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Unbonded flexible pipes consist of multiple subcomponents which interact through frictional contact. A full 3-D finite element analysis of unbonded flexible pipes is computationally expensive, and a more efficient approach for practical engineering purposes is required. This work presents a repeated unit cell (RUC) finite element model for analyzin...
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... layers such as the anti-wear, thermal isolation and anti-buckling layers are ignored in the model. The present FP-RUC model consists of four layers: a core layer, two tensile armor layers with opposite pitch directions, and an outer sheath (see Figure 3). The geometrical parameters of the flexible pipe cross section studied in this paper are listed in Table 1. ...
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... core and the outer sheath are meshed with a single element each in the thickness direction and the tensile armor wires are meshed with two elements in the thickness and width, respectively. The mesh and the geometry of the FP-RUC are illustrated in Figure 3a, and a cutaway illustration showing the internal layers of the FP-RUC is shown in Figure 3b. The mesh used in this study is comprised of 4368 elements with 35687 nodes. ...
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... core and the outer sheath are meshed with a single element each in the thickness direction and the tensile armor wires are meshed with two elements in the thickness and width, respectively. The mesh and the geometry of the FP-RUC are illustrated in Figure 3a, and a cutaway illustration showing the internal layers of the FP-RUC is shown in Figure 3b. The mesh used in this study is comprised of 4368 elements with 35687 nodes. ...
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... x and y are nodal cross sectional coordinates of the FP-RUC given in the coordinate system centered on the pipe center axis, with the directions given in Figure 3, Figure 11 and Figure 15. The FP-RUC is solved using five CPUs on a High-Performance Computing HPC cluster. ...
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... layers such as the anti-wear, thermal isolation and anti-buckling layers are ignored in the model. The present FP-RUC model consists of four layers: a core layer, two tensile armor layers with opposite pitch directions, and an outer sheath (see Figure 3). The geometrical parameters of the flexible pipe cross section studied in this paper are listed in Table 1. ...
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... tensile armor wires are meshed with two elements in the thickness whereas the core and the outer sheath is meshed with a single element in the thickness direction. The mesh and the geometry of the FP-RUC is illustrated in Figure 3a and a cutaway illustration showing the internal layers of the FP-RUC is shown in Figure 3b. The mesh used in this study is comprise of 4368 elements with 35687 nodes. ...
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... tensile armor wires are meshed with two elements in the thickness whereas the core and the outer sheath is meshed with a single element in the thickness direction. The mesh and the geometry of the FP-RUC is illustrated in Figure 3a and a cutaway illustration showing the internal layers of the FP-RUC is shown in Figure 3b. The mesh used in this study is comprise of 4368 elements with 35687 nodes. ...
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Citations
... This work was extended in Saevik and Bruaseth [27] into an FEM formulation for predicting the structural response of umbilical cross-sections subjected to tension, torsion, and bending loads, including internal and external pressure and contact mechanics. Lukassen et al. [28] introduced a numerical model designed to predict local stresses in tensile armor wires of flexible pipes, based on the repeated cell unit (RUC) methodology. Their model incorporated nonlinear periodic boundary conditions for both axisymmetric and constant curvature bending loads. ...
The present study aims to address the knowledge gaps in dynamic power cable designs suitable for large floating wind turbines and to develop three baseline power cable designs. The study includes a detailed database of structural and mechanical properties for three reference cable models rated at 33 kV, 66 kV, and 132 kV to be readily used in global dynamic response simulations. Structural properties are obtained from finite element method (FEM) models of respective cable cross-sections built in UFLEX v2.8.9—a non-linear stress analysis program. Extensive mesh sensitivity studies are performed to ensure the accuracy of the predicted structural properties. The cable’s structural design is investigated using global response simulations of an OC3 5MW reference wind turbine coupled with the dynamic power cable in a lazy wave configuration. The feasibility of the present reference cable in floating offshore wind applications is assessed through a simplified analysis of cable fatigue life and structural integrity analysis of the cable in extreme environmental conditions. The analysis results suggest that the dynamic power cable does not significantly affect the response characteristics of the floating wind turbine in the analyzed lazy wave configuration. Furthermore, a simplified fatigue analysis demonstrates that the proposed cable design can sustain representative environmental loading scenarios and shows favorable dynamic performance in a lazy wave configuration.
... These models have also been extended into flexible pipes [17][18][19], with prescribed requirements about wire number and pitch length. Based on the homogenization method, repeated unit cell (RUC) model has also been proposed and applied in flexible pipes and SPCs [20][21][22][23]. However, the kinematic restraints caused by the large curvature influence of the cable are not presented clearly in the previous studies. ...
... The coordinate of the three points: E(x 1 ,y 1 ), F(x 2 ,y 2 ) and G(x 2 ,y 2 ) are replaced into Eq. (22), then the coefficients for the circle can be obtained. The bending radius of the cable R B is: ...
... .22 presents the curvature-bending moment curves from the experiment, RUC model and the full-scale model. All of the curves have the same trend. ...
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.
... The contact between adjacent armor wires in the same tensile layer (intralayer contact) is believed to have significant effect on lateral buckling of the tensile armor wires and this will be demonstrated in this paper by making use of the newly developed intralayer contact element. By combining this element with the repeated unit cell (RUC) modeling technique [19], this paper proposes a symmetric modelling strategy with high computation efficiency for quick estimate of the lateral buckling capacity of the tensile armor wires. ...
... Repeated unit cell (RUC) model is finite element model for analyzing flexible pipes subjected to combined constant tension and uniform curvature along the flexible pipes. By taking advantage of periodic structural and loading features of the helical components, the RUC model has been proved to be appropriate in predicting stress in the tensile armor wires with extremely high computation efficiency [19]. ...
... [20] By utilizing this periodic feature, one full pitch of the helical component can be equally represented by a cell (a number of segments) with "unit" length. The number is equal to the number of tensile armor wires and the cell length corresponds to the pitch length of the same layer divided by the number of wires, as shown in Figure 12 [19]. RUC model for the 8" flexible riser is created. ...
Flexible pipes and subsea cables are often manufactured with a number of helically wound armor wire layers. Lateral buckling of tensile armor wire may occur when the flexible pipe is exposed to combined axial compressive load and cyclic bending. During installation and operation in hash offshore environments, the touch down section of the flexible pipe may subjected to compressive axial load together with cyclic bending, which can lead to severe damage to the flexible pipe due to the lateral buckling failure mode. The present study investigates the lateral buckling capacity of one 8” flexible riser using Repeated Unit Cell (RUC) modelling technique. The RUC model has been proven to be valid in predicting the onset of the material yield in the most vulnerable tensile layer by comparing the results with a full-scale test data. Development of the stress components in the tensile amor wires as a function of cyclic bending, distribution of gaps between tensile armor wires around circular position are discussed. Lateral buckling is assumed to occur when the total axial stress exceeds yield stress of the armor material. Lateral buckling capacity is defined as the ability of the cross section to withstand certain amount of axial compression when it is exposed to a certain number of cyclic bending.
... An initial stress state is introduced into the model by applying pressure to the cable outer sheath. A similar approach is applied to flexible pipe in [35]. ...
This paper proposes a numerical approach based on a detailed 3D FE model to calculate the global mechanical behaviour and local stress state of dynamic submarine power cables. The method is applied to a three-core dynamic submarine power cable under a cyclic bending load. The numerical approach is based on the homogenization theory of periodic structures. The 3D computational domain is thus reduced to the helical period of the internal cable components, which allows the geometrical complexity and contact interactions between the components to be fully considered. In addition, the mesh size is reduced by using beam element modelling of the armour components. The study investigates the sensitivity of the cable bending behaviour to frictional interactions and manufacturing residual stresses. To validate the numerical model, the results are compared with experimental data and analytical results. The first comparison focuses on the overall behaviour of the cable under a cyclic bending load, while a local analysis compares quantities such as displacement and stresses with the results of analytical models available in the literature. The close agreement between the numerical, experimental and analytical results demonstrates the accuracy of the model in predicting the non-linear bending behaviour and local stresses that are essential for the cable design process.
... Offshore operational experience has proven that the EF region is the weakest point of the flexible pipe system [4]. The study of the tension behavior of flexible pipes has a long history, and numerous researchers have investigated the mechanical behavior of flexible pipes using analytical and numerical analysis and taking into account the deformation and slip of tensile armor under tension loads [5,6]. Furthermore, Yue et al. [7] carried out an experiment on a large scale to support the results of the numerical analysis. ...
Flexible pipes are extensively used to connect seabed and floating production systems for the development of deep-water oil and gas. In the top connection area, end fitting (EF) is the connector between the flexible pipe and floating platform, as a critical component for structural failure. To address this issue, a combined numerical and experimental prediction method is proposed in this paper to investigate the failure behavior of flexible pipes EF considering tensile armor and epoxy resin debonding. In order to analyze the stress distribution of the tensile armor and the damage state of the bonding interface as the tensile load increases, a finite element model of the EF anchorage system is established based on the cohesive zone model (CZM). Additionally, the effects of the epoxy resin shear strength (ss) and the steel wire yield strength (ys) on the structural load-bearing capacity are discussed in detail. The results indicate that wire strength and interface bonding have a substantial effect on the anchorage system’s failure behavior, and the low-strength wire anchorage system has a three-stage failure behavior with wire yielding as the predominant failure mode, while the high-strength wire anchorage system has a two-stage failure behavior with interface debonding as the predominant failure mode.
... The models show great agreement with numerical models and experimental data. Lukassen et al. (2019) proposed a unite cell finite element method to analyze the tension-bending problem. A crucial point is the use of correct boundary conditions, linking the tendons in the unit cell model as to correct capture the behavior of the tendon. ...
... To show the previous model in use, simplified pipe case studies, consisting of an external sheath, two tension armor layers and a core, are conducted. The four layer pipe approach is common in the literature, especially when the interest of the study lies on behavior of the wires (see (Lu et al., 2020), (Lukassen et al., 2019) and (Vaz and Rizzo, 2011)). ...
Flexible pipes are structures responsible for several operations in offshore playing a vital role and hold immense importance in oil extraction.
Modelling such pipes is not trivial, due to its layered structure. The helical wounded wires layers, which are responsible for handling axial loads, present a challenge in modelling in special. Another important factor for consideration are layer interactions, since they play a major role in pipe behavior.
To obtain the pipe response under various loads, the authors proposed the macroelement model: a finite element model in which elements take profit of the problem geometrical characteristics, simplifying the meshing process and contact treatment, while reducing memory use and processing time.
The present article is an excerpt of this research line and focuses on the understating of the frictional behavior in layer interactions by studying a flexible pipe. The model considers all the previous developed elements to simulate a four-layered flexible pipe, consisting of two tensile armor layers and two cylindrical ones. The loading considered is pressure combined with either tension or compression and the effects of the friction coefficient are investigated.
Results
are compared to classical finite element for validation, showing excellent agreement, differences in performance and efficiency are highlighted.
... The dynamic response of flexible risers [3], including curvatures, rotation angles, axial force and moments, may be predicted from dynamic global analysis during its service life, followed by a local stress assessment via numerical or analytical models, using the loading obtained from the global analysis. Many authors have developed analytical models [4][5][6] and finite element models [7][8][9] to investigate the local stresses of armour wires in flexible risers throughout the past few decades. With the advancement of technology and computing power improvement, FEMs, including dedicated BFLEX [7] and models based on multi-purpose commercial finite element software (notably ABAQUS [10] and ANSYS [11]), have been proposed to describe the intricate mechanical behaviour of flexible risers. ...
... Some FEMs are developed to investigate the flexible riser structural response disregarding the bend stiffener, and they may be divided into two main categories: (i) 3D-Periodic or repeated unit cell models for tension and bending loads with uniform curvature, where periodic boundary conditions are introduced between the end sections to reduce the model size. The model length is usually twice the pitch of the armour wires divided by the number of wires [8,14] and (ii) models developed with less constraints for general loading conditions but also including simplification in some layers representation, such as, carcass and pressure armour layers modelled as equivalent orthotropic layers [9,12] to reduce computational time. The length of these models typically requires representation of three pitches of the armour wires [13] to avoid the influence of boundary conditions. ...
The flexible riser top connection with floating production units presents additional tensile armour integrity assessment uncertainties associated to the bend stiffener contact interaction that leads to a non-uniform curvature and contact pressure distribution in a region of large dynamic forces and moments. In this paper, a full-scale 6″ flexible riser and bend stiffener bending-tension experimental campaign is carried out in a horizontal rig. The external tensile armour wires are instrumented with strain gauges for axial strain measurement in several riser cross-sections inside and outside the bend stiffener region. The rig assembly allows the riser rotation in order to measure strains at different circumferential angular positions. The bend stiffener polyurethane hyperelastic mechanical response is obtained by uniaxial tensile tests performed at room temperature. A nonlinear finite element model (FEM), including the riser/bend stiffener contact interaction and interlayer friction mechanisms, is employed to numerically investigate the mechanical behaviour of the flexible riser subjected to the experimental loading conditions. The FEM axial strains on the tensile armour wires are compared with the measured results for pure tension and tension-bending loads. Under axisymmetric loading a relevant experimental axial strain dispersion is observed when compared to the average values. Under tension-bending loading, the interlayer friction coefficient influences on the contact pressure and curvature distribution are initially assessed with the numerical model. The strain gauges located in the cross-sections with highest values of contact pressure and curvature are selected for a detailed numerical-experimental strains comparison. In addition, a parametric study is conducted to calibrate the friction coefficient that yields the minimum mean squared error for all measured data. Generally, good correlations are found between the experimental and numerical results.
... At present, a straight piece of welded tube needs to be deformed to a selected bending radius and angle according to practical requirements. The traditional bending technologies, such as rotary-draw bending [3], tension-bending [4], and roll bending [5], were mainly used to bend the welded tube. However, with the developing trend of product customization, the demand for the bent tube component with small batch and complex configuration is increasing, as indicated by Yang et al. [6]. ...
The plastic deformation behavior of welded tube is affected by the non-uniform distribution of the mechanical properties of welded tube during the free bending process. To explore the influence of weld position on the forming quality and axis dimensional accuracy of welded tube, the free bending experiment and numerical simulation of welded tube were conducted in this paper. First, the principle of free bending was theoretically deduced and the stress distribution of bent tube was analyzed. Then, the hardness test and uniaxial tensile test were conducted to obtain the mechanical properties of weld zone and parent zone of welded tube. The material strength in the weld zone of welded tube is significantly higher than that in the parent zone. Finally, the free bending experiment and numerical simulation with different weld positions were carried out, and the influence of weld position on the bending radius, cross-sectional distortion, and wall thickness of bent tube was discussed. All these findings advance the insight into the free bending deformation behavior of welded tube and help to improve the forming quality of welded tubes and facilitate the application of free bending technology in welded tube.
... Some FEMs are developed using general purpose tools such as ABAQUS [18] and ANSYS [19] programs to investigate the structural response of a flexible riser subjected to combined tensile and bending loads [20][21][22], but the curvature distribution achieved in these models is not uniform, which does not allow a proper comparison with analytical models under the constant curvature assumption. Two alternative FEMs have been recently developed and reported in the literature combining tension and bending loads with uniform curvature: i) the repeated unit cell (RUC) method [23] and ii) equivalent thermal stain method [24]. The first model takes advantage of the structural and loading periodicities by assuming uniform wire response (one pitch of a single wire is assumed to represent the full tensile armour layer) to reduce computational time. ...
... The friction stress distribution [23] is calculated based on the stick-slip condition, summarized as: ...
The flexible riser within the bend stiffener in the top connection is a structurally vulnerable region for extreme and fatigue loads as it is subjected to large dynamic tensile forces and curvatures. This paper presents a nonlinear finite element model (FEM) for the flexible riser with bend stiffener taking into account interlayer friction and riser-bend stiffener contact interaction subjected to combined axisymmetric and bending loads. A case study with typical extreme and fatigue load cases is carried out to assess the curvature variation and bend stiffener contact pressure influence in the riser tensile armours stresses. For the extreme load case, detailed finite element results such as contact pressures and friction, normal and transverse bending stresses are compared with a uniform curvature FEM and available analytical models. A fatigue load case is also performed, where the stress amplitudes and cumulative fatigue damages for the internal tensile armour wires are compared with a uniform curvature FEM and analytical models. From the case study results under extreme loading, it can be observed that the model with bend stiffener interaction predicts larger stresses in comparison to the uniform curvature FEM and analytical models. Under typical fatigue loading conditions, significant differences in the cumulative damage are observed between the models, highlighting the importance of an accurate modeling for lifetime integrity assessment in a region of highly variable riser curvature.
... Huang et al. [3] have confirmed that flexible branch heat pipe has a larger maximum heat load than the straight pipe. Meanwhile, the other study showed that a flexible pipe with a repeated unit cell had a strong correlation between the repeated unit cell model and the analytical models with some difference in the wire bending stresses [4]. This research also found that the repeated unit cell model is robust and computationally efficient for analyzing flexible pipes [4]. ...
... Meanwhile, the other study showed that a flexible pipe with a repeated unit cell had a strong correlation between the repeated unit cell model and the analytical models with some difference in the wire bending stresses [4]. This research also found that the repeated unit cell model is robust and computationally efficient for analyzing flexible pipes [4]. Tang et al. [5] have analyzed that an increase in the winding angle of the tensile armor wires and damage to the outer sheath of the flexible pipe decreased the compressive stiffness significantly. ...
The thermal expansion can lead to the high stress on the pipe. The problem can be overcome using expansion loops in a certain length depending on the material’s elastic modulus, diameter, the amount of expansion, and the pipe’s allowable stresses. Currently, there is no exact definition for the dimension of expansion loops design both for loop width (W) and loop footing height (H) sizes. In this study, expansion loops were investigated with using ratio of width and height (W/H) variations to understand pipe stress occurring on the expansion loops and the expansion loops’ safety factor. Relationship between non dimensional stress on the expansion loop pipe was studied numerically by finite element software on several working temperatures of 400oF, 500oF, 600oF, and 700oF. It can be found that stress occurring on the pipes increases as the increases of W/H of the expansion loops and results in a lower safety factor. The safety factor of the expansion loops pipe has a value of 1 when the ratio of loop width and loop footing height (W/H) value was 1.2 for a 16-inch diameter pipe. Stress occurring on the pipe increases with the increase of the working temperature. Expansion loops pipe designed for 400oF can still work well to handle thermal extension pipe occurring on 500oF.
