Eduardo Antonio Wink de Menezes

Numerical Modelling of Helical Cables Using Beam Elements

Due to the complex geometry of helical cables and wire ropes, the available analytical models have a series of simplifications, assumptions and a limited capacity in reproducing their mechanical behavior, and 3D numerical models are often costly and time-consuming due to interwire contact. Both methods are not viable when dealing with long cables, as in cable-stayed bridges and offshore platforms applications, where they can reach more than 1500 m (ultra-deep waters). The purpose of this work is to incorporate a new 1D beam element in a commercial finite element (FE) software. A 3D FE model, previously verified by experiments, was used to calibrate the 1D element, which carries the information provided by the 3D model in its stiffness matrix. The result is a 2-node beam element with six degrees of freedom per node which is able to simulate long cables, combining both the practical implementation of an analytical model with the accuracy of a 3D FE model. The adjusted beam model fitted the 3D model with a coefficient of determination (R2) above 0.90.

Strength analysis of composite cables

Carbon Fiber Reinforced Polymer (CFRP) cables, due to their outstanding performance in terms of specific stiffness and strength, are usually found in civil construction applications and, more recently, in the Oil & Gas sector. However, experimental data and theoretical solutions for these cables are very limited. On the contrary, several theoretical and numerical approaches are available for isotropic cables (metallic wire ropes), some of them with severe simplifications, nonetheless showing good agreement with experimental data. In this study, experimental tensile results for 1×7 CRFP cables were compared to a simplified analytical model (assumed transversally isotropic) and to a 3D finite element model incorporating the experimental uncertainty in important input parameters: longitudinal elastic modulus, Poisson’s ratio, static friction coefficient and ultimate tensile strain. The average experimental breaking load of the cable was 190.25 kN (coefficient of variation of 1.74%) and the agreement with the numerical model predictions were good, with an average-value deviation of –1.15%, which is lower than the experimental variations. The simplified analytical model yielded a discrepancy above 10%, indicating that it needs further refinement although much less time consuming than the numerical model. These conclusions were corroborated by statistical analyses (i.e. Kruskal–Wallis and Mann-Whitney).

Metallic and composite cables: a brief review

For cable-moored offshore tension-lag platforms in ultra-deep waters (2000 m), the usage of metallic cables is impractical, making carbon fibre reinforced polymer (CFRP) natural substitutes. CFRP cables have been applied in different situations, such as in cable-stayed bridges, in order to take advantage of its outstanding fatigue behaviour, higher specific stiffness and strength, and good corrosion resistance. However, there are not much experimental data available in the literature for these cables and theoretical solutions still need to be further developed. On the other hand, several theoretical approaches have already been developed for isotropic (metallic) cables, some of them with many simplifications nonetheless still showing good agreement compared to experimental data. On this context, this paper aims to report recent advances on composite cables, comparing previous research results on both composite and isotropic cables on the experimental, analytical and numerical fields.

Numerical and Experimental Analysis of the Tensile and Bending Behaviour of CFRP Cables

Due to their high fatigue life, specific strength and specific stiffness in comparison with steel, carbon-fibre reinforced polymer (CFRP) cables have attracted the infrastructure industry interest in recent years, primarily for use as structural tendons. Particularly the oil and gas industry showed interest for application in offshore platform anchorage systems, because of their exceptional corrosion and creep/relaxation behaviour. In such applications, the cables need to be tensioned in service and to be bent around relatively small-diameter spools for transportation and maintenance. Therefore, their tensile and bending behaviour is a subject of great concern. The aim of this work was to perform a test program on 1 × 19 CFRP cables in two different situations: tensile loading and four-point bending loading. Finite element models were developed to simulate both conditions, including frictional contact between the cable wires. A simplified analytical model was also used to predict the cable behaviour in tension. Numerical predictions were compared to experimental data showing relatively good accuracy, unlike the verified analytical model. CFRP cables presented outstanding tensile behaviour, but bending over small radius spools could not reach the performance of steel wire ropes. Furthermore, simulation could only fairly predict bending below strains of μ1,000 μe for the external rods, beyond which the cable presented highly non-linear behaviour that could not be simulated by the numerical model.

Numerical model updating applied to the simulation of carbon fiber–reinforced polymer cables under bending and tensile stress

Wire ropes are widely used in applications where the axial stress is high and flexural and torsional stresses are relatively low. Study of their mechanical behavior encompasses many factors, bringing considerable complexity to the construction of numerical or analytical models that suitably represent their behavior, including contact stresses between rods, helical geometry, rotation of wires when extended and also, in the case of carbon fiber–reinforced polymer (composite) cables, their anisotropic behavior. In view of the lack of suitable analytical solutions, this work focuses on the updating of a finite element model by incorporating factors commonly neglected by simplified analytical approaches. The carbon fiber–reinforced polymer cable was modeled under tensile stress and under four-point bending. After that a sensitivity analysis of the main parameters governing the problem was conducted. The updating process minimized the deviation between numerical and experimental data, and the model was able to reproduce the tensile and bending behavior with deviations smaller than 1%. The adopted methodology can be extended to similar cases.