波动数值模拟的常加速度显式算法
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摘要
给出了一种将隐式时域逐步积分算法转换为显式时域逐步积分算法的方法,避免了求解耦联方程组,提高了计算效率.对于暂态波源作用下的弹性半空间,利用有限单元法划分网格、建立结构动力方程,并应用Fortran语言对中心差分算法和平均常加速度显式算法编程,求解脉冲荷载作用下的出平面运动.2种算法计算结果对比表明,常加速度显式算法可以较好地应用于工程波动数值模拟中.
Explicit time integral method of numerical simulation for engineering wave problem is an important topic in both national and international research work. An explicit time integral method transformed by corresponding implicit time integral method,avoiding solving coupled equations and improving computational efficiency,is presented in this paper. Structural dynamic equation of elastic half space under transient wave is integrated using the finite element method,and the out-plane response under impulse load is computed by central difference method and constant acceleration explicit method respectively. Comparison between the calculated results of the two methods shows that the constant acceleration explicit method can be used in engineering wave numerical simulation effectively.
Explicit time integral method of numerical simulation for engineering wave problem is an important topic in both national and international research work. An explicit time integral method transformed by corresponding implicit time integral method,avoiding solving coupled equations and improving computational efficiency,is presented in this paper. Structural dynamic equation of elastic half space under transient wave is integrated using the finite element method,and the out-plane response under impulse load is computed by central difference method and constant acceleration explicit method respectively. Comparison between the calculated results of the two methods shows that the constant acceleration explicit method can be used in engineering wave numerical simulation effectively.
引文
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[14]高小科,邓子辰,黄永安.基于三次样条插值的精细积分法[J].振动与冲击,2007,26(9):75-82.
[15]廖振鹏,刘恒,谢志南.波动数值模拟的一种显式方法-一维波动[J].力学学报,2009,41(3):350-359.
[16]刘恒,廖振鹏.波动数值模拟的一种显式方法-二维波动[J].力学学报,2010,42(6):1104-1116.
[17]谢志南,廖振鹏.波动方程数值模拟的一种显式方法[J].力学学报,2011,43(1):154-161.
[18]李长青,楼梦麟,余志武,等.近似平衡多项式加速度动力显式算法[J].应用力学学报,2011,28(5):475-480.
[19]李长青,楼梦麟.中心-偏心差分法[J].同济大学学报:自然科学版,2011,39(2):179-186.
[20]李长青,楼梦麟,蒋丽忠.结构动力方程求解中隐式格式向显式格式的转换[J].振动与冲击,2012,31(13):91-94.
[21]廖振鹏.工程波动理论导论[M].北京:科学出版社,2002.
[2]Bathe K J,Wilson E L.Stability and accuracy analysis of direct integration method[J].Earthq Eng and Struct Dynam,1973(1):283-291.
[3]Hiber H M,Hughes T J R,Tayler R L.Improned numerical dissipation for time integration algorithins in structural dynamics[J].Eathq Eng and Struct Dynam,1977,5(3):283-292.
[4]Hiber H M,Hughes T J R.Collocation dissipation and overshoot for time integration schemes in structural dynamics[J].Eathq Eng and Struct Dynam,1978,6(1):99-177.
[5]Subbara J K,Dokainish M A.A survey of direct time integration methods in computational structural dynamics(II)[J].Computers and Structures,1989,32(6):1387-1401.
[6]廖振鹏.近场波动问题的有限元解法[J].地震工程与工程振动,1984,4(2):1-14.
[7]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):74-79.
[8]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.
[9]李小军.地震工程中动力方程求解的逐步积分方法[J].工程力学,1996,13(2):110-118.
[10]周正华,李山有,侯兴民.阻尼振动方程的一种显式直接积分方法[J].世界地震工程,1999,15(1):41-44.
[11]杜修力,王进廷.阻尼弹性结构动力计算的显式差分法[J].工程力学,2000,17(5):37-43.
[12]王进廷,杜修力.有阻尼体系动力分析的一种显式差分法[J].工程力学,2002,19(3):109-112.
[13]陈学良,金星,陶夏新.求解加速度反应的显式积分格式研究[J].地震工程与工程振动,2006,26(5):60-67.
[14]高小科,邓子辰,黄永安.基于三次样条插值的精细积分法[J].振动与冲击,2007,26(9):75-82.
[15]廖振鹏,刘恒,谢志南.波动数值模拟的一种显式方法-一维波动[J].力学学报,2009,41(3):350-359.
[16]刘恒,廖振鹏.波动数值模拟的一种显式方法-二维波动[J].力学学报,2010,42(6):1104-1116.
[17]谢志南,廖振鹏.波动方程数值模拟的一种显式方法[J].力学学报,2011,43(1):154-161.
[18]李长青,楼梦麟,余志武,等.近似平衡多项式加速度动力显式算法[J].应用力学学报,2011,28(5):475-480.
[19]李长青,楼梦麟.中心-偏心差分法[J].同济大学学报:自然科学版,2011,39(2):179-186.
[20]李长青,楼梦麟,蒋丽忠.结构动力方程求解中隐式格式向显式格式的转换[J].振动与冲击,2012,31(13):91-94.
[21]廖振鹏.工程波动理论导论[M].北京:科学出版社,2002.
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