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

Sebastián Ossandón; Camilo Reyes

doi:10.1016/j.crme.2015.10.004

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

Sebastián Ossandón, Camilo Reyes

INSTITUTE OF MATHEMATICS

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	113-118
Number of pages	6
Journal	Comptes Rendus - Mecanique
Volume	344
Issue number	2
DOIs	https://doi.org/10.1016/j.crme.2015.10.004
State	Published - 1 Feb 2016

Keywords

Artificial neural network
Eigenvalues of the elasticity operator
Finite-element method
Inverse problems
Lamé coefficients
Radial basis function

Access to Document

10.1016/j.crme.2015.10.004

Cite this

@article{5556a2fa123a4eebbcaea41093a58036,

title = "On the neural network calculation of the Lam{\'e} coefficients through eigenvalues of the elasticity operator",

abstract = "A new numerical method is presented with the purpose to calculate the Lam{\'e} coefficients, associated with an elastic material, through eigenvalues of the elasticity operator. The finite element method is used to solve repeatedly, using different Lam{\'e} coefficients values, the direct problem by training a direct radial basis neural network. A map of eigenvalues, as a function of the Lam{\'e} 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.",

keywords = "Artificial neural network, Eigenvalues of the elasticity operator, Finite-element method, Inverse problems, Lam{\'e} coefficients, Radial basis function",

author = "Sebasti{\'a}n Ossand{\'o}n and Camilo Reyes",

note = "Publisher Copyright: {\textcopyright} 2015 Acad{\'e}mie des sciences.",

year = "2016",

month = feb,

day = "1",

doi = "10.1016/j.crme.2015.10.004",

language = "English",

volume = "344",

pages = "113--118",

journal = "Comptes Rendus - Mecanique",

issn = "1631-0721",

publisher = "Academie des sciences",

number = "2",

}

TY - JOUR

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

AU - Ossandón, Sebastián

AU - Reyes, Camilo

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 -

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this