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含裂纹损伤圆弧曲梁弹性屈曲的有限元网格自适应分析

王永亮

王永亮. 含裂纹损伤圆弧曲梁弹性屈曲的有限元网格自适应分析[J]. 工程力学, 2021, 38(2): 8-15. doi: 10.6052/j.issn.1000-4750.2020.03.0173
引用本文: 王永亮. 含裂纹损伤圆弧曲梁弹性屈曲的有限元网格自适应分析[J]. 工程力学, 2021, 38(2): 8-15. doi: 10.6052/j.issn.1000-4750.2020.03.0173
WANG Yong-liang. ADAPTIVE MESH REFINEMENT ANALYSIS OF FINITE ELEMENT METHOD FOR ELASTIC BUCKLING OF CRACKED CIRCULARLY CURVED BEAMS[J]. Engineering Mechanics, 2021, 38(2): 8-15. doi: 10.6052/j.issn.1000-4750.2020.03.0173
Citation: WANG Yong-liang. ADAPTIVE MESH REFINEMENT ANALYSIS OF FINITE ELEMENT METHOD FOR ELASTIC BUCKLING OF CRACKED CIRCULARLY CURVED BEAMS[J]. Engineering Mechanics, 2021, 38(2): 8-15. doi: 10.6052/j.issn.1000-4750.2020.03.0173

含裂纹损伤圆弧曲梁弹性屈曲的有限元网格自适应分析

doi: 10.6052/j.issn.1000-4750.2020.03.0173
基金项目: 国家自然科学基金项目(41877275,51608301);中央高校基本科研业务费专项资金项目(2019QL02);天津市重点实验室开放课题基金项目(2017SCEEKL003);中国矿业大学(北京)越崎青年学者计划项目(2019QN14)
详细信息
    通讯作者:

    王永亮(1985−),男,河北唐山人,副教授,博士,硕导,主要从事矿山岩体计算力学的研究(E-mail: wangyl@cumtb.edu.cn)

  • 中图分类号: O242.21

ADAPTIVE MESH REFINEMENT ANALYSIS OF FINITE ELEMENT METHOD FOR ELASTIC BUCKLING OF CRACKED CIRCULARLY CURVED BEAMS

  • 摘要: 该文建立圆弧形曲梁裂纹的截面损伤缺陷比拟方案,实现裂纹大小(深度)、位置、数目的模拟。引入变截面Euler-Bernoulli梁的h型有限元网格自适应分析方法,求解含裂纹损伤圆弧曲梁弹性屈曲问题,得到优化的网格和满足预设误差限的高精度屈曲荷载和屈曲模态解答。数值算例表明该算法中网格非均匀加密可适应裂纹损伤引起的屈曲模态变化,应用于各类曲梁夹角和裂纹损伤分布工况下的弹性屈曲研究,定量分析了裂纹损伤程度对圆弧曲梁的屈曲荷载和屈曲模态的影响,检验了该文算法的精确性和可靠性。
  • 图  1  含裂纹损伤曲梁坐标系和符号

    Figure  1.  Coordinate systems and symbols of cracked curved beam

    图  2  含裂纹损伤圆弧曲梁截面损伤和加载示意图

    Figure  2.  Diagram of cross-section damage defect and loading for circularly curved beam with crack damage

    图  3  自适应网格下屈曲模态

    Figure  3.  Buckling mode on adaptive refinement mesh

    图  4  加密网格下屈曲模态收敛情况

    Figure  4.  Convergence of buckling modes on refined meshes

    图  5  不同裂纹损伤位置下圆弧曲梁弹性屈曲

    Figure  5.  Elastic buckling of circularly curved beam with different locations of crack damage

    图  6  不同裂纹损伤大小下圆弧曲梁弹性屈曲

    Figure  6.  Elastic buckling of circularly curved beam with different magnitudes of crack damage

    图  7  各工况多裂纹分布示意图

    Figure  7.  Diagram of cases for multiple cracks distributions

    图  8  多裂纹损伤下网格分布和屈曲模态差

    Figure  8.  Mesh distribution and buckling modes of circularly curved beam with multiple cracks

    表  1  圆弧曲梁根据径厚比和夹角分类

    Table  1.   Categories of circularly curved beams according to ratio of radius and thickness and subtended angle

    按径厚比$R/h$厚曲梁中厚曲梁薄曲梁
    $R/h < 40$$R/h = 40$$R/h > 40$
    按曲梁夹角θ0浅梁中等深度梁深度梁超深度梁
    $\theta _0^{} < 40_{}^ \circ $$\theta _0^{} = 40_{}^ \circ $$40_{}^ \circ < \theta _0^{} \leqslant 180_{}^ \circ $$\theta _0^{} > 180_{}^ \circ $
    下载: 导出CSV

    表  2  单元数目与屈曲荷载结果收敛性

    Table  2.   Convergence for number of elements and buckling loads results

    单元数目屈曲荷载$q_{{\rm{nc}}}^{}$ (kN/m)
    常规有限元法组合梁模型[23]解析法[7]本文方法
    464.45077.56664.96664.406 (16个单元)
    564.45077.181
    664.43677.046
    2564.440
    5064.408
    10064.406
    下载: 导出CSV

    表  3  两端简支曲梁不同夹角下屈曲荷载值

    Table  3.   Buckling loads of of curved beam with hinged–hinged supports under different subtended angles

    曲梁夹角屈曲荷载$q_{\rm{nc}}^{}$ /(kN/m)
    能量法[9]组合梁模型[23]解析法[7]本文方法
    π/6 31.604 36.489 31.331 31.0600
    π/5 21.945 24.723 21.690 21.5690
    π/4.5 17.773 19.861 17.527 17.4710
    π/4 14.040 15.604 13.803 13.8040
    π/3.5 10.745 11.906 10.517 10.5690
    π/2 3.481 3.854 3.286 3.4511
    下载: 导出CSV

    表  4  不同裂纹损伤位置下曲梁屈曲荷载值

    Table  4.   Buckling loads of curved beam with crack damage at different locations

    损伤位置$\theta _{\rm{c}}^{}$屈曲荷载$\bar q_{\rm{c}}^{}$损伤位置$\theta _{\rm{c}}^{}$屈曲荷载$\bar q_{\rm{c}}^{}$
    0 0.999 999 π/3 0.937 817
    π/12 0.994 679 5π/12 0.924 499
    π/6 0.978 168 π/2 0.919 641
    π/4 0.958 574
    下载: 导出CSV

    表  5  不同裂纹损伤大小下曲梁屈曲荷载值

    Table  5.   Buckling loads of curved beam with crack under different magnitudes

    损伤大小$h_{\rm{c}}^{}/h$屈曲荷载$\bar q_{\rm{c}}^{}$
    0.10.995 226
    0.20.988 219
    0.30.976 756
    0.40.957 391
    0.50.919 641
    下载: 导出CSV

    表  6  多裂纹损伤不同位置下曲梁屈曲荷载值

    Table  6.   Buckling loads of curved beam with multiple cracks at different locations

    工况第1条裂纹位置第2条裂纹位置第3条裂纹位置屈曲荷载$\bar q_{\rm{c}}^{}$
    Iπ/4 (I1)π/2 (I2)3π/4 (I3)0.856 826
    IIπ/4 (II1)π/2 (II2)π/12 (II3)0.881 116
    III5π/12 (III1)π/2 (III2)7π/12 (III3)0.800 923
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-03-22
  • 修回日期:  2020-05-23
  • 网络出版日期:  2021-01-16
  • 刊出日期:  2021-01-16

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