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拱脚沉降下3D打印拱的非线性失稳研究

文新钧 刘爱荣 毛吉化

文新钧, 刘爱荣, 毛吉化. 拱脚沉降下3D打印拱的非线性失稳研究[J]. 工程力学, 2022, 39(S): 35-41, 70. doi: 10.6052/j.issn.1000-4750.2021.05.S003
引用本文: 文新钧, 刘爱荣, 毛吉化. 拱脚沉降下3D打印拱的非线性失稳研究[J]. 工程力学, 2022, 39(S): 35-41, 70. doi: 10.6052/j.issn.1000-4750.2021.05.S003
WEN Xin-jun, LIU Ai-rong, MAO Ji-hua. STUDY ON NONLINEAR INSTABILITY OF 3D PRINTING ARCH UNDER SETTLEMENT OF ARCH FOOT[J]. Engineering Mechanics, 2022, 39(S): 35-41, 70. doi: 10.6052/j.issn.1000-4750.2021.05.S003
Citation: WEN Xin-jun, LIU Ai-rong, MAO Ji-hua. STUDY ON NONLINEAR INSTABILITY OF 3D PRINTING ARCH UNDER SETTLEMENT OF ARCH FOOT[J]. Engineering Mechanics, 2022, 39(S): 35-41, 70. doi: 10.6052/j.issn.1000-4750.2021.05.S003

拱脚沉降下3D打印拱的非线性失稳研究

doi: 10.6052/j.issn.1000-4750.2021.05.S003
基金项目: 国家自然科学基金项目(51878188);高等学校学科创新引智计划项目(111计划D21021);广州市科技计划项目(20212200004)
详细信息
    作者简介:

    文新钧(1995−),男,湖南人,硕士生,主要从事打印材料拱的稳定性研究(E-mail: wxjvenn@foxmail.com)

    毛吉化(1978−),男,安徽人,高工,硕士,常务副总经理,主要从事土木工程检测研究(E-mail: 1750358980@qq.com)

    通讯作者:

    刘爱荣(1972−),女,山西人,教授,博士,主任,主要从事新型桥梁结构的静动力稳定性研究(E-mail: liuar@gzhu.edu.cn)

  • 中图分类号: U441;TU31

STUDY ON NONLINEAR INSTABILITY OF 3D PRINTING ARCH UNDER SETTLEMENT OF ARCH FOOT

  • 摘要: 该文以3D打印材料ABS-M30作为试验载体,开展了拱脚沉降下3D打印拱的非线性失稳研究。基于最小势能原理推导了失稳临界荷载的解析表达式,得到了拱脚竖向和水平变位下拱径向位移沿拱轴线的分布图;设计了可控制拱脚沉降的加载系统,试验得到了拱在加载过程中的平衡路径,并通过有限元模拟对解析与试验结果进行了验证;分析了拱脚沉降量、矢跨比和长细比对3D打印拱失稳临界荷载的影响。研究结果表明:非线性失稳临界荷载随着拱脚沉降量的增大而减小;在拱脚沉降量一定的前提下,非线性失稳荷载随着矢跨比的增大而增大,随着长细比的增大而减小,且长细比的影响最为显著。
  • 图  1  拱脚变位时圆弧拱受力图

    Figure  1.  Stress diagram of circular arch during displacement of arch foot

    图  2  拱脚竖向变位下拱径向位移沿拱轴线分布图

    Figure  2.  Distribution of arch radial displacement along arch axis under vertical displacement of arch foot

    图  3  拱脚水平变位下拱径向位移沿拱轴线分布图

    Figure  3.  Distribution of arch radial displacement along arch axis under horizontal displacement of arch foot

    图  4  加载试验全过程(以工况1为例)

    Figure  4.  Whole process of loading test (taking condition 1 as an example)

    图  5  拱的上下极值点试验值随着拱脚竖向变位的折线图

    Figure  5.  Line chart of the test value of the upper and lower extreme points of the arch with the vertical displacement of the arch foot

    图  6  拱的上下极值点试验值随着矢跨比变化的折线图

    Figure  6.  Line chart of the variation of the test value of the upper and lower extreme points of the arch with the rise span ratio

    图  7  拱的上下极值点试验值随着长细比变化的折线图

    Figure  7.  Line chart of the variation of the test value of the upper and lower extreme points of the arch with the slenderness ratio

    图  8  拱脚沉降量对失稳荷载的影响

    Figure  8.  Influence of arch foot settlement on instability load

    图  9  矢跨比对失稳荷载的影响

    Figure  9.  Influence of rise span ratio on instability load

    图  10  长细比对失稳荷载的影响

    Figure  10.  Influence of slenderness ratio on instability load

    表  1  试件材性试验结果

    Table  1.   Material property test results of test piece

    项目拉伸弹性模量/MPa泊松比拉伸强度/MPa
    平均值15400.316413.63
    标准差0.100.00400.17
    离散系数/(%)6.581.27001.25
    下载: 导出CSV

    表  2  3D打印拱试件设计参数

    Table  2.   Design parameters of 3D printing of arch specimen

    工况组矢跨比f/L跨径L/mm矢高f/mm截面宽度b/mm截面高度h/mm支撑截面高度b'/mm支撑截面高度h'/mm长细比λ拱脚变位量X/mm
    11/830037.506.003.006.001.4188.36−4.46
    21/830037.506.003.006.001.4188.360.00
    31/830037.506.003.006.001.4188.363.12
    41/830037.506.003.006.001.4188.366.25
    51/830037.506.003.006.001.4188.368.92
    61/1030030.006.003.006.001.1570.196.25
    71/930033.336.003.006.001.2778.226.25
    81/830037.506.003.006.001.4188.366.25
    91/730042.866.003.006.001.58101.576.25
    101/630050.006.003.006.001.80119.546.25
    111/830037.506.003.006.001.4188.366.25
    121/830037.506.203.106.201.4685.516.25
    131/830037.506.403.206.401.5182.836.25
    141/830037.506.603.306.601.5580.326.25
    151/830037.506.803.406.801.6077.966.25
    注:表中负号表示拱脚向上变位量。
    下载: 导出CSV

    表  3  3D打印拱临界失稳荷载误差分析表

    Table  3.   Error analysis table of 3D printing arch critical load

    误差分析项上极值点临界荷载下极值点临界荷载
    理论值X1/N试验值X2/N有限元值X3/N误差率${\varDelta _1}$/(%)理论值Y1/N试验值Y2/N有限元值Y3/N误差率${\varDelta _2}$/(%)
    工况124.6023.8823.760.509.7910.1910.041.47
    工况224.5924.2023.891.289.5510.1210.011.09
    工况324.5524.0223.830.799.7810.1710.031.38
    工况424.0523.7923.650.5910.0810.2210.071.47
    工况523.6723.5623.410.6410.2310.3810.122.50
    工况619.5819.9919.203.957.448.498.69−2.36
    工况721.3421.8221.322.298.769.499.292.11
    工况824.0523.7923.650.5910.0810.2210.071.47
    工况927.4127.2926.791.8310.2811.2510.952.67
    工况1031.3230.8230.311.6512.2612.4012.102.42
    工况1124.0523.7923.650.5910.0810.2210.071.47
    工况1227.6527.5727.031.9610.3411.9011.533.11
    工况1331.2531.1830.571.9612.5213.8313.194.63
    工况1435.1236.0034.414.4214.6516.0315.046.18
    工况1539.3940.2838.594.2016.3817.6817.093.34
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-05-26
  • 修回日期:  2022-03-18
  • 网络出版日期:  2022-05-06
  • 刊出日期:  2022-06-06

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