直接求解法在结构多点输入地震响应计算中的应用与改进
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摘要
将以绝对位移形式求解动力方程的直接求解法引入结构多点输入地震响应计算。与常用的将位移分解为拟静力绝对位移和相对动力位移的分解法相比,直接法的概念更为简洁,计算量小,且更适用于非线性计算。对于采用振型叠加法的直接法,仅使用少量低阶振型可能导致较大误差。引入静力修正方法,提出了高效的改进直接法。算例结果表明,修正直接法只需少量低阶振型即可获得足够的精度,精度与分解法相当。
The direct solving method,in which absolute displacement is utilized to solve dynamic equations,is proposed to analyze the seismic response of structures under multi-support excitations.Compared with the commonly used decomposition method,which decomposes the displacement into absolute pseudo-static displacement and relative dynamic displacement,the direct solving method is of a more concise concept as well as lower calculation complexity.And it is more suitable for nonlinear problems.As for the direct solving method combined with mode superposition method,calculation with only low order modes may cause large error.Thus static correction method is adopted to improve the precision of direct solving method.Results of numerical examples indicate that sufficient accuracy could be gained with fewer low order modes by using modified direct method.And it is also concluded that the precision of modified direct method is similar to that of decomposition method.
The direct solving method,in which absolute displacement is utilized to solve dynamic equations,is proposed to analyze the seismic response of structures under multi-support excitations.Compared with the commonly used decomposition method,which decomposes the displacement into absolute pseudo-static displacement and relative dynamic displacement,the direct solving method is of a more concise concept as well as lower calculation complexity.And it is more suitable for nonlinear problems.As for the direct solving method combined with mode superposition method,calculation with only low order modes may cause large error.Thus static correction method is adopted to improve the precision of direct solving method.Results of numerical examples indicate that sufficient accuracy could be gained with fewer low order modes by using modified direct method.And it is also concluded that the precision of modified direct method is similar to that of decomposition method.
引文
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[12]薛素铎,王雪生,曹资.基于新抗震规范的地震动随机模型参数研究[J].土木工程学报,2003,36(5):5―10.Xue Xuduo,Wang Xuesheng,Cao Zi.Parameters study on seismic random model based on the seismic code[J].China Civil Engineering Journal,2003,36(5):5―10.(in Chinese)
[2]Leger P,Ide I M,Paultre P.Multiple-support seismic analysis of large structures[J].Computers&Structures,1990,36(6):1153―1158.
[3]Kiureghian A D,Neuenhofer A.Response spectrum method for multi-support seismic excitations[J].Earthquake Engineering&Structural Dynamics,1992,21(8):713―740.
[4]Ernesto H Z,Vanmarcke E H.Seismic random-vibration analysis of multisupport-structural systems[J].Journal of Engineering Mechanics,1994,120(5):1107―1128.
[5]Lin J H,Zhang Y H,Li Q S,Williams F W.Seismic spatial effects for long-span bridges,using the pseudo excitation method[J].Engineering Structures,2004,26(9):1207―1216.
[6]Abdullateef M A,Ashraf A.An efficient multi-point support-motion random vibration analysis technique[J].Computers&Structures,2002,80:1689―1697.
[7]Clough R W,Penzien J.Dynamics of structures[M].New York:McGraw-Hill,1993.
[8]Hansteen O E,Bell K.On the accuracy of mode superposition analysis in structural dynamics[J].Earthquake Engineering&Structural Dynamics,1979,7(5):405―411.
[9]林家浩,钟万勰,张亚辉.大跨度结构抗震计算的随机振动方法[J].建筑结构学报,2000,21(1):29―36.Lin Jiahao,Zhong Wanxie,Zhang Yahui.Seismic analysis of long span structures by means of random vibration approach[J].Journal of Building Structures,2000,21(1):29―36.(in Chinese)
[10]Lin J H,Zhang W S.A fast CQC algorithm of PSD matrices for random seismic responses[J].Computers&Structures,1992,44(3):683―687.
[11]Luco J,Wong H.Response of a rigid foundation to a spatially random ground motion[J].Earthquake Engineering&Structural Dynamics,1986,14(8):891―908.
[12]薛素铎,王雪生,曹资.基于新抗震规范的地震动随机模型参数研究[J].土木工程学报,2003,36(5):5―10.Xue Xuduo,Wang Xuesheng,Cao Zi.Parameters study on seismic random model based on the seismic code[J].China Civil Engineering Journal,2003,36(5):5―10.(in Chinese)
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