A partial velocity approach to subcycling structural dynamics

✍ Scribed by W.J.T. Daniel

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 523 KB
• Volume: 192
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(02)00518-2

✦ Synopsis

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.