结构动力方程另类显式逐步积分格式研究
|
摘要
现有显式积分格式的稳定性与计算结果的取信度均远逊于常用的隐式积分格式,这是制约现有显式积分格式在大型结构动力分析软件以及其它相关软件中广泛应用的瓶颈。以解决这一瓶颈问题为研究目标,通过结合采用精确法和平均常加速度法的基本假定,推导建立了基于双重基本假定的另类显式积分格式,提出了相关的体系另类振动周期等新概念。基于另类振动周期概念并结合现有相关研究成果,导出了该格式的精度控制准则和形式上的稳定性控制准则,为开展相关的数值模拟研究准备了必要的基础和前提。概述了开展相关数值模拟研究的技术路线,对业已取得的主要数值模拟研究结果做了先期预告和初步讨论。
Both stability and reliability of calculation results of current explicit integration method are inferior to common implicit integration method,which restrict the explicit integration method widely used in large structure dynamic analysis software and other associated software. With solving this bottleneck problem as the main research objectively combining the basic assumption of accurate method with that of conslant average acceleration method,a other explicit integration method based on double basic assumption is derived,and some new concept of other vibration period of system are put forward.Based on the other vibration period and combined with current associated research results, criteria of accuracy and criteria of stability in form of the method are derived,which provide the necessary precondition and foundation for developing associated numerical simulation research.Also the technical route of associated numerical simulation research paper has been summarized and the advance notices and preliminary discussions on obtained mainly numerical simulation research results have been given.
Both stability and reliability of calculation results of current explicit integration method are inferior to common implicit integration method,which restrict the explicit integration method widely used in large structure dynamic analysis software and other associated software. With solving this bottleneck problem as the main research objectively combining the basic assumption of accurate method with that of conslant average acceleration method,a other explicit integration method based on double basic assumption is derived,and some new concept of other vibration period of system are put forward.Based on the other vibration period and combined with current associated research results, criteria of accuracy and criteria of stability in form of the method are derived,which provide the necessary precondition and foundation for developing associated numerical simulation research.Also the technical route of associated numerical simulation research paper has been summarized and the advance notices and preliminary discussions on obtained mainly numerical simulation research results have been given.
引文
[1]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.
[2]张晓志,张石磊,王伟.计算地震动长周期反应谱的转换模型和方法[J].地震工程与工程振动,2008,28(6):39-43.
[3]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.
[4]廖振鹏.工程波动理论导论[M].2版.北京:科学出版社,2002.
[5]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,2008,29(1):32-43.
[6]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.
[7]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.
[8]谭述君,高强,钟万勰.Duhamel项的精细积分方法在非线性微分方程数值求解中的应用[J].计算力学学报,2010,28(5):752- 758.
[9]谭述君,钟万勰.非齐次动力方程Duhamel项的精细积分[J].力学学报,2007,39(3):374-381.
[10]谭述君,吴志刚,钟万勰.矩阵指数精细积分方法中参数的自适应选择.力学学报,2009,41(6):961-966.
[2]张晓志,张石磊,王伟.计算地震动长周期反应谱的转换模型和方法[J].地震工程与工程振动,2008,28(6):39-43.
[3]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.
[4]廖振鹏.工程波动理论导论[M].2版.北京:科学出版社,2002.
[5]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,2008,29(1):32-43.
[6]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.
[7]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.
[8]谭述君,高强,钟万勰.Duhamel项的精细积分方法在非线性微分方程数值求解中的应用[J].计算力学学报,2010,28(5):752- 758.
[9]谭述君,钟万勰.非齐次动力方程Duhamel项的精细积分[J].力学学报,2007,39(3):374-381.
[10]谭述君,吴志刚,钟万勰.矩阵指数精细积分方法中参数的自适应选择.力学学报,2009,41(6):961-966.
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