NDLI: An integrated method for the transient solution of reduced order models of geometrically nonlinear structures

Content Provider	Springer Nature Link
Author	Lülf, Fritz Adrian Tran, Duc Minh Matthies, Hermann G. Ohayon, Roger
Copyright Year	2015
Abstract	For repeated transient solutions of geometrically nonlinear structures, the numerical effort often poses a major obstacle. Thus it may become necessary to introduce a reduced order model which accelerates the calculations considerably while taking into account the nonlinear effects of the full order model in order to maintain accuracy. This work yields an integrated method that allows for rapid, accurate and parameterisable transient solutions. It is applicable if the structure is discretised in time and in space and its dynamic equilibrium described by a matrix equation. The projection on a reduced basis is introduced to obtain the reduced order model. Three approaches, each responding to one of the requirements of rapidity, accuracy and parameterisation, are united to form the integrated method. The polynomial formulation of the nonlinear terms renders the solution of the reduced order model autonomous from the finite element formulation and ensures a rapid solution. The update and augmentation of the reduced basis ensures the accuracy, because the simple introduction of a constant basis seems to be insufficient to account for the nonlinear behaviour. The interpolation of the reduced basis allows adapting the reduced order model to different external parameters. A Newmark-type algorithm provides the backbone of the integrated method. The application of the integrated method on test-cases with geometrically nonlinear finite elements confirms that this method enables a rapid, accurate and parameterisable transient solution.
Starting Page	327
Ending Page	344
Page Count	18
File Format	PDF
ISSN	01787675
Journal	Computational Mechanics
Volume Number	55
Issue Number	2
e-ISSN	14320924
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2015-01-20
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Structural dynamics Geometric nonlinearities Model reduction Reduced bases Normal modes Tangent modes Basis update Parameters Theoretical and Applied Mechanics Computational Science and Engineering Classical Continuum Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Ocean Engineering Computational Theory and Mathematics Mechanical Engineering Computational Mechanics Computational Mathematics

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