Alternative Solutions of the Geodesic Differential Equations Applied to the Mechanical Analysis of the Tensile Armors of Flexible Pipes under Bending

Abstract

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.

Mathematical Modelling of Bonded Marine Hoses for Single Point Mooring (SPM) Systems, with Catenary Anchor Leg Mooring (CALM) Buoy Application—A Review

“…In principle, the stability of marine hoses is a function of their slenderness ratio, as they are slender structures. Due to the high span-to-diameter ratio of a marine hose, especially when connected as a hose string, as well as its flexible characteristics, the bending effects are not negligible, unlike flexible riser systems or models [208,284,285].…”

“…The modal shapes are considered in the deformation and buckling of the marine hose, by using the dynamic responses of the marine hose system. This approach is utilised in the FEM of flexible risers [284,285,294,295]. In the third approach, it is assumed that the time-dependent terms are harmonic, with the form shown in Equation (136), with respect to time.…”