Alternative solutions of the geodesic differential equations applied to the mechanical analysis of the tensile armors of flexible pipes under bending
type: Item
instance of: scholarly article
title: Alternative solutions of the geodesic differential equations applied to the mechanical analysis of the tensile armors of flexible pipes under bending
zbMATH Open document ID: 1426.74027
DOI: 10.1155/2018/1040973
author: Gabriel M. Gonzalez
author: João Paulo R. Cortina
author: Luís V. S. Sagrilo
author: José Renato M. De Sousa
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: In some mechanical models, the tensile armors of bent flexible pipes are treated as geodesics on a torus and, based on this hypothesis, the curvatures of these curves are calculated to obtain the acting stresses. However, a closed-form solution of the geodesic differential equations is not possible, which imposes difficulties on determining these curvatures. This work, therefore, proposes two alternative solutions to the nonlinear geodesic differential equations. The first relies on an artificial neural network (ANN) and the second is obtained by symbolic regression (SR). Both employ data from the numerical solution of the geodesic differential equations and showed good correlation with the complete dataset. Nevertheless, when tested against new data, the SR equations led to results almost equal to those obtained with the numerical solution of the differential equations and to null geodesic curvature. Despite also agreeing well with the numerical solution, the ANN indicates nonnull geodesic curvatures. Moreover, when compared to equations often employed in the design of flexible pipes, the SR equations may indicate different results, which can impact, for example, the fatigue or the instability analysis of the tensile armors of these pipes.
Mathematics Subject Classification ID: 74A10
Mathematics Subject Classification ID: 34E13
Mathematics Subject Classification ID: 53Z05
zbMATH DE Number: 7018446
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/1040973
OpenAlex ID: W2792477565
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Wikidata QID: Q130194680
description: scientific article; zbMATH DE number 7018446