摘要
基于微分求积法则,提出了一种求解动力学常微分方程的高效高精度微分求积时间单元方法(DQTEM)。给出了DQTEM施加初始位移和初始速度的方法,其结果相当于构造了C1时间单元。与递推格式的直接积分方法不同,对于考虑的时间域通常只需用一个微分求积时间单元。与RK法和Newmark法相比,用少量时间结点的DQTEM结果就与精确解吻合。稳定性分析表明,DQTEM通常是条件稳定的。
Based on differential quadrature rule,an accurate and efficient differential quadrature time element method（DQTEM） is proposed for solving dynamical ordinary differential equation,whose numerical dissipation and phase error are much smaller than the conventional direct integration method.The method of imposing initial displacements and velocities of DQTEM is given;subsequently the C1 time element is constructed.On the contrary to the recursive direct integration method,one differential quadrature time element is usually enough for the whole time domain under consideration.Compared with the RK method and the Newmark method,DQTEM solutions with an evidently smaller number of sampling points agree extremely well with the exact solutions.Stability analysis indicates that DQTEM is usually conditionally stable.
出处
《振动工程学报》
EI
CSCD
北大核心
2012年第1期84-89,共6页
Journal of Vibration Engineering
基金
国家自然科学基金资助项目(11172028
10772014)
关键词
微分求积法则
直接积分方法
时间单元
相位误差
数值耗散
differential quadrature rule
direct integration method
time element
phase error
numerical dissipation
