TY - JOUR

T1 - On the neural network calculation of the Lamé coefficients through eigenvalues of the elasticity operator

AU - Ossandón, Sebastián

AU - Reyes, Camilo

N1 - Publisher Copyright:
© 2015 Académie des sciences.

PY - 2016/2/1

Y1 - 2016/2/1

N2 - 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.

AB - 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.

KW - Artificial neural network

KW - Eigenvalues of the elasticity operator

KW - Finite-element method

KW - Inverse problems

KW - Lamé coefficients

KW - Radial basis function

UR - http://www.scopus.com/inward/record.url?scp=84958093396&partnerID=8YFLogxK

U2 - 10.1016/j.crme.2015.10.004

DO - 10.1016/j.crme.2015.10.004

M3 - Article

AN - SCOPUS:84958093396

SN - 1631-0721

VL - 344

SP - 113

EP - 118

JO - Comptes Rendus - Mecanique

JF - Comptes Rendus - Mecanique

IS - 2

ER -