基于无单元法的平面框架地震反应分析
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摘要
无单元法在动力计算领域中的应用目前多以梁、板等简单构件的自振特性分析为主,对建筑结构的动力计算,尤其是地震反应分析尚未涉及.文中推导了无单元法的离散动力方程,以轴力杆、欧拉梁模型为基础,将简单构件的无单元动力计算推进到实际结构的地震反应分析,并给出了数值实现的基本流程.最后以一个十一层钢筋混凝土高层结构为算例,实现了多层多跨平面框架的无单元地震反应分析,达到了预期的效果,验证了无单元法应用于平面框架地震反应分析的可行性和有效性.
Dynamic characteristic analysis of beams and plates is the main subject investigated of Element-Free Galerkin Method (EFG) presently in dynamic calculation,but dynamic calculation of structures in engineering,especially earthquake response analysis is not involved.In this paper,discrete dynamic equation for EFG is deduced.Based on axial pole model and Euler beam model,the new method is advanced from simple members to a construction and the flow of numerical calculation is given.An eleven-storey reinforced concrete building is calculated.In the history of EFG research,the earthquake response analysis of planar frame is first made and achieved the anticipated effect.It is confirmed that the new method is feasible and effective for the study of earthquake response analysis of planar frame.
Dynamic characteristic analysis of beams and plates is the main subject investigated of Element-Free Galerkin Method (EFG) presently in dynamic calculation,but dynamic calculation of structures in engineering,especially earthquake response analysis is not involved.In this paper,discrete dynamic equation for EFG is deduced.Based on axial pole model and Euler beam model,the new method is advanced from simple members to a construction and the flow of numerical calculation is given.An eleven-storey reinforced concrete building is calculated.In the history of EFG research,the earthquake response analysis of planar frame is first made and achieved the anticipated effect.It is confirmed that the new method is feasible and effective for the study of earthquake response analysis of planar frame.
引文
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[8]徐小丽,殷祥超,朱福先.无网格法在振动分析中的应用初探[J].太原理工大学学报,2005,36(6):630-633.(Xu Xiaoli,Yin Xiangchao,Zhu Fuxian.Preli mi-nary study of application in vibration analysis with meshless method[J].Journal of Taiyuan University of Technology,2005,36(6):630-633.(in Chinese))
[9]秦雅菲,张伟星,张其林.无单元法求解正交各向异性板自由振动问题[J].力学季刊,2006,27(1):153-161.(Qin Yafei,Zhang Weixing,Zhang Qilin.Element free method in vibration problemof anisotropic plates[J].Chinese Quarterly of Mechanics,2006,27(1):153-161.(in Chinese))
[10]张雄,刘岩.无网格法[M].北京:清华大学出版社,2004,8.(Zhang Xiong,Liu Yan.Meshless Methods[M].Beijing:Tsinghua University Publishing House,2004,8.(in Chinese))
[11]Atluri S N,Cho J Y,Ki m H G.Analysis of thin beams,using the meshless local Petrov-Galerkin method,with generalized moving least squares inter-polations[J].Computational Mechanics,1999,24:334-324.
[2]Belytschko T,Lu Y Y,Gu L.Element-free Galerkin methods[J].International Journal for Numerical Methods in Engineering,1994,37:229-256.
[3]Nagashi ma Toshio.Node-by-node meshless approach and its applications to structural analyses[J].Inter-national Journal for Numerical Method s in Engineer-ing,1999,46:341-385.
[4]Liu WK,Jun S,Zhang Y F.Reproducing kernel parti-cle methods for structural dynamics[J].International Journal for Numerical Methods in Engineering,1995,38:1655-1679.
[5]Ouatouati A EI,Johnson D A.New approach for nu-merical modal analysis using the element-free method[J].International Journal for Numerical Methods in Engineering,1999,46:1-27.
[6]Liu G R,Chen X L.A mesh-free methodfor static and free vibration analyses of thin plates of complicated shape[J].Journal of Sound and Vibration,2001,241(5),839-855.
[7]李卧东,陈胜宏.无单元法在结构动力分析中的应用[J].武汉大学学报(工学版),2003,36(2):15-19.(Li Wodong,Chen Shenghong.Application of element-free method to structural vibration analysis[J].Engi-neering Journal of Wuhan University,2003,36(2):15-19.(in Chinese))
[8]徐小丽,殷祥超,朱福先.无网格法在振动分析中的应用初探[J].太原理工大学学报,2005,36(6):630-633.(Xu Xiaoli,Yin Xiangchao,Zhu Fuxian.Preli mi-nary study of application in vibration analysis with meshless method[J].Journal of Taiyuan University of Technology,2005,36(6):630-633.(in Chinese))
[9]秦雅菲,张伟星,张其林.无单元法求解正交各向异性板自由振动问题[J].力学季刊,2006,27(1):153-161.(Qin Yafei,Zhang Weixing,Zhang Qilin.Element free method in vibration problemof anisotropic plates[J].Chinese Quarterly of Mechanics,2006,27(1):153-161.(in Chinese))
[10]张雄,刘岩.无网格法[M].北京:清华大学出版社,2004,8.(Zhang Xiong,Liu Yan.Meshless Methods[M].Beijing:Tsinghua University Publishing House,2004,8.(in Chinese))
[11]Atluri S N,Cho J Y,Ki m H G.Analysis of thin beams,using the meshless local Petrov-Galerkin method,with generalized moving least squares inter-polations[J].Computational Mechanics,1999,24:334-324.
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