工程力学 ›› 2019, Vol. 36 ›› Issue (1): 165-174.doi: 10.6052/j.issn.1000-4750.2017.11.0842

• 土木工程学科 • 上一篇    下一篇

考虑杆件初弯曲的网壳弹塑性稳定性的弱形式求积元分析

汤宏伟, 钟宏志   

  1. 清华大学土木工程系, 北京 100084
  • 收稿日期:2017-11-09 修回日期:2018-03-09 出版日期:2019-01-29 发布日期:2019-01-10
  • 通讯作者: 钟宏志(1964-),男,黑龙江人,教授,博士,主要从事求积元法及应用研究(E-mail:hzz@tsinghua.edu.cn). E-mail:hzz@tsinghua.edu.cn
  • 作者简介:汤宏伟(1993-),男,湖南人,硕士研究生,主要从事网壳稳定性研究(E-mail:2504239782@qq.com).
  • 基金资助:
    国家自然科学基金项目(51378294)

ELASTO-PLASTIC STABILITY ANALYSIS OF LATTICED SHEELS WITH INITIALLY CURVED MEMBERS BY WEAK-FORM QUADRATURE ELEMENTS

TANG Hong-wei, ZHONG Hong-zhi   

  1. Department of Civil Engineering, Tsinghua University, Beijing 100084, China
  • Received:2017-11-09 Revised:2018-03-09 Online:2019-01-29 Published:2019-01-10

摘要: 初始缺陷是影响网壳稳定性的主要因素之一。技术规程建议的一致缺陷模态法综合考虑了结点的位置偏差与杆件的初弯曲,但现有计算方法难于便捷地单独全面体现初弯曲的影响。该文基于几何精确梁理论构造了一种弱形式求积元模型。通过引入纤维模型模拟材料非线性,结合柱面弧长法实现了对空间曲梁结构的弹塑性大位移分析,通过算例验证了提出模型的有效性。该模型构建不需具体指定位移形函数,避免了使用有限元软件中的复杂建模过程。运用该模型计算了几类典型网壳在杆件初弯曲方向随机分布,不同弯曲挠度下的极限承载力。计算结果表明,在现有钢结构生产工艺下杆件初弯曲的缺陷对于网壳稳定性的影响较小,不起控制作用。通过与一致缺陷模态法的计算结果和空间网格结构技术规程计算的承载力进行对比,对规范的承载力计算公式提出了考虑特殊网壳形式及材料屈服强度的改进建议。

关键词: 几何精确梁, 弱形式求积元法, 初弯曲, 网壳稳定性, 弹塑性

Abstract: Initial imperfection is one of the major influential factors for the stability of a latticed shell. The consistent imperfection mode method recommended by current technical specifications consider both nodal deviation and initial curvature of members, but the sole influence of initial curvature cannot be easily identified. In this study, a weak form quadrature beam element model was formulated based on the geometrically exact beam theory. Incorporating the fiber model for material nonlinearity and the arc length algorithm, elasto-plastic large displacement analysis of spatial curved beam structures was conducted. Examples were examined to verify the effectiveness of the proposed model. By the use of the proposed model, displacement shape functions are not necessarily designated and delicate modeling of curved beams in other finite element software can be avoided. In the analysis, ultimate loads of several typical latticed shells consisting of members with random initial curvature were obtained. It is found that the member defect of initial curvature had little effect on the load-carrying capacity of a latticed shell and therefore was not the main factor for stability under the circumstances of current steel-production quality control technique. Results were compared with those from the consistent imperfection mode approach and the technical specification for space frame structures. It is suggested that the yield strength of material and the specific form of a latticed shell should be considered in the formula of the technical codes and standards.

Key words: geometrically exact beam, weak form quadrature element method, initial curvature, stability of latticed shell, elasto-plasticity

中图分类号: 

  • TU311.4
[1] 符立勇. 大跨度单层球面网壳的稳定性分析[D]. 成都:西南交通大学, 2002. Fu Liyong. The stability analysis of large-span singlelayer spherical lattice shell[D]. Chengdu:Southwest Jiaotong University, 2002. (in Chinese)
[2] 沈世钊, 陈昕. 网壳结构稳定性[M]. 北京:科学出版社, 1999:53-56, 88-102. Shen Shizhao, Chen Xin. Stability of reticulated shells[M]. Beijing:Science Press, 1999:53-56, 88-102. (in Chinese)
[3] Bathe K, Bolourchi S. Large displacement analysis of three-dimensional beam structures[J]. International Journal for Numerical Methods in Engineering, 1979, 14(7):961-986.
[4] 张闰. 基于几何精确模型的结构非线性弱形式求积元分析[D]. 北京:清华大学, 2015. Zhang Run. Nonlinear weak form quadrature element analysis of structures[D]. Beijing:Tsinghua University, 2015. (in Chinese)
[5] Reissner E. On one-dimensional finite-strain beam theory:The plane problem[J]. Zeitschrift Für Angewandte Mathematik Und Physik Zamp, 1972, 23(5):795-804.
[6] Simo J C. A finite strain beam formulation. The three-dimensional dynamic problem. Part I[J]. Computer Methods in Applied Mechanics & Engineering, 1985, 49(1):55-70.
[7] Ibrahimbegović A. On finite element implementation of geometrically nonlinear Reissner's beam theory:threedimensional curved beam elements.[J]. Computer Methods in Applied Mechanics & Engineering, 1995, 122(1):11-26.
[8] Zhong H, Yu T. Flexural vibration analysis of an eccentric annular Mindlin plate[J]. Archive of Applied Mechanics, 2007, 77(4):185-195.
[9] Kani I M, Mcconnel R E. Collapse of shallow lattice domes[J]. Journal of Structural Engineering, 1987, 113(8):1806-1819.
[10] 曹正罡, 范峰, 沈世钊. K6型单层球面网壳的弹塑性稳定[J]. 空间结构, 2005, 11(3):22-26. Cao Zhenggang, Fan Feng, Shen Shizhao. Elasticplasstic stablity of K6 single layer latticed domes[J]. Spatial Structures, 2005, 11(3):22-26. (in Chinese)
[11] 曹正罡, 孙瑛, 范峰. 肋环斜杆型球面网壳弹塑性稳定特性[J]. 哈尔滨工业大学学报, 2007, 39(6):849-852. Cao Zhenggang, Sun Ying, Fan Feng. Elasto-plastic stability behavior of schwedler domes[J]. Journal of Harbin Institute of Technology, 2007, 39(6):849-852. (in Chinese)
[12] 曹正罡, 孙瑛, 范峰, 等. 单层双曲椭圆抛物面网壳弹塑性稳定性能[J]. 建筑结构学报, 2009, 30(2):70-76. Cao Zhenggang, Sun Ying, Fan Feng, et al. Elasto-plastic stability of single-layer elliptic paraboloidal reticulated shells[J]. Journal of Building Structures, 2009, 30(2):70-76. (in Chinese)
[13] 严佳川, 范峰, 曹正罡. 杆件初弯曲对网壳结构弹塑性稳定性能影响研究[J]. 建筑结构学报, 2012, 33(12):63-71. Yan Jiachuang, Fan Feng, Cao Zhenggang. Research on influence of initial curvature of members on elastoplastic stability of reticulated shells[J]. Journal of Building Structures, 2012, 33(12):63-71. (in Chinese)
[14] JGJ 7-2010, 空间网格结构技术规程[S]. 北京:中国建筑工业出版社, 2010. JGJ 7-2010, Technical specification for space frame structures[S]. Beijing:China Architecture & Building Press, 2010. (in Chinese)
[15] Zhang R, Zhong H. Weak form quadrature element analysis of planar slender beams based on geometrically exact beam theory[J]. Archive of Applied Mechanics, 2013, 83(9):1309-1325.
[16] 肖乃佳. 基于几何精确梁理论的框架的弱形式求积元分析[D]. 北京:清华大学, 2011. Xiao Naijia. Weak-form quadrature element analysis of frames based on geometrically exact beam theory[D]. Beijing:Tsinghua University, 2011. (in Chinese)
[17] Mcrobie F A, Lasenby J. Simo-Vu Quoc rods using Clifford algebra[J]. International Journal for Numerical Methods in Engineering, 2015, 45(4):377-398.
[18] Park M S, Lee B C. Geometrically non-linear and elastoplastic three-dimensional shear flexible beam element of von-Mises-type hardening material[J]. International Journal for Numerical Methods in Engineering, 2015, 39(3):383-408.
[19] 叶康生, 吴可伟. 空间杆系结构的弹塑性大位移分析[J]. 工程力学, 2013, 30(11):1-8. Ye Kangsheng, Wu Kewei. Elasto-plastic large displacement analysis of spatial skeletal structures[J]. Engineering Mechanics, 2013, 30(11):1-8. (in Chinese)
[20] 陈绍蕃, 顾强. 钢结构. 上册, 钢结构基础[M]. 第3版. 北京:中国建筑工业出版社, 2014:88. Chen Shaofan, Gu Qiang. Steel structures volume one:Basic knowledge of steel structures[M]. 3rd ed. Beijing:China Architecture & Building Press, 2014:88. (in Chinese)
[1] 关少钰, 白涌滔. 基于双剪统一强度理论应变退化模型的隧道结构稳定性分析[J]. 工程力学, 2018, 35(S1): 205-211.
[2] 楚留声, 刘静, 王伸伟, 赵军. SRC柱-钢梁混合框架直接基于位移的抗震设计方法研究[J]. 工程力学, 2018, 35(8): 100-110.
[3] 王宇航, 余洁, 吴强. 复杂循环路径下钢材弹塑性屈曲行为研究[J]. 工程力学, 2018, 35(7): 24-38.
[4] 孔宪京, 陈楷, 邹德高, 刘锁, 余翔. 一种高效的FE-PSBFE耦合方法及在岩土工程弹塑性分析中的应用[J]. 工程力学, 2018, 35(6): 6-14.
[5] 原园, 成雨, 张静. 基于分形的三维粗糙表面弹塑性接触力学模型与试验验证[J]. 工程力学, 2018, 35(6): 209-221.
[6] 王小雯, 张建民. 随机波浪作用下饱和砂质海床弹塑性动力响应规律[J]. 工程力学, 2018, 35(6): 240-248,256.
[7] 李勇, 闫维明, 刘晶波, 解梦飞. 近断层高架连续梁桥地震易损性与振动台试验研究[J]. 工程力学, 2018, 35(4): 52-60,86.
[8] 张爱林, 郭志鹏, 刘学春, 李超. 装配式建筑双槽钢组合截面梁整体稳定系数研究[J]. 工程力学, 2018, 35(2): 67-75.
[9] 孙宝印, 古泉, 张沛洲, 欧进萍. 考虑P-Δ效应的框架结构弹塑性数值子结构分析[J]. 工程力学, 2018, 35(2): 153-159.
[10] 杨博雅, 吕西林. 预应力预制混凝土剪力墙结构直接基于位移的抗震设计方法及应用[J]. 工程力学, 2018, 35(2): 59-66,75.
[11] 连鸣, 苏明周, 李慎. Y形高强钢组合偏心支撑框架结构基于性能的塑性设计方法研究[J]. 工程力学, 2017, 34(5): 148-162.
[12] 张鹏飞, 罗尧治, 杨超. 基于有限质点法的三维固体弹塑性问题求解[J]. 工程力学, 2017, 34(4): 5-12.
[13] 王萌, 钱凤霞, 杨维国, 杨璐. 低屈服点钢材与Q345B和Q460D钢材本构关系对比研究[J]. 工程力学, 2017, 34(2): 60-68.
[14] 张耀庭, 张江, 杨力. 预应力度对预应力混凝土框架结构抗震性能影响研究[J]. 工程力学, 2017, 34(2): 129-136.
[15] 顾永超, 陈伟球, 刘伟, 杨庆大. 弹塑性杆非线性断裂问题的新型增强有限元法[J]. 工程力学, 2017, 34(11): 1-8.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
[1] 李天娥, 孙晓颖, 武岳, 王长国. 平流层飞艇气动阻力的参数分析[J]. 工程力学, 2019, 36(1): 248 -256 .
[2] 管俊峰, 姚贤华, 白卫峰, 陈记豪, 付金伟. 由小尺寸试件确定混凝土的断裂韧度与拉伸强度[J]. 工程力学, 2019, 36(1): 70 -79,87 .
[3] 高良田, 王键伟, 王庆, 贾宾, 王永魁, 石莉. 破冰船在层冰中运动的数值模拟方法[J]. 工程力学, 2019, 36(1): 227 -237 .
[4] 高彦芳, 陈勉, 林伯韬, 金衍. 多相非饱和多重孔隙介质的有效应力定律[J]. 工程力学, 2019, 36(1): 32 -43 .
[5] 于潇, 陈力, 方秦. 一种量测松散介质对应力波衰减效应的实验方法及其在珊瑚砂中的应用[J]. 工程力学, 2019, 36(1): 44 -52,69 .
[6] 罗大明, 牛荻涛, 苏丽. 荷载与环境共同作用下混凝土耐久性研究进展[J]. 工程力学, 2019, 36(1): 1 -14,43 .
[7] 袁驷, 蒋凯峰, 邢沁妍. 膜结构极小曲面找形的一种自适应有限元分析[J]. 工程力学, 2019, 36(1): 15 -22 .
[8] 高山, 郑向远, 黄一. 非高斯随机过程的短期极值估计:复合Hermite模型[J]. 工程力学, 2019, 36(1): 23 -31 .
[9] 白鲁帅, 李钢, 靳永强, 李宏男. 一种隔离损伤的桁架结构性态识别方法[J]. 工程力学, 2019, 36(1): 53 -60 .
[10] 崔兆彦, 徐明, 陈忠范, 王飞. 重组竹钢夹板螺栓连接承载力试验研究[J]. 工程力学, 2019, 36(1): 96 -103,118 .
X

近日,本刊多次接到来电,称有不法网站冒充《工程力学》杂志官网,并向投稿人收取高额费用。在此,我们郑重申明:

1.《工程力学》官方网站是本刊唯一的投稿渠道(原网站已停用),《工程力学》所有刊载论文必须经本刊官方网站的在线投稿审稿系统完成评审。我们不接受邮件投稿,也不通过任何中介或编辑收费组稿。

2.《工程力学》在稿件符合投稿条件并接收后会发出接收通知,请作者在接到版面费或审稿费通知时,仔细检查收款人是否为“《工程力学》杂志社”,千万不要汇款给任何的个人账号。请广大读者、作者相互转告,广为宣传!如有疑问,请来电咨询:010-62788648。

感谢大家多年来对《工程力学》的支持与厚爱,欢迎继续关注我们!

《工程力学》杂志社

2018年11月15日