基于动力特征分区的显式-精细混合积分法
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摘要
大型动力系统中常因局部的高频振动及非线性等特性限制了系统的积分步长而导致整体计算量激增,针对此问题提出一种分区域异步长显式—精细混合积分方法。在特性复杂的局部区域采取显式积分法,根据精度和稳定性要求取较小的时间步长求解;在其余常规区域则应用精细积分方法,采取可以跨越显式积分区周期的大积分步长求解。对于精细积分区域边界荷载,提出一种基于离散FFT变换的线性项与主频谐波项的组合表示方法,并给出了此种荷载形式下的精细积分计算格式。数值算例结果表明该法能够明显提高计算效率,在显式积分区域和精细积分区域都有很高的精度。
Large-scale dynamic systems with local high-frequency vibration and local nonlinearity require small integration time step which greatly decreases the effeciency of the direct integration method.A combined direct integration method is proposed to improve the efficiency of the direct integration method.The explicit integration method is applied for non-linear and stiff regions,and small time-step is adopted to keep the numerical precision and stability.For the rest linear regions,the high precision direct(HPD) integration method is implemented and large time-step which may cover periods of high-frequency vibration existing in regions for the explicit integration method is used.Load in linear regions is decomposed into linear and harmonic terms using FFT transformation and a HPD algorithm for such a load form is developed.Numerical examples demonstrate that the proposed method can obviously increase computation efficiency and has higher accuracy in both kinds of integration regions.
Large-scale dynamic systems with local high-frequency vibration and local nonlinearity require small integration time step which greatly decreases the effeciency of the direct integration method.A combined direct integration method is proposed to improve the efficiency of the direct integration method.The explicit integration method is applied for non-linear and stiff regions,and small time-step is adopted to keep the numerical precision and stability.For the rest linear regions,the high precision direct(HPD) integration method is implemented and large time-step which may cover periods of high-frequency vibration existing in regions for the explicit integration method is used.Load in linear regions is decomposed into linear and harmonic terms using FFT transformation and a HPD algorithm for such a load form is developed.Numerical examples demonstrate that the proposed method can obviously increase computation efficiency and has higher accuracy in both kinds of integration regions.
引文
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[2]翟婉明.车辆轨道耦合动力学[M].北京:中国铁道出版社,2001,109—115.
[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]文明,邓子辰.基于精细积分法的干摩擦隔振系统稳定性的研究[J].振动与冲击,2003,22(3):6—8.
[5]周晚林.智能板动荷载监测的压电单元模态法[J].振动与冲击,2005,24(5):8—10.
[6]赵岩,林家浩,唐光武.复杂结构局部非线性地震反应精细时程分析[J].大连理工大学学报,2004,42(2):190—194.
[7]梅树立,张森文,徐加初等.非线性动力学方程的自适应精细积分[J].暨南大学学报,2005,26(3):319—323.
[8]张素英,邓子辰.非线性动力方程的增维精细积分法[J].计算力学学报,2003,20(4):424—426.
[9]Lin Jiahao,Shen Weiping,Williams F W.A high precisiondirect integration scheme for structures subjected to transientdynamic loading[J].Computers&Structures,1995,56(1):113—120.
[10]小西一郎[日]编.韩毅等译.钢桥(第七分册)[M].北京:中国铁道出版社,1982,26—29.
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