结构地震反应分析的一种新精细积分法
|
摘要
将Newmark法中常平均加速度法的基本假定与更新精细积分方法结合起来,提出了一种新精细积分法,并应用于结构的地震反应分析中。推导了该方法的计算公式,对其稳定性进行了分析。与更新精细积分法相比,在实现动力微分方程降阶后,矩阵尺度和方程个数减少一半;并且迭代公式直观,可以非常方便地求出结构在地震作用下的位移、速度和加速度反应。提出的方法虽然是条件稳定的,但是其稳定性条件极易满足。算例表明方法的有效性及对地震作用的较好的适应性。
Combining the RPTSIM (renewal precise time step integration method) with the basic assumptions of constant average acceleration method of the Newmark family, a new precise integration method is presented and applied to structural seismic response analysis. Calculation formulas and stability of the proposed method are analyzed. When the order of dynamic differential equation is reduced, the size of matrices and equations of the proposed method are only half of that of the RPTSIM. Iterative formulas are straight-forward and the seismic response of displacement, velocity and acceleration can be obtained more conveniently. Although the presented method is conditionally stable, the conditions are very easy to be satisfied. Numerical studies indicate that the proposed method is effective and applicable to analyzing earthquake action.
Combining the RPTSIM (renewal precise time step integration method) with the basic assumptions of constant average acceleration method of the Newmark family, a new precise integration method is presented and applied to structural seismic response analysis. Calculation formulas and stability of the proposed method are analyzed. When the order of dynamic differential equation is reduced, the size of matrices and equations of the proposed method are only half of that of the RPTSIM. Iterative formulas are straight-forward and the seismic response of displacement, velocity and acceleration can be obtained more conveniently. Although the presented method is conditionally stable, the conditions are very easy to be satisfied. Numerical studies indicate that the proposed method is effective and applicable to analyzing earthquake action.
引文
[1]Newmark N M.A method of computation for structural dynamics[J].Journal of Engineering Mechanics Division,1959,85:67~94.
[2]Golley B W.A time-stepping procedure for structural dynamics using Gauss point collocation[J].International Journal for Numerical Methods in Engineering,1996,39:3985~3998.
[3]Tarnow N,Simo J C.How to render second order accurate time stepping algorithms fourth order accurate while retaining the stability and conservation properties[J].Computer Methods in Applied Mechanics and Engineering,1994,115:233~252.
[4]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,34(2):131~136.Zhong Wanxie.On precise time-integration method for structural dynamics[J].Journal of Dalian University ofTechnology,1994,34(2):131~136.(in Chinese)
[5]Zhong W X,Williams F W.A precise time step integration method[J].Journal of Mechanical Engineering Science,1994,208:427~430.
[6]张洪武.关于动力分析精细积分算法精度的讨论[J].力学学报,2001,33(6):847~852.Zhang Hongwu.Discussion on the accuracy of precise integration method in dynamic analysis[J].Acta Mechanica Sinica,2001,33(6):847~852.(in Chinese)
[7]汪梦甫,周锡元.结构动力方程的更新精细积分方法[J].力学学报,2004,36(2):191~195.Wang Mengfu,Zhou Xiyuan.Renewal precise time step integration method of structural dynamic analysis[J].Acta Mechanica Sinica,2004,36(2):191~195.(in Chinese)
[8]钟万勰.子域精细积分及偏微分方程数值解[J].计算结构力学及其应用,1995,12(3):253~260.Zhong Wanxie.Subdomain precise integration method and numerical solution of partial differential equation[J].Computational Structural Mechanics and Applications,1995,12(3):253~260.(in Chinese)
[9]孙焕纯,曲乃泗,林家浩.高等计算结构动力学[M].大连:大连理工大学出版社,1992.Sun Huanchun,Qu Naisi,Lin Jiahao.Higher computational structural dynamics[M].Dalian:Dalian University of Technology Press,1992.(in Chinese)
[10]张晓志,程岩,谢礼立.结构动力反应分析的三阶显式方法[J].地震工程与工程振动,2002,22(3):1~8.Zhang Xiaozhi,Cheng Yan,Xie Lili.A new explicit solution of dynamic response analysis[J].Earthquake Engineering and Engineering Vibration,2002,22(3):1~8.(in Chinese)
[2]Golley B W.A time-stepping procedure for structural dynamics using Gauss point collocation[J].International Journal for Numerical Methods in Engineering,1996,39:3985~3998.
[3]Tarnow N,Simo J C.How to render second order accurate time stepping algorithms fourth order accurate while retaining the stability and conservation properties[J].Computer Methods in Applied Mechanics and Engineering,1994,115:233~252.
[4]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,34(2):131~136.Zhong Wanxie.On precise time-integration method for structural dynamics[J].Journal of Dalian University ofTechnology,1994,34(2):131~136.(in Chinese)
[5]Zhong W X,Williams F W.A precise time step integration method[J].Journal of Mechanical Engineering Science,1994,208:427~430.
[6]张洪武.关于动力分析精细积分算法精度的讨论[J].力学学报,2001,33(6):847~852.Zhang Hongwu.Discussion on the accuracy of precise integration method in dynamic analysis[J].Acta Mechanica Sinica,2001,33(6):847~852.(in Chinese)
[7]汪梦甫,周锡元.结构动力方程的更新精细积分方法[J].力学学报,2004,36(2):191~195.Wang Mengfu,Zhou Xiyuan.Renewal precise time step integration method of structural dynamic analysis[J].Acta Mechanica Sinica,2004,36(2):191~195.(in Chinese)
[8]钟万勰.子域精细积分及偏微分方程数值解[J].计算结构力学及其应用,1995,12(3):253~260.Zhong Wanxie.Subdomain precise integration method and numerical solution of partial differential equation[J].Computational Structural Mechanics and Applications,1995,12(3):253~260.(in Chinese)
[9]孙焕纯,曲乃泗,林家浩.高等计算结构动力学[M].大连:大连理工大学出版社,1992.Sun Huanchun,Qu Naisi,Lin Jiahao.Higher computational structural dynamics[M].Dalian:Dalian University of Technology Press,1992.(in Chinese)
[10]张晓志,程岩,谢礼立.结构动力反应分析的三阶显式方法[J].地震工程与工程振动,2002,22(3):1~8.Zhang Xiaozhi,Cheng Yan,Xie Lili.A new explicit solution of dynamic response analysis[J].Earthquake Engineering and Engineering Vibration,2002,22(3):1~8.(in Chinese)
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心