Simulation-free hyper-reduction for geometrically nonlinear structural dynamics: A quadratic manifold lifting approach

Shobhit Jain, Paolo Tiso*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

23 Citations (Scopus)

Abstract

We present an efficient method to significantly reduce the offline cost associated with the construction of training sets for hyper-reduction of geometrically nonlinear, finite element (FE)-discretized structural dynamics problems. The reduced-order model is obtained by projecting the governing equation onto a basis formed by vibration modes (VMs) and corresponding modal derivatives (MDs), thus avoiding cumbersome manual selection of high-frequency modes to represent nonlinear coupling effects. Cost-effective hyper-reduction is then achieved by lifting inexpensive linear modal transient analysis to a quadratic manifold (QM), constructed with dominant modes and related MDs. The training forces are then computed from the thus-obtained representative displacement sets. In this manner, the need of full simulations required by traditional, proper orthogonal decomposition (POD)-based projection and training is completely avoided. In addition to significantly reducing the offline cost, this technique selects a smaller hyper-reduced mesh as compared to POD-based training and therefore leads to larger online speedups, as well. The proposed method constitutes a solid alternative to direct methods for the construction of the reduced-order model, which suffer from either high intrusiveness into the FE code or expensive offline nonlinear evaluations for the determination of the nonlinear coefficients.

Original languageEnglish
Article number071003
JournalJournal of Computational and Nonlinear Dynamics
Volume13
Issue number7
DOIs
Publication statusPublished - 2018
Externally publishedYes

Keywords

  • ECSW
  • hyper-reduction
  • modal derivatives
  • model order reduction
  • quadratic manifold
  • simulation-free reduction

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