A new numerical method is presented with the purpose to calculate the Lamé coefficients, associated with an elastic material, through eigenvalues of the elasticity operator. The finite element method is used to solve repeatedly, using different Lamé coefficients values, the direct problem by training a direct radial basis neural network. A map of eigenvalues, as a function of the Lamé constants, is then obtained. This relationship is later inverted and refined by training an inverse radial basis neural network, allowing calculation of mentioned coefficients. A numerical example is presented to prove the effectiveness of this novel method.
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@article{CRMECA_2016__344_2_113_0,
author = {Sebasti\'an Ossand\'on and Camilo Reyes},
title = {On the neural network calculation of the {Lam\'e} coefficients through eigenvalues of the elasticity operator},
journal = {Comptes Rendus. M\'ecanique},
pages = {113--118},
publisher = {Elsevier},
volume = {344},
number = {2},
year = {2016},
doi = {10.1016/j.crme.2015.10.004},
language = {en},
}
TY - JOUR AU - Sebastián Ossandón AU - Camilo Reyes TI - On the neural network calculation of the Lamé coefficients through eigenvalues of the elasticity operator JO - Comptes Rendus. Mécanique PY - 2016 SP - 113 EP - 118 VL - 344 IS - 2 PB - Elsevier DO - 10.1016/j.crme.2015.10.004 LA - en ID - CRMECA_2016__344_2_113_0 ER -
%0 Journal Article %A Sebastián Ossandón %A Camilo Reyes %T On the neural network calculation of the Lamé coefficients through eigenvalues of the elasticity operator %J Comptes Rendus. Mécanique %D 2016 %P 113-118 %V 344 %N 2 %I Elsevier %R 10.1016/j.crme.2015.10.004 %G en %F CRMECA_2016__344_2_113_0
Sebastián Ossandón; Camilo Reyes. On the neural network calculation of the Lamé coefficients through eigenvalues of the elasticity operator. Comptes Rendus. Mécanique, Volume 344 (2016) no. 2, pp. 113-118. doi : 10.1016/j.crme.2015.10.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.10.004/
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