关于ATAM应用时注意的几个问题
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摘要
在《与荷载同步变化的时间步自动调整方法》~([1])中提出的时间步自动调整方法,不同于以往的后验式误差评估时间自适应方法,它是先验式误差评估研究领域的一次有益尝试(Apriori Time Adaptive Method,ATAM)。为了使ATAM更好的应用到实践中,就ATAM的适用条件和如何使用的问题进行了探讨,得出了几点非常重要的结论和建议。
The time step automatic adjustment method proposed in "Time step automatic adjustment method synchronously varying with load changes" is different from the past posteriori error estimation time adaptive one, it is a useful attempt in the field of apriori error estimation study, and it is called the apriori time adaptive method(ATAM). In order to better apply the ATAM in practice, its applicable conditions and some problems how to use it were explored here, and some very important conclusions and recommendations were drawn.
The time step automatic adjustment method proposed in "Time step automatic adjustment method synchronously varying with load changes" is different from the past posteriori error estimation time adaptive one, it is a useful attempt in the field of apriori error estimation study, and it is called the apriori time adaptive method(ATAM). In order to better apply the ATAM in practice, its applicable conditions and some problems how to use it were explored here, and some very important conclusions and recommendations were drawn.
引文
[1] 李彬,唐小微.与荷载同步变化的时间步自动调整方法[J].振动与冲击,2018,37(11):5-11.LI Bin,TANG Xiaowei.A time step automatic adjustment method with load synchronous change[J].Journal of Vibration and Shock,2018,37(11):5-11.
[2] 王林,蔡改改,高冠琪.基于改进MP的稀疏表示快速算法及其滚动轴承故障特征提取应用[J].振动与冲击,2017,36(3):176-182.WANG Lin,CAI Gaigai,GAO Guanqi.Fast sparse representation algorithm based on improved MP and its applications in fault feature extraction of rolling bearings[J].Journal of Vibration and Shock,2017,36(3):176-182.
[3] 祝志文,黄炎.大跨度桥梁脉动风场模拟的插值算法[J].振动与冲击,2017,36(7):156-163.ZHU Zhiwen,HUANG Yan.Interpolation algorithm for fluctuating wind field simulation of long-span bridges[J].Journal of Vibration and Shock,2017,36(7):156-163.
[4] ZIENKIEWICZ O C,XIEY M.A simple error estimator and adaptive time stepping procedure for dynamic analysis[J].Earthquake Engineering & Structural Dynamics,1991,20(9):871-887.
[5] ZENG L F,WIBERG N E,LI X D.A posteriori local error estimation and adaptive time-stepping for newmark integration in dynamic analysis[J].Earthquake Engineering & Structural Dynamics,1992,21(7):555-571.
[6] WIBERG N E,LI X D.A post-processing technique and an a posteriori error estimate for the newmark method in dynamic analysis[J].Earthquake Engineering & Structural Dynamics,1993,22(6):465-489.
[7] KAVETSKI D,BINNING P,SLOAN S W.Adaptive backward Euler time stepping with truncation error control for numerical modelling of unsaturated fluid flow[J].International Journal for Numerical Methods in Engineering,2002,53(6):1301-1322.
[8] KUO S R,YAU J D,YANG Y B.A robust time-integration algorithm for solving nonlinear dynamic problems with large rotations and displacements[J].International Journal of Structural Stability and Dynamics,2012,12(6):1250051(1-24).
[9] 王开加,程建生,段金辉.基于时间步长自适应技术的海上浮基风电平台绕流数值模拟分析[J].船舶与海洋工程,2013(2):52-57.WANG Kaijia,CHENG Jiansheng,DUAN Jinhui.Numerical simulation analysis of offshore floating wind power generation platform based on time step adaptive method[J].Naval Architecture and Ocean Engineering,2013(2):52-57.
[10] 毛卫南,刘建坤.自适应时间步长法在土体冻结水热耦合模型中的应用[J].防灾减灾工程学报,2014,34(4):510-516.MAO Weinan,LIU Jiankun.Application of adaptive time step method to water-heat coupling model of soil freezing[J].Journal of Disaster Prevention and Mitigation Engineering,2014,34(4):510-516.
[11] LI B,TANG X W,YANG G.Time-step optimization method to improve calculation efficiency and feasibility validation reliance[J].Engineering Optimization,2018:1-12.
[12] NAVEED A,VOLKER J.Adaptive time step control for higher order variational time discretizations applied to convection-diffusion-reaction equations[J].Computer Methods in Applied Mechanics and Engineering,2015,285:83-101.
[13] VAHID Z R,SHEN Y X.Massive parallelization of the phase field formulation for crack propagation with time adaptivity[J].Computer Methods in Applied Mechanics and Engineering,2016,312:224-253.
[14] MARC L,SERGE P,KRISTOFFER G Z.Preface to the special issue on error estimation and adaptivity for nonlinear and time-dependent problems[J].Computer methods in applied mechanics and engineering,2015,288:1.
[15] 李彬,唐小微.动力时程分析时间步预判方法及其有效性验证[J].应用力学学报,2018,35(5):933-937.LI Bin,TANG Xiaowei.Time step anticipation method of dynamic time history analysis and the effectiveness verification[J].Chinese Journal of Applied Mechanics,2018,35(5):933-937.
[16] LIN Y H,TRETHEWEY M W.Finite element analysis of elastic beams subjected to moving dynamic loads[J].Journal of Sound and Vibration,1990,136(2):323-342.
[17] FRYBA L.Vibration of solids and structures under moving loads[M].London:Thomas Telford,1999.
[2] 王林,蔡改改,高冠琪.基于改进MP的稀疏表示快速算法及其滚动轴承故障特征提取应用[J].振动与冲击,2017,36(3):176-182.WANG Lin,CAI Gaigai,GAO Guanqi.Fast sparse representation algorithm based on improved MP and its applications in fault feature extraction of rolling bearings[J].Journal of Vibration and Shock,2017,36(3):176-182.
[3] 祝志文,黄炎.大跨度桥梁脉动风场模拟的插值算法[J].振动与冲击,2017,36(7):156-163.ZHU Zhiwen,HUANG Yan.Interpolation algorithm for fluctuating wind field simulation of long-span bridges[J].Journal of Vibration and Shock,2017,36(7):156-163.
[4] ZIENKIEWICZ O C,XIEY M.A simple error estimator and adaptive time stepping procedure for dynamic analysis[J].Earthquake Engineering & Structural Dynamics,1991,20(9):871-887.
[5] ZENG L F,WIBERG N E,LI X D.A posteriori local error estimation and adaptive time-stepping for newmark integration in dynamic analysis[J].Earthquake Engineering & Structural Dynamics,1992,21(7):555-571.
[6] WIBERG N E,LI X D.A post-processing technique and an a posteriori error estimate for the newmark method in dynamic analysis[J].Earthquake Engineering & Structural Dynamics,1993,22(6):465-489.
[7] KAVETSKI D,BINNING P,SLOAN S W.Adaptive backward Euler time stepping with truncation error control for numerical modelling of unsaturated fluid flow[J].International Journal for Numerical Methods in Engineering,2002,53(6):1301-1322.
[8] KUO S R,YAU J D,YANG Y B.A robust time-integration algorithm for solving nonlinear dynamic problems with large rotations and displacements[J].International Journal of Structural Stability and Dynamics,2012,12(6):1250051(1-24).
[9] 王开加,程建生,段金辉.基于时间步长自适应技术的海上浮基风电平台绕流数值模拟分析[J].船舶与海洋工程,2013(2):52-57.WANG Kaijia,CHENG Jiansheng,DUAN Jinhui.Numerical simulation analysis of offshore floating wind power generation platform based on time step adaptive method[J].Naval Architecture and Ocean Engineering,2013(2):52-57.
[10] 毛卫南,刘建坤.自适应时间步长法在土体冻结水热耦合模型中的应用[J].防灾减灾工程学报,2014,34(4):510-516.MAO Weinan,LIU Jiankun.Application of adaptive time step method to water-heat coupling model of soil freezing[J].Journal of Disaster Prevention and Mitigation Engineering,2014,34(4):510-516.
[11] LI B,TANG X W,YANG G.Time-step optimization method to improve calculation efficiency and feasibility validation reliance[J].Engineering Optimization,2018:1-12.
[12] NAVEED A,VOLKER J.Adaptive time step control for higher order variational time discretizations applied to convection-diffusion-reaction equations[J].Computer Methods in Applied Mechanics and Engineering,2015,285:83-101.
[13] VAHID Z R,SHEN Y X.Massive parallelization of the phase field formulation for crack propagation with time adaptivity[J].Computer Methods in Applied Mechanics and Engineering,2016,312:224-253.
[14] MARC L,SERGE P,KRISTOFFER G Z.Preface to the special issue on error estimation and adaptivity for nonlinear and time-dependent problems[J].Computer methods in applied mechanics and engineering,2015,288:1.
[15] 李彬,唐小微.动力时程分析时间步预判方法及其有效性验证[J].应用力学学报,2018,35(5):933-937.LI Bin,TANG Xiaowei.Time step anticipation method of dynamic time history analysis and the effectiveness verification[J].Chinese Journal of Applied Mechanics,2018,35(5):933-937.
[16] LIN Y H,TRETHEWEY M W.Finite element analysis of elastic beams subjected to moving dynamic loads[J].Journal of Sound and Vibration,1990,136(2):323-342.
[17] FRYBA L.Vibration of solids and structures under moving loads[M].London:Thomas Telford,1999.