框筒结构弯扭耦合分析的精细积分法
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摘要
筒体结构被广泛应用于建筑结构中,但是筒体结构在弯扭荷载作用下存在着纵向翘曲位移,降低了结构的整体空间刚度,使得筒体结构向更高的高度发展时候存在困难,筒体结构的研究备受学者关注。经典的弯曲理论对筒体结构并不适用。所以对筒体结构的内力和位移研究具有重要意义。本文根据连续化原理,把框筒等效连续化为由各向异性板和角柱围成的等效实腹薄壁筒,引入纵向位移的插值函数,建立了结构在水平和竖向荷载影响下的框筒结构弯扭分析的哈密顿对偶求解体系,用精细积分法求该体系的高精度数值解。具体研究内容如下:
(1)本文根据连续化原理,把框筒等效连续化为由正交各向异性板和角柱围成的等效实腹薄壁筒,建立了筒体的等效连续化力学模型。
(2)根据能量原理,导出了考虑框筒结构弯扭问题的对偶求解体系。对框筒结构进行二阶分析和动力特性分析.
(3)利用有限元软件ETABS对框筒结构进行模拟分析,所得结果与本文结果进行对比。利用对柱轴向内力的模拟计算从而反映出结构的纵向内力分布。
(4)对上述求解体系应用精细积分法求解,此求解过程可通过在MATLAB语言平台下编制的程序来实现,分析了筒体结构在弯扭作用下的侧移和轴向内力,计算了一定算例并通过与其它方法有限元软件对比,结果吻合较好,表明了本文方法的合理性与可行性。
本文应用的是基于精细积分的差值函数分析筒体结构的理论方法。所编制程序无论对于对双轴称截面还是对单轴称截面,能解决在常见的多种水平荷载和扭矩同时作用下筒体的位移和内力计算。应用本课题的研究成果对工程设计具有一定的指导意义。
The tube structure is widely used in tall building, however, there is an especial feature of tube action on horizontal load—Shear Lag Effect. Then, the unitary special strength is falling. Problems come when building is much higher. Tube structure anslysis attracts schilar. The classic banding theory is invalid. It is significant in tube sutructure analysis. According to the continuous principle, frame-tube structure is made equal to solid thin-walled tube which is enclosed with orthotropic plates and corner column, and its continuous mechanical model is founded. The thesis introduces the vertical displacement of interpllateing function and establishs Hamilton duality solution system of rube strucrure. The high precision numerial solution is solved through precise time-step nitegration method.
(1) According to the continuous principle, frame-tube structure is made equal to solid thin-walled tube which is enclosed with orthotropic plates and corner column, and its continuous mechanical model is founded. And make analysis of second-order and dynamic characteristcs about tube structure.
(2) According to the energy principle, deduces the duality solution system of tube structure. And make analysis of second-order and dynamic characteristcs about tube structure.
(3) Finite element analysis software ETABS is used to analyze and simulate the tube strcture. The results are compared with the article. Calculate the axit internal force and reflect the axit internal force of instruction.
(4) Precise integration method is applied to solving solution system above which is implemented by program upon MATLAB language. The lateral displacement and Axial internal force can be gained, and the result is compared with those from other methods which turns out to be good agreement. It proves that the method in this thesis is reasonable and feasible. By comparing the results of Hamilton duality solution system, it shows that the shear-lag effect can’t be ignored in tube structure. Detail analysis about shear-lag effect and several factors which may influence the effect are made. The load type, variable-section or uniform-section, the ratio of height to width and the ratio of hole on the shear-lag effect are studied.
A new method to analyze the tube structure is offered in this paper. Both symmetric and asymmetric section, uniform and non-uniform section tube structure under usual types of load and twist moment can all be solved. The research findings of this paper can guide the design in engineering.
(1)本文根据连续化原理,把框筒等效连续化为由正交各向异性板和角柱围成的等效实腹薄壁筒,建立了筒体的等效连续化力学模型。
(2)根据能量原理,导出了考虑框筒结构弯扭问题的对偶求解体系。对框筒结构进行二阶分析和动力特性分析.
(3)利用有限元软件ETABS对框筒结构进行模拟分析,所得结果与本文结果进行对比。利用对柱轴向内力的模拟计算从而反映出结构的纵向内力分布。
(4)对上述求解体系应用精细积分法求解,此求解过程可通过在MATLAB语言平台下编制的程序来实现,分析了筒体结构在弯扭作用下的侧移和轴向内力,计算了一定算例并通过与其它方法有限元软件对比,结果吻合较好,表明了本文方法的合理性与可行性。
本文应用的是基于精细积分的差值函数分析筒体结构的理论方法。所编制程序无论对于对双轴称截面还是对单轴称截面,能解决在常见的多种水平荷载和扭矩同时作用下筒体的位移和内力计算。应用本课题的研究成果对工程设计具有一定的指导意义。
The tube structure is widely used in tall building, however, there is an especial feature of tube action on horizontal load—Shear Lag Effect. Then, the unitary special strength is falling. Problems come when building is much higher. Tube structure anslysis attracts schilar. The classic banding theory is invalid. It is significant in tube sutructure analysis. According to the continuous principle, frame-tube structure is made equal to solid thin-walled tube which is enclosed with orthotropic plates and corner column, and its continuous mechanical model is founded. The thesis introduces the vertical displacement of interpllateing function and establishs Hamilton duality solution system of rube strucrure. The high precision numerial solution is solved through precise time-step nitegration method.
(1) According to the continuous principle, frame-tube structure is made equal to solid thin-walled tube which is enclosed with orthotropic plates and corner column, and its continuous mechanical model is founded. And make analysis of second-order and dynamic characteristcs about tube structure.
(2) According to the energy principle, deduces the duality solution system of tube structure. And make analysis of second-order and dynamic characteristcs about tube structure.
(3) Finite element analysis software ETABS is used to analyze and simulate the tube strcture. The results are compared with the article. Calculate the axit internal force and reflect the axit internal force of instruction.
(4) Precise integration method is applied to solving solution system above which is implemented by program upon MATLAB language. The lateral displacement and Axial internal force can be gained, and the result is compared with those from other methods which turns out to be good agreement. It proves that the method in this thesis is reasonable and feasible. By comparing the results of Hamilton duality solution system, it shows that the shear-lag effect can’t be ignored in tube structure. Detail analysis about shear-lag effect and several factors which may influence the effect are made. The load type, variable-section or uniform-section, the ratio of height to width and the ratio of hole on the shear-lag effect are studied.
A new method to analyze the tube structure is offered in this paper. Both symmetric and asymmetric section, uniform and non-uniform section tube structure under usual types of load and twist moment can all be solved. The research findings of this paper can guide the design in engineering.
引文
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[2] Fazler.R.KhanA,N.R.Amln.Analysis and Design of Framed Tube Structures for Tall Concrete Building,Publication SOP-36,ACI,1973.
[3]黄本才.高层建筑结构计算与设计[M].上海:同济大学出版社,1997.
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[6]黄本才.高层建筑结构计算与设计[M].上海:同济大学出版社,1997.
[7] Burgan B.A.,Dowling P.J.The treatment of shear lag in design[J].Thin—Walled Structures,1990,(9):121~134
[8]陈岳辉,陈荣毅,刘斌.角柱刚度对筒体结构剪力滞后效应影响的研究[J].四川建筑科学研究,1999,(1):3~5
[9]高雁,李正良.高层筒体结构剪力滞后研究[J].西南科技大学学报.2006,21(2):15~19
[10]王荫长.高层建筑筒体结构的计算[M].北京:科学出版社,1988.
[11]朱幼麟.筒中筒结构的简化计算[J].建筑结构学报,1984, (2):921
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[13]丁皓江等.弹性和塑性力学中的有限单元法(第二版).北京:机械工业出版社,1989
[14]张文福,姚芳.三角形高层框筒结构在水平荷载作用下剪力滞后的有限元分析[J].四川建筑科学研究,2005,31(1):45~47
[15]艾长东等.矩形高层框筒结构在水平荷载作用下剪力滞后的有限元分析[J].大庆石油学院学报,2005,29(3):80~82
[16] Maffatt K R,Dowling P J.Share lag in steel box girder bridges[J].Structure Engineering.1975,53(10):439~448
[17]经柏林,邵旭东,鲍卫刚.变截面长悬臂宽箱梁桥翼缘有效宽度研究[J].中南公路工程.1998,23(4):24~26
[18]程祥云,李立峰.对连续箱梁翼缘有效宽度公式的评述[J].公路.2001,(3):7~9
[19]李景涌.有限元法[M].北京邮电大学出版社,1999
[20] CheungYK.结构分析的有线条元法[M].谢秀松等译.北京:人民交通出版社,1980
[21] A.K.H.Kwan.Equivalence of finite elements and analogous frame modules for shear/core wall analysis,Computers and Structures,1995(2)
[22] P.C.Boggs,D.A.Gasparinis.Rateral stiffness of core–outrigger systerms,AISC Engineering Journal, 1983(1)
[23]胡绍隆,徐建平.用有限条法计算高层建筑筒体结构[J].建筑结构,1983,13(5):71~76
[24]陈刚,李家宝.广义位移的有限条法及其在高层建筑结构分析中的应用[J].建筑结构学报,1988,9(3):152~158
[25]钱伟长.变分法及有限元(上册),北京:科学出版社,1980
[26]刘开国.结构简化计算原理及其应用[M].北京:科学技术出版社,1996
[27]刘开国.高层建筑结构的能量变分解[J].建筑结构学报,1982,3(3):23~24
[28]龙驭球,辛克贵.多边形截面框筒结构的能量变分解法[J].建筑结构学报,1985,6(3):10~16
[29]刘开国.变截面高层框筒结构的矩阵传递法.力学与实践,2004,(4):34-37
[30]徐彬,夏峰,梁启智.考虑剪力滞后框筒结构位移解析解[J].昆明理工大学学报, 1998,23(6) 75-83.
[31]陆铁坚.高层建筑筒体结构静力,动力特性和稳定分析[D].西安:西安建筑科技大学建筑工程系,1987
[32]包世华,周坚.薄壁杆件结构力学[M].中国建筑工业出版社.2006.
[33]包世华.高层建筑结构解析-半解析微分方程求解器解法系列.[J]中国学术期刊文摘增刊.1995.135.
[34]包世华,李华煜.高层建筑结构分析的半解析微分方程求解器法.[J]工程力学增刊.1993.7~18.
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