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Abstract:The instability of the tensile armor wire of flexible pipes is a failure mode associated with deep and ultra-deep water applications. Real compressive forces acting on the pipe are necessary to trigger this process. The loss of stability may be divided into two distinct processes, according to the main direction of the wire's displacement: radial or lateral instability. This study aims at proposing a numerical tool for predicting lateral and radial critical buckling loads for the tensile armor wires of flexible pipes. A simple finite element model, based on springs and beams elements, was developed in ABAQUS® to deal with this problem in an efficient and reliable manner. A parametric study was conducted concerning the behavior of the critical load when the laying angle, the initial curvature and the total pipe length are varied. The results were consistent with previously published literature data and analytical expressions, proving its applicability to pipe engineering projects. It also has the advantage of approaching the problem three-dimensionally, which allows further modelling modifications, such as including friction effects.

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.

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