa G12/GPa ν12 Value 115.2 7.72 4.7 0.3 Notes: Ex, Ey and Gxy—Elastic constants of the woven fabric with νxy Poisson's ratio; E11, E22 and G12—Elastic constants of the unidirectional fabric with ν12 Poisson's ratio. 表 7 本文方法与参考书目提供的试验值、有限元方法计算值对比
Table 7. Results comparison of proposed formulation, experiments and FEA provided by reference book
表 8 Z型复合材料加筋板蒙皮铺层参数上下限
Table 8. Bounds of skin’s stacking parameters of sttiffened panel with Z-shape ribs
Stacking parameters ξ1Ask ξ2Ask ξ3Ask ξ1Dsk ξ2Dsk ξ3Dsk Lower bound 0.2308 0 0.6923 0.2198 0.1315 0.6240 Upper bound 0.4615 0.0769 0.0769 0.3195 0.2189 0.3609 表 9 Z型加筋板筋条铺层参数上下限
Table 9. Bounds of stiffener’s stacking parameters of sttifened panel with Z-shape ribs
Stacking parame-ters ξ1Ast ξ2Ast ξ3Ast ξ1Dst ξ2Dst ξ3Dst Lower bound 0.1429 0 0.7143 0.2303 0.1224 0.6443 Upper bound 0.4286 0 0.1429 0.3411 0.2099 0.3178 表 10 优化前后Z型加筋壁板屈曲载荷计算值
Table 10. Calculation values of buckling load of Z-shape stiffened panel before and after optimization
Method Buckling loads before
optimization/(N·m−1)Buckling loads after
optimization/(N·m−1)Improvement of
buckling loads/%Energy based method 268.84 314.25 16.90 Finite element method 259.03 304.02 17.37 Relative error/% 3.65 3.26 — -
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