A new numerical strategy to remedy high-frequency issues caused by finite element discretization in structural dynamic problems has been proposed. A noteworthy characteristic of this advocated approach is that it is based upon the use of the proper orthogonal decomposition (POD) incorporated in conjunction with implicit or explicit numerically non-dissipative time integration schemes to substantially improve or eliminate undesirable effects due to high-frequency instabilities. Original systems with high-frequency issues are reduced via POD based on an adequate choice of a numerically dissipative scheme so that the resulting reduced systems contain no high-frequency participation. This approach confers the inherent advantages that numerically non-dissipative mechanical integrators, e.g., energy–momentum conserving or variational integrators, can be used to solve the reduced systems, fulfilling the requisite conservation laws in the projected basis and therefore provides a robust simulation. Linear and nonlinear numerical applications are shown to demonstrate the benefits and feasibility of this technique.
|Original language||English (US)|
|Number of pages||16|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|State||Published - Oct 1 2017|
Bibliographical notePublisher Copyright:
© 2017 Elsevier B.V.
Copyright 2017 Elsevier B.V., All rights reserved.
- Computational dynamics
- Proper orthogonal decomposition
- Time integration