基于有限元和Duhamel积分的移动力问题分析方法研究  

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

作　　者：朱丹阳[1] 张亚辉[1] 

机构地区：[1]工业装备结构分析国家重点实验室(大连理工大学),辽宁大连116024

出　　处：《应用数学和力学》2014年第12期1287-1298,共12页Applied Mathematics and Mechanics

基　　金：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)~~

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.Based on the finite element （FE） method and Duhamel integration, a numerical-an- alytical combined method for the dynamic response problem of an FE bridge under moving loads was proposed, and the conditions of resonance and cancellation for the bridge subjected to multiple moving loads were derived. The FE modes of the bridge structure were first compu- ted and then converted into an analytical form constructed over all the elements of the bridge deck with the element shape functions. The analytical dynamic responses of the bridge were de- rived from Duhamel integration, and transformed into a simple integration and a summation of the previous results through elimination of the time variable from the integration, which enables the computation process more efficient. The proposed approach has the vemafility of the FE method in dealing with structures of arbitrary configurations and the special efficiency and con- venience of the analytical method in dealing with moving loads. In the numerical examples, the present method is verified with the Newmark method and the traditional analytical method based on a simply supported beam bridge and a 3-span continuous beam bridge. The results show that the accurate solution of the FE structures subjected to moving loads is obtained with the present method, and no approximation is introduced during the computation process. The conditions of resonance and cancellation are discussed for the problems with multiple moving load, and the influence of the load distances on the responses of the bridge is also revealed.

关 键 词：移动力 桥梁 有限元法 共振和相消 

分 类 号：O326[理学—一般力学与力学基础]