Submarine power cables (SPCs) are vital for the offshore wind industry, particularly as wind farms expand into deeper and remoter ocean areas rich in wind resources. These environments subject SPCs, especially dynamic power cables (DPCs) connected to floating wind platforms, to repetitive loadings and consequent fatigue failures, posing substantial challenges within the industry.

Predicting the fatigue life of SPCs involves several critical steps, with local mechanical analysis acting as a pivotal bridge that significantly impacts overall fatigue life estimation. This analysis assesses overall cable behaviours, such as stiffness, and detailed component behaviours, such as stress and strain conditions. The accuracy of the local mechanical analysis crucially influences the ultimate fatigue life estimation. Currently, large safety factors are employed in engineering to compensate for uncertainties due to insufficient understanding of local mechanical behaviours. Therefore, there is a need for a modelling method that can accurately estimate the local mechanical behaviour of SPCs.

This PhD project is dedicated to developing an effective modelling method for the local mechanical analysis of SPCs. An extensive literature review on SPC configurations, design processes, and methods for determining mechanical behaviours is presented in Chapter 2. This chapter focuses on prevalent loadings of tension and bending and discusses the complexity of SPC structures, particularly due to their unbonded, multi-layer, helical component nature and associated stick-slip issues. Two approaches—analytical and numerical—are used to capture these behaviours, with numerical methods preferred for their ability to handle complex structures. However, these methods struggle with efficiency when detailed analysis is necessary. The balance between accuracy and efficiency in developing an effective numerical model hinges on resolving three specific issues: constructing appropriate finite element, managing contact issues, and establishing suitable boundary conditions.

Chapter 3 addresses the aforementioned challenges. First, it introduces an element combination—beam plus surface elements—to simulate the helical metals within SPCs, a method previously validated for accuracy and efficiency. This combination undergoes further verification in subsequent chapters. Secondly, the contact issue, particularly the initial residual stress from extruded polymers during manufacturing, is tackled using contact damping to simulate its effects, enhancing model efficiency and convergence. Lastly, the challenge of setting appropriate boundary conditions is addressed through periodic boundary conditions derived from the homogenization method, applied to a repetitive unit cell (RUC) whose length is reduced to increase computational efficiency. The resulting model, referred to as the RUC model, is applied to SPC samples and validated against test data on tension and bending.

The effectiveness of the RUC model under tension is confirmed in Chapter 4 through material tests and a tension test on a DPC sample. The model demonstrates superior performance in terms of accuracy and efficiency compared to traditional full-scale models. Similarly, Chapter 5 validates the RUC model under bending conditions using tests on both three-core DPC and single-core SPCs. The model is verified against traditional full-scale models, affirming its robustness.

Subsequently, Chapter 6 explores the RUC model’s application in analyzing the combined effects of tension and bending on DPCs. The study extends to parametric analysis of internal components and helical pitch lengths, providing crucial insights for cable design.

Finally, Chapter 7 concludes the dissertation by summarizing the key findings and offering recommendations for further research building on the current study. Additionally, it outlines guidelines for employing the proposed model in practical scenarios
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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.

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The structural complexity of submarine power cables (SPCs) presents significant challenges in their local mechanical analysis. This paper introduces an advanced modeling method developed for analyzing the mechanical behavior of SPCs under tension, emphasizing both accuracy and efficiency. The method’s accuracy is validated through a comparison of simulation results with tension tests conducted on a three-core SPC sample. Efficiency is demonstrated by the superior calculation speed of our model relative to traditional full-scale models. This improved performance is achieved by adopting periodic boundary conditions derived from the homogenization method applied to slender beam-like structures, and by employing a specialized combination of elements to model the helical metal components within the SPCs. The resulting model provides robust capabilities for the mechanical analysis of SPCs under tension and demonstrates significant possibility in accommodating various other loadings.@en

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.

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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.

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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.

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Helical wires are a type of structure winding around on an underneath layer in flexible structures. They constitute a structure layer that provides mechanical protection and sufficient flexibility. The cross section of a helical wire could differ from round to rectangular. The curvature increments of a helical wire on a bent flexible structure can be influenced by the cross section shape due to the contact restriction from the neighbouring layer. The shape effect causes a different mechanical behaviour of the wire itself. However, this effect is not fully understood up till now. This paper mainly investigates the curvature increments of helical wires with rectangular and round cross section by using numerical method. This model takes advantage of the properties belonging to solid elements and beam elements by embedding the latter into the former. The solid element is able to retain the geometry detail of the cross section as much as possible in order to get deep insight of the shape effect. The beam element based on Timoshenko beam theory with well defined Frenet-Serret frames can accurately output the curvature increments in three local directions. Then widly-used analytical models are presented and deployed to verify the numerical results. The research results show the application condition of the analytical expressions and benefit the cable/umbilical/flexible pipe designers.@en

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.

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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.

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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.

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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.

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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.

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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.

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