Indirect reduced-order modelling: using nonlinear manifolds to conserve kinetic energy

DOI10.1098/rspa.2020.0589zbMath1472.74200OpenAlexW3101832965WikidataQ104574396 ScholiaQ104574396MaRDI QIDQ5161185

Evangelia Nicolaidou, T. L. Hill, Simon A. Neild

Publication date: 29 October 2021

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://europepmc.org/articles/pmc7735295

zbMATH Keywords

geometric nonlinearitystructural dynamicsmathematical modellingnonlinear normal modesfinite-element analysismechanical engineeringreduced-order modellingnonlinear manifold

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Dynamical systems in solid mechanics (37N15) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Thin bodies, structures (74Kxx) Nonlinear modes (70K75)

Uses Software

• ABAQUS
• Abaqus2Matlab

Cites Work

• Unnamed Item
• Unnamed Item
• Nonlinear model order reduction for flexible multibody dynamics: a modal derivatives approach
• A reduction method for nonlinear structural dynamic analysis
• Reduced-order models for large-amplitude vibrations of shells including in-plane inertia
• Normal modes for large amplitude vibration of a cantilever beam
• A FINITE ELEMENT TIME DOMAIN MODAL FORMULATION FOR LARGE AMPLITUDE FREE VIBRATIONS OF BEAMS AND PLATES
• Model reduction tools for nonlinear structural dynamics
• A load-dependent basis for reduced nonlinear structural dynamics
• Adaptive reduced integration method for nonlinear structural dynamic analysis
• Normal Modes for Non-Linear Vibratory Systems
• Normal Modes of Vibration for Non-Linear Continuous Systems
• Recipes for Continuation
• Stability of Nonlinear Oscillations of an Elastic Rod
• Nonlinear modal analysis of structural systems using multi-mode invariant manifolds