另类显式逐步积分格式性态的数值模拟研究
|
摘要
通过初始条件激励下多自由度体系动力响应数值模拟以及对不同模拟方法加速度序列模拟结果的比较分析,研究了PJ方法、BW方法和LL方法的性态,如收敛性、稳定性、精度以及相关问题。取得的主要研究结果是:积分步长Δt=0.1Tzmin可以作为保证BW方法数值精度和稳定性的充分条件;在该条件得到满足情况下,BW方法较之PJ和LL方法均有显著的综合优势,特别是相对精度方面的优势可以达到数量级水平。研究结果表明,显式方法可在大型有限元动力分析软件中逐渐起到更加重要的作用。
By numerical simulation for dynamic responses of multi-degree-of-freedom system under excitation of initial condition,and comparative analysis of acceleration sequence simulation results from different simulation method,the behavior of PJ method,BW method and LL method,such as convergence,stability,accuracy and other relevant problems are studied.The main research results are: integral step Δt=0.1Tzmincan be used as sufficient condition to guarantee numerical stability and precision of BW method;if this condition is satisfied,BW method has significant comprehensive advantages,it is better than PJ and LL method,especially the relative calculation accuracy can reach magnitude level.Research results show that the explicit method may gradually play an important role in large finite element dynamic analysis software.
By numerical simulation for dynamic responses of multi-degree-of-freedom system under excitation of initial condition,and comparative analysis of acceleration sequence simulation results from different simulation method,the behavior of PJ method,BW method and LL method,such as convergence,stability,accuracy and other relevant problems are studied.The main research results are: integral step Δt=0.1Tzmincan be used as sufficient condition to guarantee numerical stability and precision of BW method;if this condition is satisfied,BW method has significant comprehensive advantages,it is better than PJ and LL method,especially the relative calculation accuracy can reach magnitude level.Research results show that the explicit method may gradually play an important role in large finite element dynamic analysis software.
引文
[1]张晓志,刘龙江,曹玲.结构动力方程另类显式逐步积分格式研究[J].世界科技研究与发展,2011,33(6):981-985.ZHANG Xiaozhi,LIU Longjiang,CAO Ling.Research on other explicit integration method of structural dynamic equations[J].World Sci-tech R&D2011,33(6):981-985.(in Chinese)
[2]李小军,廖振鹏,杜修力.有阻尼体系动力问题的一种显式差分解法[J].地震工程与工程振动,1992,12(4):74-80.LI Xiaojun,LIAO Zhenpeng,DU Xiuli.An explicit finite difference method for viscoelastic dynamic problem[J].Journal of Earthquake Engineer-ing and Engineering Vibration,1992,12(4):74-80.(in Chinese)
[3]刘恒,廖振鹏.结构动力学方程的显式积分格式[J].地震工程与工程振动,2009,29(1):32-43.LU Heng,LIAO Zhenpeng.An explicit time integration method for structural dynamic equations[J].Journal of Earthquake Engineering and Engi-neering Vibration,2009,29(1):32-43.(in Chinese)
[4]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)
[5]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 equations[J].Computational Structural Me-chanics and Applications,1995,12(3):253-260.(in Chinese)
[6]高强,吴锋,张洪武,等.大规模动力系统改进的快速精细积分方法[J].计算力学学报,2011,28(4):493-498.GAO Qiang,WU Feng,ZHANG Hongwu,et al.A fast precise integration method for large-scale dynamic structures[J].Chinese Journal of Com-putational Mechanics,2011,28(4):493-498.(in Chinese)
[2]李小军,廖振鹏,杜修力.有阻尼体系动力问题的一种显式差分解法[J].地震工程与工程振动,1992,12(4):74-80.LI Xiaojun,LIAO Zhenpeng,DU Xiuli.An explicit finite difference method for viscoelastic dynamic problem[J].Journal of Earthquake Engineer-ing and Engineering Vibration,1992,12(4):74-80.(in Chinese)
[3]刘恒,廖振鹏.结构动力学方程的显式积分格式[J].地震工程与工程振动,2009,29(1):32-43.LU Heng,LIAO Zhenpeng.An explicit time integration method for structural dynamic equations[J].Journal of Earthquake Engineering and Engi-neering Vibration,2009,29(1):32-43.(in Chinese)
[4]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)
[5]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 equations[J].Computational Structural Me-chanics and Applications,1995,12(3):253-260.(in Chinese)
[6]高强,吴锋,张洪武,等.大规模动力系统改进的快速精细积分方法[J].计算力学学报,2011,28(4):493-498.GAO Qiang,WU Feng,ZHANG Hongwu,et al.A fast precise integration method for large-scale dynamic structures[J].Chinese Journal of Com-putational Mechanics,2011,28(4):493-498.(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