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基于有限元和Duhamel积分的移动力问题分析方法研究

朱丹阳 张亚辉

朱丹阳, 张亚辉. 基于有限元和Duhamel积分的移动力问题分析方法研究[J]. 应用数学和力学, 2014, 35(12): 1287-1298. doi: 10.3879/j.issn.1000-0887.2014.12.001
引用本文: 朱丹阳, 张亚辉. 基于有限元和Duhamel积分的移动力问题分析方法研究[J]. 应用数学和力学, 2014, 35(12): 1287-1298. doi: 10.3879/j.issn.1000-0887.2014.12.001
ZHU Dan-yang, ZHANG Ya-hui. A Methodology Based on FEM and Duhamel Integration for Bridges Subjected to Moving Loads[J]. Applied Mathematics and Mechanics, 2014, 35(12): 1287-1298. doi: 10.3879/j.issn.1000-0887.2014.12.001
Citation: ZHU Dan-yang, ZHANG Ya-hui. A Methodology Based on FEM and Duhamel Integration for Bridges Subjected to Moving Loads[J]. Applied Mathematics and Mechanics, 2014, 35(12): 1287-1298. doi: 10.3879/j.issn.1000-0887.2014.12.001

基于有限元和Duhamel积分的移动力问题分析方法研究

doi: 10.3879/j.issn.1000-0887.2014.12.001
基金项目: 国家自然科学基金(11172056);国家重点基础研究发展计划(973计划)(2014CB046803)
详细信息
    作者简介:

    朱丹阳(1985—),男,湖南郴州人,博士生(E-mail: zhudy@mail.dlut.edu.cn);张亚辉(1972—),男,河北昌黎人,教授,博士生导师(通讯作者. E-mail: zhangyh@dlut.edu.cn).

  • 中图分类号: O326

A Methodology Based on FEM and Duhamel Integration for Bridges Subjected to Moving Loads

Funds: The National Natural Science Foundation of China(11172056);The National Basic Research Program of China (973 Program)(2014CB046803)
  • 摘要: 针对桥梁在移动力作用下的动力响应问题,提出了一种基于有限元模型和Duhamel积分的半解析分析方法,以此为基础,推导了多个移动力作用下桥梁动力响应的共振和相消条件.该方法基于桥梁有限元模型的振型,通过单元形函数构造桥面分段连续振型,得到Duhamel积分在任意桥面单元内的解析表达,将时间变量从被积函数中分离出去并利用积分的可加性,使得前面时刻的积分不必重复计算,因此每一个计算时间节点仅需计算一次简单积分和一次求和,这样极大地减少了计算时间.该方法在计算中未引入任何近似,且其精度与时间积分步长无关,是有限元模型下的解析解答.在数值算例中,分别针对简支梁和三跨连续桥梁,通过与解析解和Newmark法的对比,验证了该方法的精确性;然后针对多个移动力问题,验证了桥梁动力响应的共振和相消条件,探讨了载荷间距对复杂结构动力响应共振和相消的影响.
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出版历程
  • 收稿日期:  2014-10-08
  • 修回日期:  2014-10-21
  • 刊出日期:  2014-12-15

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