| 微分求积时间单元方法 |
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| 引用本文： | 郭静,邢誉峰. 微分求积时间单元方法[J]. 振动工程学报, 2012, 25(1): 84-89 |
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| 作者姓名： | 郭静 邢誉峰 |
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| 作者单位： | 北京航空航天大学固体力学研究所,北京,100191 |
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| 基金项目： | 国家自然科学基金资助项目(11172028,10772014) |
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| 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.
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| 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 time element method |
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| GUO Jing , XING Yu-feng. Differential quadrature time element method[J]. Journal of Vibration Engineering, 2012, 25(1): 84-89 |
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| Authors: | GUO Jing XING Yu-feng |
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| Affiliation: | (The Institute of Solid Mechanics,Beihang University,Beijing 100191,China) |
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| Abstract: | 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. |
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| Keywords: | differential quadrature rule direct integration method time element phase error numerical dissipation |
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