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Computational Mechanics
Erschienen in: Computational Mechanics 6/2014

01.12.2014 | Original Paper

Virtual charts of solutions for parametrized nonlinear equations

verfasst von: Matthieu Vitse, David Néron, Pierre-Alain Boucard

Erschienen in: Computational Mechanics | Ausgabe 6/2014

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Abstract

During many decades, engineers relied on experimental abaci to design and optimize mechanical structures. Virtual charts are based on numerical computations and aim at making the design and optimization of structures faster and cheaper as it requires less (or no) experimentation. The parametric problems are solved offline and the associated charts are used for online design. However, in this context, the cost associated to the resolution of parametric problems can be extremely prohibitive. Model reduction techniques are an answer to circumvent this issue. This paper provides the developments of an algorithm for solving nonlinear parametric problems, based on the LATIN method for the treatment of the nonlinear aspects and the PGD for the parameter dependency. A full time–space-parameter decomposition of the solution is introduced into the LATIN algorithm, numerical examples on academic problems are given so as to point out the advantages of this extension and leads on possible improvements to the strategy are given.
Vorheriger Artikel An extended molecular statics algorithm simulating the electromechanical continuum response of ferroelectric materials
Nächster Artikel A generalized 2D non-local lattice spring model for fracture simulation

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Metadaten
Titel
Virtual charts of solutions for parametrized nonlinear equations
verfasst von
Matthieu Vitse
David Néron
Pierre-Alain Boucard
Publikationsdatum
01.12.2014
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 6/2014
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-014-1073-6

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