工程力学 ›› 2018, Vol. 35 ›› Issue (7): 94-103,149.doi: 10.6052/j.issn.1000-4750.2017.03.0197

• 土木工程学科 • 上一篇    下一篇

考虑荷载分布模式的弯剪型结构最优刚度分布解析研究

何浩祥1,2, 王文涛1, 范少勇1   

  1. 1. 北京工业大学工程抗震与结构诊治北京市重点实验室, 北京 100124;
    2. 首都世界城市顺畅交通北京市协同创新中心, 北京 100124
  • 收稿日期:2017-03-14 修回日期:2017-12-28 出版日期:2018-07-25 发布日期:2018-07-26
  • 通讯作者: 何浩祥(1978-),男,辽宁人,教授,博士,从事结构抗震减震及健康监测研究(E-mail:hhx7856@163.com). E-mail:hhx7856@163.com
  • 作者简介:王文涛(1991-),男,河北人,硕士生,主要从事结构抗震减震研究(E-mail:S201504183@emails.bjut.edu.cn);范少勇(1992-),男,河北人,硕士生,主要从事结构抗震减震研究(E-mail:fansghaoyon@emails.bjut.edu.cn).
  • 基金资助:
    国家自然科学基金项目(51478024);工程抗震与结构诊治北京市重点实验室重点项目(USDE201403).

ANALYTICAL STUDY ON OPTIMAL STIFFNESS DISTRIBUTION OF BEND-SHEAR STRUCTURES CONSIDERING LOAD DISTRIBUTION

HE Hao-xiang1,2, WANG Wen-tao1, FAN Shao-yong1   

  1. 1. Beijing Key Lab of Earthquake Engineering and Structural Retrofit, Beijing University of Technology, Beijing, 100124, China;
    2. Beijing Collaborative Innovation Center for Metropolitan Transportation, Beijing 100124, China
  • Received:2017-03-14 Revised:2017-12-28 Online:2018-07-25 Published:2018-07-26

摘要: 如果结构在外部激励下产生均匀损伤或均匀变形,则可避免出现薄弱层且可提高承载能力和安全性,以此为目标进行结构优化具有重要意义。将弯剪型结构简化为连续变截面悬臂杆,假定结构截面函数具有自然指数型和幂函数型等形式,将地震和风荷载等外部激励等效为均布、倒三角和惯性相关等三种荷载分布模式。根据均匀变形准则将结构绝对位移曲线关于高度的二次导数为零作为优化目标,建立结构连续化位移方程并进行优化求解,获得了考虑荷载分布形式的弯剪型结构最优刚度和截面分布解析解。理论和数值分析结果表明:截面按幂函数变化的结构能够实现均匀损伤,不同荷载分布模式下的最优刚度或截面分布有所不同。有限元静动力分析结果进一步验证了解析解的准确性和实用性。

关键词: 均匀损伤, 最优截面, 刚度分布, 层间位移角, 地震作用

Abstract: For structures subjected to external excitation, the weak layers can be avoided and the bearing capacity and safety can be improved if all the damage degrees or the relative displacements of each story are the same, i.e., the uniform damage or uniform deformation occurs. It is significant to carry out structural optimization with uniform damage as the optimization objective. The bend-shear structure is simplified as a continuous variable cross-section cantilever. The assumed cross section functions include the forms of a natural exponential function and a power function. The external excitation such as earthquake effects and wind loads are idealized to three load modes, that is, the uniform distribution, the inverted triangle distribution and the inertia correlation distribution. According to the uniform deformation criterion, to make the second derivative of the absolute displacement curve of the structure equals zero is taken as the optimization target. The continuous displacement equation is established and the optimization results are discussed. The analytical solution of the optimal stiffness and the cross section distribution of the bend-shear structure is obtained. According to the theoretical and numerical results, the uniform damage can be realized if the cross section function is taken as power function, and the optimal distributions of stiffness and cross sections are different for different load distribution modes. The accuracy and the practicability of the analytical solution is verified by static-dynamic analysis based on the finite element method.

Key words: uniform damage, optimal section, stiffness distribution, story drift angle, earthquake action

中图分类号: 

  • TU311.1
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