Publication: A generic approach for the solution of nonlinear residual equations. Part I: The Diamant toolbox
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A generic approach for the solution of nonlinear residual equations. Part I: The Diamant toolbox

- Article in a journal -
 

Author(s)
Yao Koutsawa , Isabelle Charpentier , El Mostafa Daya , Mohammed Cherkaoui

Published in
Computer Methods in Applied Mechanics and Engineering

Year
2008

Abstract
Sufficiently smooth nonlinear PDE problems may be addressed through the higher order derivative computations of the so-called Asymptotic Numerical Method (ANM). In this paper, we theoretically discuss the generic solution of nonlinear residual equations. We then propose a Matlab implementation of the ANM based on Automatic Differentiation which allows for significant improvements in genericity and ease of use. The Diamant toolbox we construct is applied to the study of the geometrical nonlinear behavior of a laminated glass beam. Numerical results and experimental performances demonstrate the efficiency of the Diamant tool.

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Diamant

BibTeX
@ARTICLE{
         Koutsawa2008Aga,
       title = "A generic approach for the solution of nonlinear residual equations. {Part I}: The
         {D}iamant toolbox",
       journal = "Computer Methods in Applied Mechanics and Engineering",
       volume = "198",
       number = "3--4",
       pages = "572--577",
       year = "2008",
       issn = "0045-7825",
       doi = "DOI: 10.1016/j.cma.2008.09.003",
       url =
         "http://www.sciencedirect.com/science/article/B6V29-4TFW973-1/2/0c02e0c05f296b632dbe9150485e8b01",
       author = "Yao Koutsawa and Isabelle Charpentier and El Mostafa Daya and Mohammed Cherkaoui",
       keywords = "Geometrical nonlinearities",
       abstract = "Sufficiently smooth nonlinear PDE problems may be addressed through the higher
         order derivative computations of the so-called Asymptotic Numerical Method (ANM). In this paper, we
         theoretically discuss the generic solution of nonlinear residual equations. We then propose a Matlab
         implementation of the ANM based on Automatic Differentiation which allows for significant
         improvements in genericity and ease of use. The Diamant toolbox we construct is applied to the study
         of the geometrical nonlinear behavior of a laminated glass beam. Numerical results and experimental
         performances demonstrate the efficiency of the Diamant tool.",
       ad_tools = "Diamant"
}


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