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考虑屈曲的复合材料加筋壁板铺层顺序优化

王彬文 张长兴 郭文杰 罗利龙 聂小华

王彬文, 张长兴, 郭文杰, 等. 考虑屈曲的复合材料加筋壁板铺层顺序优化[J]. 复合材料学报, 2021, 38(12): 4123-4137. doi: 10.13801/j.cnki.fhclxb.20210210.001
引用本文: 王彬文, 张长兴, 郭文杰, 等. 考虑屈曲的复合材料加筋壁板铺层顺序优化[J]. 复合材料学报, 2021, 38(12): 4123-4137. doi: 10.13801/j.cnki.fhclxb.20210210.001
WANG Binwen, ZHANG Changxing, GUO Wenjie, et al. Stacking sequence optimization of composite stiffened panel considering buckling[J]. Acta Materiae Compositae Sinica, 2021, 38(12): 4123-4137. doi: 10.13801/j.cnki.fhclxb.20210210.001
Citation: WANG Binwen, ZHANG Changxing, GUO Wenjie, et al. Stacking sequence optimization of composite stiffened panel considering buckling[J]. Acta Materiae Compositae Sinica, 2021, 38(12): 4123-4137. doi: 10.13801/j.cnki.fhclxb.20210210.001

考虑屈曲的复合材料加筋壁板铺层顺序优化

doi: 10.13801/j.cnki.fhclxb.20210210.001
基金项目: 广东省重点研发计划(2019B090911003)
详细信息
    通讯作者:

    郭文杰,硕士,工程师,研究方向为结构优化设计 E-mail:blacks_man@sina.com

  • 中图分类号: TB33;V229+.7

Stacking sequence optimization of composite stiffened panel considering buckling

  • 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。

     

  • 图  1  蒙皮及其两侧筋条示意图

    Figure  1.  Illustration of skin with its siding ribs

    kL—Elastic constraint stiffness on the left side of skin; kR—Elastic constraint stiffness on the right side of skin

    图  2  帽型加筋壁板示意图

    Figure  2.  Illustration of cap-shape stiffened panel structure

    图  3  帽型加筋壁板截面视图

    Figure  3.  Illustration of the section of cap-shape stiffened panel

    b1—Distance between the adjacent stiffeners’ right and left side; b2—Width of the top end of stiffener; b3—Inner distance of the stiffener at its bottom end; bf—Width of stiffener’s foot; h—Height of the stiffener

    图  4  两种方法下闭剖面蒙皮屈曲载荷对比

    Figure  4.  Buckling loads of the closed section shin with the two different methods

    图  5  T型加筋壁板示意图

    Figure  5.  Illustration of local T-shape stiffened panel structure

    图  6  T型加筋壁板局部视图

    Figure  6.  Local illustration of T-shape stiffened panel structure

    图  7  两种方法下开剖面蒙皮屈曲载荷对比

    Figure  7.  Buckling loads of the open section shin with the two different methods

    图  8  Z型筋条板元分解

    Figure  8.  Partition Z-shape rib into plate elements

    ba—Width of flange; bw—Width of web

    图  9  帽型加筋壁板剖面示意图

    Figure  9.  Illustration of the section of plate with cap-shape ribs

    Unit: mm

    图  10  Z型加筋壁板剖面示意图

    Figure  10.  Illustration of the section of plate with Z-shape ribs

    图  11  T型加筋壁板剖面示意图

    Figure  11.  Illustration of the section of plate with T-shape ribs

    图  12  HAJIF系统复合材料铺层工程数据库

    Figure  12.  Composite stacking engineering library of HAJIF

    图  13  复合材料加筋壁板铺层顺序优化流程示意图

    Figure  13.  Sketch of the optimization process of stacking sequence optimization of composite stiffened panel

    图  14  Z型复合材料加筋板结构剖面尺寸示意图

    Figure  14.  Cross-section size sketch of stiffened panel with Z-shape ribs

    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

    PropertyE1/GPaE2/GPaG12/GPaν12
    Value 98 10.78 5.194 0.31
    Notes: E1, E2,G12—Elastic constants of the material; ν12—Poisson's ratio.
    下载: 导出CSV

    表  2  帽型加筋壁板基本参数

    Table  2.   Basic parameters of cap-shape stiffened panel

    No.b2/mmb3/mmh/mmbf/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
    下载: 导出CSV

    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

    PropertyE1/GPaE2/GPaG12/GPaν12
    Value59.2583.770.32
    下载: 导出CSV

    表  4  T型加筋壁板基本参数

    Table  4.   Basic parameters of T-shape stiffened panel

    No.b2/mmb3/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
    下载: 导出CSV

    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

    PropertyE1/GPaE2/GPaG12/GPaν12
    Value1188.113.750.31
    下载: 导出CSV

    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 propertyEx/GPaEy/GPaGxy/GPaνxy
    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.
    下载: 导出CSV

    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

    ShapeExperiment
    values[27]/(N·m−1)
    Finite element
    method[27]/(N·m−1)
    Proposed method/
    (N·m−1)
    Relative error
    of proposed method/%
    Cap-shape 196.30 189.70 194.95 0.68
    Z-shape 266.60 259.03 268.84 0.84
    T-shape 51.55 52.63 52.80 2.42
    下载: 导出CSV

    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 parametersξ1Askξ2Askξ3Askξ1Dskξ2Dskξ3Dsk
    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
    下载: 导出CSV

    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-tersξ1Astξ2Astξ3Astξ1Dstξ2Dstξ3Dst
    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
    下载: 导出CSV

    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

    MethodBuckling 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
    下载: 导出CSV
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  • 收稿日期:  2020-12-07
  • 录用日期:  2021-01-28
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