An efficient Artificial Neural Network algorithm for solving boundary integral equations in elasticity

This study presents a novel numerical integration technique based on Artificial Neural Network (ANN) algorithms to overcome intrinsic limitations characterizing the Boundary Element Method (BEM). The proposed approach, taking advantage of some peculiar properties of the BEM equations, provides an ef...

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Bibliographic Details
Published in:Engineering analysis with boundary elements Vol. 156; pp. 379 - 391
Main Authors: Ruocco, E., Fusco, P., Musone, V.
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.11.2023
Subjects:
ANN
BEM
Elasticity
Numerical integration
Elasticity
ANN
Numerical integration
BEM
ISSN:0955-7997, 1873-197X
Online Access:Get full text
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Summary:This study presents a novel numerical integration technique based on Artificial Neural Network (ANN) algorithms to overcome intrinsic limitations characterizing the Boundary Element Method (BEM). The proposed approach, taking advantage of some peculiar properties of the BEM equations, provides an effective alternative to traditional numerical techniques for evaluating the integrated kernels required to compute the displacements and stresses of a two-dimensional solid. Assuming isotropy and homogeneity, and modeling both the geometry and the mechanical parameters using quadratic shape functions, all the integrals in the classical BEM formulation can be expressed as the sum of two terms that are independent of the constitutive properties and solely dependent on four geometric parameters: three components of two distance vectors and a parameter representing the element’s curvature. This interesting property of boundary integral equations in elasticity makes them particularly amenable to numerical evaluation using artificial neural networks. Results from numerical tests, which were conducted using increasingly complex integrals, demonstrate the high precision of the proposed approach as long as the integration and collocation points are sufficiently separated to avoid issues with singularity.
ISSN:0955-7997
1873-197X
DOI:10.1016/j.enganabound.2023.08.020