An integrated method for the transient solution of reduced order models of geometrically nonlinear structural dynamic systems
type: Dataset
description: For repeated transient solutions of geometrically nonlinear structures the numerical effort often poses a major obstacle. Thus, the introduction of a reduced order model, which takes the nonlinear effects into account and accelerates the calculations considerably, is often necessary.This work yields a method that allows for rapid, accurate and parameterisable solutions by means of a reduced model of the original structure. The structure is discretised and its dynamic equilibrium described by a matrix equation. The projection on a reduced basis is introduced to obtain the reduced model. A comprehensive numerical study on several common reduced bases shows that the simple introduction of a constant basis is not sufficient to account for the nonlinear behaviour. Three requirements for an rapid, accurate and parameterisable solution are derived. The solution algorithm has to take into account the nonlinear evolution of the solution, the solution has to be independent of the nonlinear finite element terms and the basis has to be adapted to external parameters.Three approaches are provided, each responding to one requirement. These approaches are assembled to the integrated method. The approaches are the update and augmentation of the basis, the polynomial formulation of the nonlinear terms and the interpolation of the basis. A Newmark-type time-marching algorithm provides the frame of the integrated method. The application of the integrated method on test-cases with geometrically nonlinear finite elements confirms that this method leads to the initial aim of a rapid, accurate and parameterisable transient solution.
identifier: NNT: 2013CNAM0884
issued: 2026-05-06T02:23:25.605625
language: en
modified: 2026-05-06T02:23:25.605629
contact point: Organization
  fn: CCSD
keyword: bases-reduites
keyword: basis-update
keyword: decomposition-orthogonale-propre
keyword: dynamique-de-structures
keyword: geometric-nonlinearities
keyword: infoeu-reposemanticsdoctoralthesis
keyword: linear-normal-modes
keyword: mise-a-jour-de-la-base-reduite
keyword: model-reduction
keyword: modes-propres
keyword: nonlinearites-geometriques
keyword: parameters
keyword: parametres
keyword: physmecastruphysics-physicsmechanics-physicsstructural-mechanics-physicsclass-ph
keyword: proper-orthogonal-decomposition
keyword: reduced-bases
keyword: reduction-du-modele
keyword: structural-dynamics
keyword: theses
landing page: https://theses.hal.science/tel-00957455

An integrated method for the transient solution of reduced order models of geometrically nonlinear structural dynamic systems
type: Distribution
format: HTML
issued: 2026-05-06T02:23:25.607934
modified: 2026-05-06T02:23:25.574292
access URL: https://theses.hal.science/tel-00957455

test_moissonnage_selune
type: Agent