非线性精细积分方法及其在拟动力试验中的应用
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摘要
将精细积分方法和预估-校正Adams-Bashforth-Moulton多步法相结合,构造了一种避免状态矩阵求逆、隐式预估-校正、四阶精度的精细积分多步法,可用于多自由度结构体系的非线性地震反应分析。基于精细积分多步法,构造了一种实用的显式拟动力试验数值积分方法,该方法在成倍地增大时间步长后的计算精度比中心差分法高,稳定性较好,试验工作可大量减少。最后,将显式方法应用于组合筒体结构拟动力试验中。
Combining precise integration method and Adams-Bashforth-Moulton's predict-correct multi-step method,a precise integration method for nonlinear dynamic equations was put forward,it was implicit predict-correct,with four order accuracy,multi-step and not calculating inversion of state matrix.Based on the advanced multi-step method of nonlinear precise integration,a new applicable numerical integration method for pseudodynamic test of structures was constructed.Its accuracy was superior to center difference method by enlarging time step twice or fourfold and its stability also was better.Thus,the testing task would be largely reduced.Finally,a pseudodynamic test of a combined tube structure was performed with the proposed method.
Combining precise integration method and Adams-Bashforth-Moulton's predict-correct multi-step method,a precise integration method for nonlinear dynamic equations was put forward,it was implicit predict-correct,with four order accuracy,multi-step and not calculating inversion of state matrix.Based on the advanced multi-step method of nonlinear precise integration,a new applicable numerical integration method for pseudodynamic test of structures was constructed.Its accuracy was superior to center difference method by enlarging time step twice or fourfold and its stability also was better.Thus,the testing task would be largely reduced.Finally,a pseudodynamic test of a combined tube structure was performed with the proposed method.
引文
[1]田石柱,赵桐.抗震拟动力试验技术研究[J].世界地震工程,2001,17(4):60—66.
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[3]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.
[4]Jiahao Lin,Weiping Shen and F W Williams.A high preci-sion direct integration scheme for structures subjected to tran-sient dynamic loading[J].Computer&Structures,1995,6(1):120—130.
[5]储德文,王元丰.精细直接积分法的积分方法选择[J].工程力学,2002,19(6):115—119.
[6]裘春航,吕和祥,蔡志勤.哈密顿体系下分析非线性动力学问题[J].计算力学学报,2000,17(2):127—132.
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[8]闫海青,唐晨,张皋等.任意阶显式精细积分多步法的常用形式及其高阶次数值计算[J].计算物理,2004,21(3):333—338.
[9]闫海青,唐晨,刘铭等.任意阶显式精细积分多步法在刚性方程中的应用研究[J].工程数学学报,2004,21(6):1037—1040.
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[11]陈伯望.筒体结构拟动力试验及理论研究[D].长沙:湖南大学,2006.
[2]邱法维,钱稼茹,陈志鹏著.结构抗震实验方法[M].北京:科学出版社,2000.
[3]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.
[4]Jiahao Lin,Weiping Shen and F W Williams.A high preci-sion direct integration scheme for structures subjected to tran-sient dynamic loading[J].Computer&Structures,1995,6(1):120—130.
[5]储德文,王元丰.精细直接积分法的积分方法选择[J].工程力学,2002,19(6):115—119.
[6]裘春航,吕和祥,蔡志勤.哈密顿体系下分析非线性动力学问题[J].计算力学学报,2000,17(2):127—132.
[7]裘春航,吕和祥,钟万勰.求解非线性动力学方程的分段直接积分法[J].力学学报,2002,34(3):369—378.
[8]闫海青,唐晨,张皋等.任意阶显式精细积分多步法的常用形式及其高阶次数值计算[J].计算物理,2004,21(3):333—338.
[9]闫海青,唐晨,刘铭等.任意阶显式精细积分多步法在刚性方程中的应用研究[J].工程数学学报,2004,21(6):1037—1040.
[10]徐萃薇,孙绳武.计算方法引论(第二版)[M].北京:高等教育出版社,2002.
[11]陈伯望.筒体结构拟动力试验及理论研究[D].长沙:湖南大学,2006.
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