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

A new numerical method is presented with the purpose to calculate the Lame coefficients, associated with an elastic material, through eigenvalues of the elasticity operator. The finite element method is used to solve repeatedly, using different Lame coefficients values, the direct problem by training a direct radial basis neural network. A map of eigenvalues, as a function of the Lame 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. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.