Submarine power cables (SPCs) are subjected to complex mechanical loadings during service, including tension, bending, torsion, and their combinations. However, systematic studies on the behavior of SPCs – particularly multi-core configurations – under such combined environmental loadings remain limited. This lack of comprehensive analysis hampers a full understanding of their mechanical responses and consequently restricts the design and development of these critical structures. Building upon our previously validated Representative Unit Cell (RUC) model for local mechanical analysis under pure tension and pure bending, this paper extends the investigation to a three-core SPC under a range of combined load cases. In addition, full-scale models are developed to study the torsional response in greater detail. The findings of this study provide valuable guidance for cable engineers, offering new insights into the internal interactions within SPCs and supporting more robust cable design.

The complex interplay of numerous helical components within submarine power cables (SPCs), especially those with significant contact issues due to initial residual stress, complicates their modelling and limits our understanding of these structures. In this paper we proposed an effective modelling method designed for the local mechanical analysis of SPCs under bending. The method was developed based on three key aspects: (1) constructing appropriate finite elements to reduce the number of elements required; (2) employing contact damping to address the effects of initial residual stress at contact interfaces; and (3) applying periodic boundary conditions on a repeated unit cell (RUC) to reduce the model size. The accuracy of this method was validated through extensive testing on both single-core and three-core SPC samples, and its efficiency was confirmed by comparing these results with those obtained from traditional full-scale models. Following validation, the model was employed to illustrate the local mechanical behaviours of SPCs under bending, both at the overall level and at the component level. This model serves as a powerful tool for cable engineers, offering deeper insights into the internal interplays of SPCs. All relevant codes developed in this paper are freely available at https://pan-fang.github.io/Codes/.

As the wind industry expands into remoter and deeper areas of the open sea with abundant wind energy, environmental loadings become harsher. This increases the requirements for submarine power cables (SPCs), which serve as the ‘lifeline’ for transporting electricity. Consequently, a more advanced design based on a thorough understanding of this structure is needed. However, the complex configuration and intensive contact issues within SPCs limit our understanding and make them black boxes for cable engineers. To gain more insights, methods for performing local mechanical analysis of SPCs are necessary. Despite this need, a comprehensive review of existing methods for local mechanical analysis of SPC is still lacking. Therefore, it is essential to review the available methods and provide guidelines for utilizing and developing these methods.

The complex structure and material property of a cable, particularly the stick-slip issue among its components pose the challenge for the bending analysis of submarine power cables. The calculation time and convergence problem of a full model makes the simulation unpractical during the design phase. This paper takes advantage of the peculiar structural property of helical components inside a cable, proposing a computational homogenization approach for analyzing the cable behavior under bending from global and local perspectives. This method assumes a macro model that is based on the theory of periodic beamlike structure, and a short-size micro model that is solved through a detailed finite element study. Results demonstrate the efficiency and capability of the proposed model that considers the structure nonlinearity and contact condition of a multi-layer cable with helical wires.

In this article, we’ll show how to solve the time-fractional seventh-order Lax’s Korteweg–de Vries and Kaup–Kupershmidt equations analytically using the homotopy perturbation approach, the Adomian decomposition method, and the Elzaki transformation. The KdV equation is a general integrable equation with an inverse scattering transform-based solution that arises in a variety of physical applications, including surface water waves, internal waves in a density stratified fluid, plasma waves, Rossby waves, and magma flow. Fractional derivative is described in the Caputo sense. The solutions to fractional partial differential equation is computed using convergent series. The numerical computations and graphical representations of the analytical results obtained using the homotopy perturbation and decomposition techniques. Moreover, plots that are simple to grasp are used to compare the integer order and fractional-order solutions. After only a few iterations, we may easily obtain numerical results that provide us better approximations. The exact solutions and the derived solutions were observed to be very similar. The suggested methods have also acquired the highest level of accuracy. The most prevalent and convergent techniques for resolving nonlinear fractional-order partial differential issues are the applied techniques.

Wire ropes are widely observed in many industries such as marine engineering and civil engineering, as a type of structure that can bear huge axial force. There are various kinds of wire ropes in practical engineering, corresponding to different usage scenarios. This paper focuses on 6 × 36SW + 1WR with a diameter of 16 mm. The axial mechanical properties of the wire rope are investigated by experimental, theoretical, and numerical methods. The stress–strain curve and ultimate strength of the steel wire rope obtained in the test are compared with the corresponding results from the finite element simulation. The comparison demonstrates the accuracy and reliability of the finite element model. In addition, a series of parametric studies are conducted to investigate the influence of pitch length and friction coefficient, etc. The purpose of this paper is to propose an accurate and efficient finite element model for the mechanical analysis of wire ropes.

Predicting the bending behaviours of a submarine power cable (SPC) is always a tough task due to its complex geometry and inner layer contact, not to mention the stick–slip mechanism. A full-scale finite element model is cumbersome during the early design stage and a more efficient model for practical use is required. Therefore, in this paper, a repeated unit cell (RUC) technique-based FE model is developed, which simplifies the bending analysis of SPCs using a short-length representative cell with periodic conditions. The verification of this RUC model is conducted from cable and component levels, respectively. The cable overall response is validated by the curvature-moment relationships from our cable bending tests regarding four cable samples whose material properties are obtained through a set of material tests. As for the component level, the behaviours of particular components are studied and compared with the results from a full-scale numerical model. Discrepancy is observed between the RUC model and the test, which can be explained by the distinctions of boundary conditions between these two methods. The proposed Cable-RUC model has been found robust and computationally efficient for studying SPCs under bending.

Composite structures, such as the fiberglass reinforced structure studied in this paper, have been normally treated in previous research as homogeneous anisotropic laminated plates regarding the investigation of their mechanical properties. Throughout this paper, this specific structure is considered in a different way in which the fiberglass and polyethylene matrix are treated separately. By using the proposed method, the material plasticity of polyethylene and the fracture stress of the fiberglass can be taken into account, and thus the fracture of the fiberglass inside the fiberglass reinforced flexible pipes(FGRFP) can be predicted. The mechanical behaviour behavior of FGRFP under two real-life main loadings(tension and internal pressure) is investigated by using analytical and numerical methods based on the proposed technique. Experiments are used to verify the results.

Submarine power cables are considered lifelines in wind farm engineering, playing a key role in transporting electric current produced by wind turbines or wave converters. The bending behaviour of a power cable is a complex issue due to both its various materials and multi-layer structures. The copper conductor in the middle of a power cable is especially complex as it is composed of numerous helical copper wires. The influence of the copper conductor on the overall bending behaviour is still not clear due to rare studies regarding this topic. This paper focuses on the pure bending test of a naked copper conductor from a real cable, then theoretical and numerical methods are used to generate the bending stiffness in order to compare it with each other. The pros and cons of each method are clarified and the obtained conclusions will pave the way for the study of the overall power cable.

Metallic strip flexible pipes (MSFP), a relatively new style of unbonded flexible pipes, are considered as an attractive alternative to traditional submarine pipes. During its reeling operation, it will inevitably confront various complicated loads, which may affect the integrity and safety of MSFP's utilization. In this paper, the tension-extension and moment-curvature relation of MSFP were obtained by laboratorial tests. The mechanical properties were then imported into the global model established in ABAQUS. The finite element model was adopted to predict the deformation and mechanical responses of MSFP during the operation process. Besides, the effects of reeling length, the diameter of the coiling drum, and the pulling force were discussed. The obtained conclusions will provide some references for optimizing MSFP design and preventing possible damage in the reeling operation.

A numerical model in slice configuration was applied to the Central Andaman Sea in order to derive metocean operational and design criteria associated to internal solitary waves which are large amplitude interfacial waves. For that purpose, a 10 year hindcast was generated. The model was driven by tides at the open boundary and included realistic stratification and topogra-phy. The results have been compared to data mostly taken from satellites and proved to be accurate in determining parameters such as phase speed and interpacket distance. The phase speeds range from 2.21 m/s in March to 2.5 m/s in November. Corresponding interpacket distances range from 99 km to 111 km in close agreement with available data. According to the model results internal solitary waves are more/less frequent in March/August. Model outputs were specifically analyzed at 2 arbi-trary locations. Maximum current speeds obtained with the model at those locations occur in November reaching a value close to 1.5 m/s. The computed velocities associated to return periods of 1, 10, 50, 100 and 1000 years are, respectively, 1.67 m/s, 1.76 m/s, 1.8 m/s, 1.81 m/s and 1.84 m/s.

Submarine power cables are considered lifelines in wind farm engineering, playing a key role in transporting electric current produced by wind turbines or wave converter. Cables inevitably confront combined loadings in deep-sea areas, affecting the integrity and safety during their installation and application. In this paper, the mechanical behaviour of submarine power cables subject to axisymmetric loadings(tension, torsion and external pressure) is investigated through both analytical and numerical methods. The objective of the analytical method is to predict the tension and torsion stiffness of cables and evaluate the stress of armour wires. These values from the two methods are essentially in agreement with each other. In addition, the effects of wire layers, winding angles and external pressure are discussed through the analytical method. The obtained conclusions will benefit the cross-section design of power cables and relative practical engineering.

Fibreglass reinforced flexible pipe (FGRFP) is a kind of composite thermoplastic pipe serving as a preferred application in the field of oil transportation. This paper studies the mechanical behaviour of FGRFPs under pure bending by experimental, numerical and theoretical methods. Full-scale four-point bending tests are conducted and the curvature-bending moment relations of specimens are recorded. In the numerical simulation method (NSM), a detailed finite element model considering both material and geometric nonlinear behaviour is established, and the composite is defined as an orthotropic elastic-plastic material. Based on the Euler–Bernoulli beam theory, a simplified theoretical method (STM) is proposed to predict the ultimate bending moment. In the parametric study, a simple formula is introduced to modify STM to make it more accurate. Good agreements proves the reasonability of the proposed NSM and STM. Additionally, STM could make a contribution to engineers in terms of a concise and relatively accurate way in ultimate status analysis.