Reduced-order modelling of nonlinear dynamic structures

Abstract

With the ever-increasing demand for better performance, modern engineering structures continue to tend towards thin, low-weight, and highly flexible designs. As a result, they are often required to undergo large deformations or rotations during operation, and experience geometric nonlinearity. However, performing nonlinear dynamic analysis of large models can pose prohibitively high computational costs during the design and optimisation of structures. Reduced-order modelling methods aim to ease this bottleneck, by constructing low-dimensional models which are able to capture the salient dynamics of the full-order model in a much more efficient manner.
The aim of this thesis is to further the current state-of-the-art of nonlinear reduced-order modelling methodologies, which are applicable to geometrically nonlinear structures built using commercial finite element software. The methods proposed herein build on existing techniques, exploiting their merits and aiming to address their limitations. Specifically, the focus of this thesis is on so-called force-based indirect reduction techniques, such as the Implicit Condensation and Expansion (ICE) method, which rely on a static condensation procedure to achieve reduction for structures characterised by slow/fast dynamics.
In this thesis, several developments of the ICE method are proposed. First it is shown that, in order to fully account for the effect of the statically condensed modes, the reduced dynamics must include not only higher orders of nonlinearity, compared to the full-order model, but also some additional velocity- and acceleration-dependent terms. The latter components capture the kinetic energy of the condensed modes, which the standard method neglects, thus extending its applicability to a far wider range of structures whilst maintaining accuracy to higher deflection amplitudes.
Then, a method for efficiently detecting the existence of internal resonances between reduced and condensed modes is proposed. This may serve as a tool for guiding the reduction basis selection process, as well as verifying the accuracy of reduced-order models, without the need for full-order simulations.
Finally, the ICE method is extended to nonconservative structures, such that forced response curves may be computed directly. The proposed formulation is such that any energy gained or dissipated by the condensed modes is accounted for in the reduced dynamics, enabling features such as parametric resonances — which would otherwise be neglected — to be accurately captured.

Date of Award	6 Dec 2022
Original language	English
Awarding Institution	University of Bristol
Supervisor	Tom L Hill (Supervisor) & Simon Neild (Supervisor)