Differential quadrature time element method for structural dynamics  

作　　者：Yu-Feng Xing Jing Guo 

机构地区：[1]The Solid Mechanics Research Center,Beihang University,100191 Beijing,China

出　　处：《Acta Mechanica Sinica》2012年第3期782-792,共11页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (11172028,10772014)

摘　　要：An accurate and efficient differential quadrature time element method （DQTEM） is proposed for solving ordi- nary differential equations （ODEs）, the numerical dissipation and dispersion of DQTEM is much smaller than that of the direct integration method of single/multi steps. Two methods of imposing initial conditions are given, which avoids the tediousness when derivative initial conditions are imposed, and the numerical comparisons indicate that the first method, in which the analog equations of initial displacements and velocities are used to directly replace the differential quadra- ture （DQ） analog equations of ODEs at the first and the last sampling points, respectively, is much more accurate than the second method, in which the DQ analog equations of initial conditions are used to directly replace the DQ analog equations of ODEs at the first two sampling points. On the contrary to the conventional step-by-step direct integration schemes, the solutions at all sampling points can be obtained simultaneously by DQTEM, and generally, one differential quadrature time element may be enough for the whole time domain. Extensive numerical comparisons validate the effi- ciency and accuracy of the proposed method.An accurate and efficient differential quadrature time element method （DQTEM） is proposed for solving ordi- nary differential equations （ODEs）, the numerical dissipation and dispersion of DQTEM is much smaller than that of the direct integration method of single/multi steps. Two methods of imposing initial conditions are given, which avoids the tediousness when derivative initial conditions are imposed, and the numerical comparisons indicate that the first method, in which the analog equations of initial displacements and velocities are used to directly replace the differential quadra- ture （DQ） analog equations of ODEs at the first and the last sampling points, respectively, is much more accurate than the second method, in which the DQ analog equations of initial conditions are used to directly replace the DQ analog equations of ODEs at the first two sampling points. On the contrary to the conventional step-by-step direct integration schemes, the solutions at all sampling points can be obtained simultaneously by DQTEM, and generally, one differential quadrature time element may be enough for the whole time domain. Extensive numerical comparisons validate the effi- ciency and accuracy of the proposed method.

关 键 词：Differential quadrature rule Direct integrationmethod Time element Phase error. Artificial damping 

分 类 号：O175.1[理学—数学] TU311.3[理学—基础数学]