层状地基矩形板结构系统动力响应的一种数值解法
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摘要
为解决矩形板在动荷载作用下的动力反应,以矩形板和层状地基组成的系统为研究对象,建立有限元与无限元耦合模型,根据哈密尔顿原理推出系统的动力方程.用静力凝聚法及接触面的节点位移和板中面节点位移的几何关系,将地基反力用板中面节点位移和地基等效刚度来表示,从而把地基反力从系统中解耦出来,采用Wilson法导出系统的等效刚度矩阵和等效荷载列向量,求解出系统在弹性阶段的动力响应.结果表明:应用空间有限元与无限元模型很好的解决了人工边界的不足,使计算与实际更接近;解决了板与地基的耦合和无限元的质量矩阵的确定的难题,为无限元的应用提供有效的方法.
To solve the dynamic response of rectangle plate under dynamic load,the system composed of layered soil and rectangle plate is studied and the motion equation is deduced by the Hamilton's Principle.According to the static condensation and geometrical relationship of the nodes displacement on the contact surface and middle plane,the subgrade reaction is expressed by the nodes displacement of the middle plane and subgrade equivalent stiffness,so the subgrade reaction is decoupled out from the system.The equivalent stiffness matrix and equivalent load vector are deduced by Wilson method,and the dynamic responses in elastic step are solved.The results show that the coupling model solves the deficiency of artificial boundary condition,and the results agree with reality.The coupling problem of plate and foundation and the mass matrix of infinite element are solved,providing effective method for the application of infinite element.
To solve the dynamic response of rectangle plate under dynamic load,the system composed of layered soil and rectangle plate is studied and the motion equation is deduced by the Hamilton's Principle.According to the static condensation and geometrical relationship of the nodes displacement on the contact surface and middle plane,the subgrade reaction is expressed by the nodes displacement of the middle plane and subgrade equivalent stiffness,so the subgrade reaction is decoupled out from the system.The equivalent stiffness matrix and equivalent load vector are deduced by Wilson method,and the dynamic responses in elastic step are solved.The results show that the coupling model solves the deficiency of artificial boundary condition,and the results agree with reality.The coupling problem of plate and foundation and the mass matrix of infinite element are solved,providing effective method for the application of infinite element.
引文
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[2]UNGLESS R F.Aninfinite finite element[M].M A Sc.Thesis:University of British Columbia,1973.
[3]王元汉,李丽娟,李银平.有限元法基础与程序设计[M].广州:华南理工大学出版社,2002.WANG Yuan-han,LI Li-juan,LI Yin-ping.Finite element method base and programming[M].Guangzhou:SouthChina University of Technology Press,2002.
[4]QUEK S S,龙述尧,侯淑娟.有限元法实用教程[M].长沙:湖南大学出版社,2004.QUEK S S,LONG Shu-yao,HOU Shu-juan.Finite element method practical course[M].Changsha:Hunan Uni-versity Press,2004.
[5]潘昌实.隧道力学数学方法[M].北京:中国铁道出版社,1995.PAN Chang-shi.Tunnel mechanical mathematical method[M].Beijing:China Rail way Publishing House,1995.
[6]Bathe KJ,Wilson E L.Numerical Methods in Finite Element Analysis[M].Prentice-Hall,Inc,1976.
[7]姜忻良,徐余,郑刚.地下隧道-土体系地震反应分析的有限元与无限元耦合法[J].地震工程与工程振动,1999,19(3):22-26.JIANG Xin-liang,XU Yu,ZHENG Gang.Finite element and infinite element coupling method for seismic analysisof soil-underground tunnel system[J].Journal of Earthquake Engineering and Engineering Vibration,1999,19(3):22-26.
[8]徐赵东,郭迎庆.Matlab语言在建筑抗震工程中的应用[M].北京:科学出版社,2004.XU Zhao-dong,GUO Ying-qing.The application of Matlab in building seismic engineering[M].Beijing:SciencePress,2004.
[9]黄义,何芳社.弹性地基上的梁、板、壳[M].北京:科学出版社,2005.HUANG Yi,HE Fang-she.Beam,plate and shell on elastic foundation[M].Beijing:Science Press,2005.
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