Alternative Solutions of the Geodesic Differential Equations Applied to the Mechanical Analysis of the Tensile Armors of Flexible Pipes under Bending
Joint Authors
Sagrilo, Luís V. S.
de Sousa, José Renato M.
Gonzalez, Gabriel M.
Cortina, João Paulo R.
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-02-26
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Gonzalez, Gabriel M.& Cortina, João Paulo R.& de Sousa, José Renato M.& Sagrilo, Luís V. S.. 2018. Alternative Solutions of the Geodesic Differential Equations Applied to the Mechanical Analysis of the Tensile Armors of Flexible Pipes under Bending. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-16.
https://search.emarefa.net/detail/BIM-1205470
Modern Language Association (MLA)
Gonzalez, Gabriel M.…[et al.]. Alternative Solutions of the Geodesic Differential Equations Applied to the Mechanical Analysis of the Tensile Armors of Flexible Pipes under Bending. Mathematical Problems in Engineering No. 2018 (2018), pp.1-16.
https://search.emarefa.net/detail/BIM-1205470
American Medical Association (AMA)
Gonzalez, Gabriel M.& Cortina, João Paulo R.& de Sousa, José Renato M.& Sagrilo, Luís V. S.. Alternative Solutions of the Geodesic Differential Equations Applied to the Mechanical Analysis of the Tensile Armors of Flexible Pipes under Bending. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-16.
https://search.emarefa.net/detail/BIM-1205470
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1205470