高层结构动力响应的波动分析方法
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摘要
目的提出高层结构动力响应的波动分析方法.方法取楼板及上下各半层结构建立控制体,基于Timoshenko梁理论,对其控制方程组进行空间离散,建立控制体平动和转动的动力学方程,给出层间弯矩和楼板转角关系式以及层间剪力与楼板位移和楼板转角的关系式.利用这些离散型方程组,在时间域上交替递推计算,给出高层结构动力响应数值计算的波动分析方法.结果与有限元方法进行对比,验证了该方法的有效性;数值算例表明,高层结构受地震作用时,其转动惯性和剪切变形对结构响应影响较大,进行结构动力分析时不应忽略.结论该方法适用于计算高层结构的地震响应问题,从波动角度为研究高层结构的动力响应分析提供了一种新的途径.
The numerical method based on the wave approach is presented for the dynamic response analysis of high-rise structure by applying Timoshenko beam theory.The typical controlled volume was constructed with the floor and the upper and lower half-storey.The dynamic equilibrium equations and the rotation equations of the controlled volumes were established after the discretization of the governing equations of Timoshenko beam theory.The relationship between the bending moment of the interlayer and the rotational angles of the floors,and the relationship between the shear force of the interlayer and floor displacements as well as the rotational angles of the floors were given.By applying the equations provided above and computing alternately in time domain,the numerical method was presented for the dynamic response analyses of high-rise structure from the wave point of view.The validity of the method was tested by comparing its computational results with the corresponding results of the finite element method.Investigations demonstrate that the rotational inertia and the shear deformation of the structure should not be omitted in the dynamic response analyses when the high-rise structure is subjected to seismic loading.The method provides a new approach from the wave point of view for analyzing the dynamic responses of high-rise structure subjected to seismic loading.
The numerical method based on the wave approach is presented for the dynamic response analysis of high-rise structure by applying Timoshenko beam theory.The typical controlled volume was constructed with the floor and the upper and lower half-storey.The dynamic equilibrium equations and the rotation equations of the controlled volumes were established after the discretization of the governing equations of Timoshenko beam theory.The relationship between the bending moment of the interlayer and the rotational angles of the floors,and the relationship between the shear force of the interlayer and floor displacements as well as the rotational angles of the floors were given.By applying the equations provided above and computing alternately in time domain,the numerical method was presented for the dynamic response analyses of high-rise structure from the wave point of view.The validity of the method was tested by comparing its computational results with the corresponding results of the finite element method.Investigations demonstrate that the rotational inertia and the shear deformation of the structure should not be omitted in the dynamic response analyses when the high-rise structure is subjected to seismic loading.The method provides a new approach from the wave point of view for analyzing the dynamic responses of high-rise structure subjected to seismic loading.
引文
[1]Anil K.Chopra.结构动力学理论及其在地震工程中的应用[M].谢礼立,吕大刚译.北京:高等教育出版社,2007.
[2]赵振东.钢混结构物受外来飞射体撞击的破坏效应研究[J].地震工程与工程振动,2003,23(5):88-94.
[3]王元清,黄怡,石永久,等.超高层钢结构建筑动力特性与抗震性能的有限元分析[J].土木工程学报,2006,39(5):65-71.
[4]Yakut A,Gulkan P.Numerical simulation of dynamicshear wall tests:A benchmark study[J].Computersand Structures,2006,84:549-562.
[5]Rocha P,Delgado P,Costa A.Seismic retrofit of RCframes[J].Computers and Structures,2004,82:1523-1534.
[6]Jun Ji,Elnashai A S,Kuchma D A.An analyticalframework for seismic fragility analysis of RC high-rise buildings[J].Engineering Structures,2007,29:3197-3209.
[7]Wilkinson S M,Hiley R A.A non-linear responsehistory model for the seismic analysis of high-riseframed buildings[J].Computers and Structures,2006,84:318-329.
[8]Yong Lu.An analytical model for dynamic response ofbeam-column frames to impulsive ground excitations[J].International Journal of Solids and Structures,2007,44:779-798.
[9]Dong-Guen Leea,Sang-Kyoung Ahnb,Dae-KonKimc.Efficient seismic analysis of building structureincluding floor slab[J].Engineering Structures,2005,27:675-684.
[10]Tarnow N,Simo J C.How to render second order ac-curate time-stepping algorithms fourth order accu-rate while retaining the stability and conservationproperties[J].Computer Methods in Applied Me-chanics and Engineering,1994,115:233-252.
[11]Liu Tielin,Liu Kaishin,Zhang Jinxiang.Unstructuredgird method for stress wave propagation in elastic me-dia[J].Comput.Methods Appl Mech.Engrg.,2004,193(23-26):2427-2452.
[12]Liu T,Liu K,Zhang J.Triangular grid method forstress-wave propagation in 2-D orthotropic mate-rials[J].Archive of Applied Mechanics,2005,74:477-488.
[13]刘铁林,张俏,钟伟.弹性介质中SH波传播的三角形格子法[J].沈阳建筑大学学报:自然科学版,2007,23(5):709-712.
[2]赵振东.钢混结构物受外来飞射体撞击的破坏效应研究[J].地震工程与工程振动,2003,23(5):88-94.
[3]王元清,黄怡,石永久,等.超高层钢结构建筑动力特性与抗震性能的有限元分析[J].土木工程学报,2006,39(5):65-71.
[4]Yakut A,Gulkan P.Numerical simulation of dynamicshear wall tests:A benchmark study[J].Computersand Structures,2006,84:549-562.
[5]Rocha P,Delgado P,Costa A.Seismic retrofit of RCframes[J].Computers and Structures,2004,82:1523-1534.
[6]Jun Ji,Elnashai A S,Kuchma D A.An analyticalframework for seismic fragility analysis of RC high-rise buildings[J].Engineering Structures,2007,29:3197-3209.
[7]Wilkinson S M,Hiley R A.A non-linear responsehistory model for the seismic analysis of high-riseframed buildings[J].Computers and Structures,2006,84:318-329.
[8]Yong Lu.An analytical model for dynamic response ofbeam-column frames to impulsive ground excitations[J].International Journal of Solids and Structures,2007,44:779-798.
[9]Dong-Guen Leea,Sang-Kyoung Ahnb,Dae-KonKimc.Efficient seismic analysis of building structureincluding floor slab[J].Engineering Structures,2005,27:675-684.
[10]Tarnow N,Simo J C.How to render second order ac-curate time-stepping algorithms fourth order accu-rate while retaining the stability and conservationproperties[J].Computer Methods in Applied Me-chanics and Engineering,1994,115:233-252.
[11]Liu Tielin,Liu Kaishin,Zhang Jinxiang.Unstructuredgird method for stress wave propagation in elastic me-dia[J].Comput.Methods Appl Mech.Engrg.,2004,193(23-26):2427-2452.
[12]Liu T,Liu K,Zhang J.Triangular grid method forstress-wave propagation in 2-D orthotropic mate-rials[J].Archive of Applied Mechanics,2005,74:477-488.
[13]刘铁林,张俏,钟伟.弹性介质中SH波传播的三角形格子法[J].沈阳建筑大学学报:自然科学版,2007,23(5):709-712.
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