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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A partial velocity approach to subcycling structural dynamics
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A partial velocity approach to subcycling structural dynamics

机译：局部速度子循环对结构动力学的影响

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摘要

Subcycling, or the use of different timesteps at different nodes, can be an effective way of improving the computational efficiency of explicit transient dynamic structural solutions. The method that has been most widely adopted uses a nodal partition, extending the central difference method, in which small timestep updates are performed interpolating on the displacement at neighbouring large timestep nodes. This approach leads to narrow bands of unstable timesteps or "statistical stability". It also can be in error due to lack of momentum conservation on the timestep interface. The author has previously proposed energy conserving algorithms that avoid the first problem of statistical stability. However, these sacrifice accuracy to achieve stability. An approach to conserve momentum on an element interface by adding partial velocities is considered here. Applied to extend the central difference method, this approach is simple, and has accuracy advantages. The method can be programmed by summing impulses of internal forces, evaluated using local element timesteps, in order to predict a velocity change at a node. However, it is still only statistically stable, so an adaptive timestep size is needed to monitor accuracy and to be adjusted if necessary. By replacing the central difference method with the explicit generalized alpha method, it is possible to gain stability by dissipating the high frequency response that leads to stability problems. However, coding the algorithm is less elegant, as the response depends on previous partial accelerations. Extension to implicit integration, is shown to be impractical due to the neglect of remote effects of internal forces acting across a timestep interface.
机译：子循环或在不同节点上使用不同时间步长可能是提高显式瞬态动力结构解决方案的计算效率的有效方法。最广泛采用的方法是使用节点分区，扩展了中心差分方法，在该方法中，对相邻大时间步长节点上的位移进行小时间步长更新。这种方法导致不稳定的时间步长或“统计稳定性”的狭窄范围。由于在时间步界面上缺少动量守恒，因此也会出错。作者之前已经提出了节能算法，可以避免统计稳定性的第一个问题。但是，这些牺牲准确性来实现稳定性。这里考虑一种通过增加部分速度来在单元界面上保持动量的方法。应用于扩展中心差分法，该方法简单，具有精度优势。该方法可以通过对使用局部元素时间步长评估的内力脉冲求和来编程，以预测节点处的速度变化。但是，它仍然只是统计上稳定的，因此需要一个自适应的时间步长来监视准确性，并在必要时进行调整。通过将中心差方法替换为显式的广义alpha方法，可以通过消除导致稳定性问题的高频响应来获得稳定性。但是，对算法进行编码不太优雅，因为响应取决于先前的部分加速度。由于忽略了跨时间步界面作用的内力的远程影响，因此扩展到隐式积分是不切实际的。

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