A finite element model for unbonded flexible pipe under combined axisymmetric and bending loads

Flexible pipes are key equipment for offshore oil and gas production systems, conveying fluids between the platform and subsea wells. The structural arrangement of unbonded flexible pipes is quite complex, encompassing several layers with polymeric, metallic and textile materials. Different topologies and a large amount of intricate nonlinear contact interactions between and within their components, especially because of the relative stick-slip mechanism during bending, makes numerical analysis challenging. This paper presents an alternative three-dimensional nonlinear finite element model that describes the response of flexible pipes subjected to combined axisymmetric and bending loads. To simulate the response of a flexible pipe under axial tension or compression combined with uniform curvature, an equivalent thermal loading is employed on the external sheath, which is modelled as an orthotropic thermal expansion material with temperature-independent mechanical properties. To assess the feasibility of the proposed model, the bending moment versus curvature of the finite element solution is compared with experimental results obtained in literature and good agreements are found between them. Detailed finite element results such as contact pressures, armour wire slip displacements and friction, normal and transverse bending stresses are also shown and compared with available analytical models.     

Theoretical and numerical analysis of bending behavior of unbonded flexible risers

This paper presents theoretical and numerical study on bending properties of unbonded flexible risers. To capture nonlinearities in layer's sliding, the stress component due to slip-stick behavior is considered and energy conservation principle considering sliding-caused heat consumption is employed in the analytical model. Besides, a finite element model estimating mechanics of unbonded flexible risers' bending is proposed. In the finite element model, couplings between bending moment–curvature and axial stress as well as contact interaction among layers and tendons have been considered. The theoretical and numerical results were validated against the corresponding experimental data in literature and mutually compared in analyzing nonlinear bending behavior of flexible risers. Moreover, the impacts of axisymmetric loads on riser's bending behavior have been further investigated.     

非粘结柔性立管静态分析

海洋柔性立管因材料和结构上的复杂性在设计分析中存在许多技术难题。本文在变形能原理和能量守恒的基础上,推导出了柔性立管各层的刚度矩阵。将各层刚度矩阵进行叠加,得到柔性立管总体刚度矩阵,并用总体刚度矩阵求解静载荷作用下立管变形响应。同时基于ABAQUS软件建立八层非粘结柔性立管有限元模型,并将有限元计算结果和刚度矩阵计算结果进行比较。结果分析表明：运用推导得到的刚度矩阵求解静态载荷下立管的变形是一种简便且准确的方法。     

Application of analytical model in the prediction of dynamic responses and fatigue damage of flexible risers: Part I – Improvement of analytical model considering shear deformation and varying tension effects

Flexible risers have been widely utilized for the transfer of oil and gas products from a well to production units. The components of flexible risers, unlike steel risers, experience complex contact phenomena during bending. The contact between helical wires and adjacent layers especially causes a significant level of bending nonlinearity, making it hard to estimate the structural responses. Accordingly, a large-scale dynamic analysis of flexible risers usually involves an analytical model that predicts the bending moment and axial stress of helical wires based on theoretical approaches. The analytical model consists of an axis-symmetrical model and a bending model. Among them, the bending model plays a critical role in the prediction of the bending responses of flexible risers. The conventional bending models usually neglect the shear deformation of internal layers and continuity of sliding force, which leads to a significant error of analysis. Furthermore, the previous bending models assume that the contact pressure on helical wires is constant during bending. In real operating conditions, however, most flexible risers experience a considerable change of tension that governs the slip of helical wires. Hence, the current study presents a new dynamic analysis method for flexible risers. The suggested analytical model improves the bending model based on an accurate estimation of the internal strain field considering the shear deformation and continuous sliding force. Also, this study proposes a stiffness update method to reflect the effect of varying tension in the dynamic analysis. The presented method updates the bending property of flexible risers considering the continuous change of the contact pressure from varying tension. For the validation of suggested method, the current study carries out numerical simulations with a pure bending and varying tension for the internal diameter 7 inches flexible risers. It is identified that the suggested analytical model provides accurate analysis results. Moreover, it is found that the effect of varying tension gives a significant impact on the bending behavior of flexible risers by changing the slip condition of helical wires. Part I of this series of papers describes the detailed formulation method for the analytical model and with some verification examples. The suggested analytical model is expanded to the large-scale dynamic analysis in Part II for the investigation of the effect of shear deformation and varying tension.     

A model for the biaxial dynamic bending of unbonded flexible pipes

An analytical model is given to investigate the behavior of unbonded flexible pipes under biaxial dynamic bending. The stick-slip conditions of each wire are studied in the framework of incremental analysis by an operator splitting of the time step into a stick-state prediction and a slip-state correction step. The tension gradient is calculated using the classical return-mapping algorithm and the obtained tension gradients are integrated numerically to find the axial tension by imposing appropriate boundary conditions. From the axial tension the bending moments with respect to the principal bending axes of the pipe are obtained. Poisson's effect, bending induced tension in the wire, shear deformations of the supporting plastic layer and the changes of the effective torsion and curvature increments of the wire after slip occurs are taken into account in the model. The results of bending moment–curvature relationship from this model are compared with the test data from simple bending and good correlations are found. The comparison of the biaxial bending moment results between this model and the available model also shows good agreement.     

Application of analytical model in the prediction of dynamic responses and fatigue damage of flexible risers: Part II – Dynamic analysis of flexible risers in large-scale domain using a direct moment correction method

In recent years, the dynamic responses of flexible risers have been the focus of many researchers. Most flexible risers undergo a substantial level of irregular motion from environmental loadings, which involves a continuous slip of helical wires. The slip of helical wires especially leads to a hysteretic effect by reducing the bending stiffness, making it hard to predict the dynamic responses of flexible risers. The current study, as an extension to Part I, presents a new large-scale dynamic analysis method for flexible risers. The suggested method creates a large-scale model for the dynamic analysis that considers a geometric and bending nonlinearity of flexible risers. The kinematics of each beam element is formulated based on a Green-Lagrangian strain and the interaction with the seabed, providing a realistic analysis of flexible risers. In particular, the current study introduces a direct moment correction method that modifies the internal force vector using an improved analytical model. The improved analytical model is assigned at each node of the large-scale model and estimates an accurate bending hysteresis curve considering the effect of shear deformation and varying tension. The suggested method corrects the bending moment and shear force of all beam elements based on the bending hysteresis curves obtained from the improved analytical model, by which a complex bending behavior of flexible risers is reflected in a large-scale domain. As a result, this study achieves a more accurate prediction of the dynamic responses and fatigue damage of flexible risers. A new dynamic analysis program, called OPFLEX, is developed herein based on the suggested analysis method. Using the developed program, the current study conducts several numerical investigations to identify the effect of the shear deformation and varying tension. Consequently, it is confirmed that the shear deformation of internal layers reduces the fatigue damage of helical wires by delaying the increase of internal stress. It is also identified that the effect of varying tension deteriorates the fatigue life of flexible risers through a continuous change of contact pressure during bending.     

Axisymmetric structural behaviours of composite tensile armoured flexible pipes

To address the weight and corrosion challenge in deep-water, replacing the steel tensile armour in flexible pipes with composite materials is an alternative conceptual approach. An axisymmetric structural responses model is built for this novel composite armoured flexible pipe, with interlayer gaps that may occur in the unbonded structure considered through an iterative algorithm. The tensile strength of steel and composite armoured pipes are predicted based on different constitutive relations of steel and composite. Essential quantities are obtained, such as tensile stiffness, deformations of each layer and interlayer gaps or contact pressures. Considering the helix form of carcass and pressure armour, a finite element model is established for the verification of the theoretical model. Case study shows that the tensile stiffness of flexible pipe is overestimated with the interlayer gap ignored. Compared with steel armoured flexible pipe, the composite armoured pipe, whose tensile stiffness decreases less as external pressure increases, meanwhile has higher values of tensile ultimate strength and torsion stiffness. Some suggestions about fiber types and volume fraction for composite tensile strips are given to ensure good performance of axial tensile strength and stiffness.     

A finite element model for flexible pipe armor wire instability

The constructive disposition of metallic and plastic layers confers flexible pipes with high and low axial stiffness respectively when tensile and compressive loads are applied. Under certain conditions typically found during deepwater installation or operation, flexible pipes may be subjected to high axial compression, sometimes accompanied by bending. If not properly designed, the structure may not be able to withstand this loading and fails. From practical experience observed offshore and in laboratory tests two principal mechanisms, which will be discussed in this paper, have been identified regarding the configuration of the armor wires. When the pipe fails by compression the armor wires may exhibit localized lateral or radial deflections, consequently permanent damage is observed in the armor wires with a sudden reduction of the structure’s axial stiffness. The pressure armor may also unlock, thus causing potential fluid leakage.In this work a finite element model is developed to estimate the critical instability load and failure modes. An axi-symmetric model is constructed employing a complex combination of beam and spring elements. For each armor layer only one wire needs to be modeled, hence the computational cost is minimized without compromising the phenomenon characterization. A parametric case study is performed for a typical flexible pipe structure, where the friction coefficient between the wire armors and the external pressure are varied, and the critical instability loads and failure modes are obtained and results are discussed.     

考虑平台作用的顶张式立管动力分析

上层浮式平台的运动幅度比固定式平台大,对立管的影响更明显.为了解平台对顶张式立管动力的影响,提出一种动力分析方法.在一定的条件下建立立管的数学模型,采用软件Tube2D对平台和立管进行动力响应和弯曲应力分析,得到考虑平台作用的立管扶正器布置间距参数的敏感性和立管弯曲应力的变化.结果表明:对于考虑平台作用的立管模型而言,内套管与油管在立管上部更容易发生碰撞,从避碰的角度考虑,应适当减小立管上部扶正器的布置间距;各层立管的弯曲应力按弯曲刚度之比分配的结果与实际计算结果不符,应根据耦合立管模型的计算结果对各层立管进行强度校核.     

Bending behavior modeling of unbonded flexible pipes considering tangential compliance of interlayer contact interfaces and shear deformations

Rigorous analytical formulations are given to describe the gross slip initiation and progression in tensile armor layers of unbonded flexible pipes. Then two mechanisms are thought to contribute to the decrease of layer stiffness before gross slip begins. The first one considers the micro-slip occurred at the interlayer contact interfaces. The relative displacement between an armor wire and the underlying layer is determined according to the theory of contact mechanics. Shear deformations of the supporting plastic layer are taken into account in the other mechanism where plane sections no longer remain plane. The results of bending moment-curvature relationship from the presented models are compared with the available test data and good correlations are found. The shear model is seen to describe the slip transition better than other models do.     

压力载荷下非粘结柔性立管应变影响因素分析

基于Abaqus/Explicit准静态和质量放大方法研究了一类典型非粘结柔性立管在压力载荷作用下应变响应特性,对影响立管整体轴向延伸率和绕轴向扭转角度的因素进行了分析。数值模型计入金属层实际截面形状、铺设角度以及几何、接触、材料非线性。计算结果表明：数值解与理论值吻合较好;立管端部边界条件对轴向延伸率影响不大但对绕轴向扭转角度影响较大;抗压铠装层为径向压力主要受力构件,其铺设角度虽然对压溃性能不大,但在应变分析中不可忽略;拉伸铠装层铺设角度对应变影响同样较大。文中数值方法可弥补理论方法限定在小位移、小变形范围,无法计入层间摩擦、材料非线性及初始制造椭圆率等缺陷。     

Structural response of a flexible pipe with damaged tensile armor wires under pure tension

This article studies the structural response of a 6.0” flexible pipe under pure tension considering intact and damaged conditions. In the damaged condition, several wires of the tensile armor layers are assumed to be broken. A three-dimensional nonlinear finite element (FE) model devoted to analyze the local mechanical response of flexible pipes is employed in this study. This model is capable of representing each tensile armor wire and, therefore, localized defects, including total rupture, may be adequately represented. Results from experimental tests validate the FE predictions and indicate a reduction in the axial stiffness of the pipe, a non-uniform redistribution of forces among the remaining intact wires of the damaged tensile armor layers and high stress concentrations in the wires near the broken ones. Moreover, the FE model indicates that significant normal bending stresses may arise in the pressure armor and inner carcass due to an uneven pressure distribution on these layers. Finally, the results obtained are employed to estimate the pull out capacity of the studied flexible pipe.     

Finite element study on circular armour wire lateral buckling in umbilicals

The present paper addresses the circular armour wire lateral buckling in umbilicals. An asymmetric non-linear finite element model is developed to analyze a single armour wire subjected to combined constant axial compression and uniform cyclic curvatures. A parametric case study is performed for an armour wire from a nine-hose umbilical cable, where the armour wire pitch number, applied axial compressive load and minimum and maximum curvatures in the applied cyclic bending are varied. The armour wire end shortenings, transverse sliding in cyclic bending, the buckling shapes and equilibrium paths after numerous bending cycles, the critical buckling loads, the stress states at the onset of lateral buckling, and the required number of bending cycles that triggers lateral buckling are obtained and extensively discussed. The critical buckling loads given by the FE model have been compared with an existing analytical formulation, indicating that the analytical model is reliable for small cyclic curvatures. Moreover, an empirical model is proposed for the required number of bending cycles to trigger the lateral buckling and good correlation with the FE results has been observed.     

Flexible riser-bend stiffener top connection analytical model with I-tube

The flexible riser top connection to the floating unit is a critical region considering extreme loading and fatigue lifetime assessment and is generally protected by a bend stiffener to limit the curvature in this region. The top connection usually interface the floating unit with two main configurations: i) end-fitting and bend stiffener directly connected to a riser balcony or ii) riser connected to the floating unit in the end of an I-tube, which reduces the end-fitting bending loading, and bend stiffener assembled to a bellmouth with a given inclination in relation to the I-tube longitudinal axis. The traditional modeling approach considers the riser/bend stiffener system attached to the floating unit, representative of the first configuration. A more realistic modeling approach, capturing the complex interactions of flexible riser/bend stiffener with I-tube interface can be employed for preliminary assessment with less conservatism. In this work, a large deflection analytical beam model is developed for the riser top connection with I-tube considering the bellmouth transition region with a straight rigid surface followed by a curved section. The riser follows a nonlinear bending behavior described by a bilinear moment vs curvature function and the bend stiffener polyurethane material exhibits nonlinear elastic symmetric response represented by a power law function. It is assumed that there is no gap between the riser and the bend stiffener and the riser is fixed in the end-fitting position. The mathematical formulation of the statically indeterminate system results in three systems of coupled differential equations combined with the corresponding multipoint boundary conditions to be numerically solved by an iterative procedure. A case study is carried out with a 7” flexible riser protected by a bend stiffener connected to an inclined I-tube bellmouth. The system is subjected to extreme loading conditions and the influence of the sleeve shape and I-tube length on the riser curvature distribution, including the end-fitting position, and contact forces between the riser/sleeve and riser/bend stiffener sections are assessed.     

无粘结柔性管抗拉伸层结构分析

柔性管抗拉伸层是复杂的空间螺旋线结构,其结构响应分析对柔性管疲劳分析、强度分析和屈曲分析有重要作用。文章基于曲梁理论,应用斜驶螺旋线假设和测地线假设两种空间曲线公式,以空间细长杆理论及胡克定律本构方程为基础,采用格林应变张量与第二Kirchoff应力张量度量,对深海无粘结柔性管抗拉伸层螺旋形钢缆结构平衡方程进行了推导,编写了分析程序。利用该程序,分析了抗拉伸层钢缆在轴对称载荷下和弯矩作用下的曲率变化和结构响应;同时利用三维直梁有限元模型与曲梁有限元模型建立数值模型,将程序结果与数值模拟模型结果进行了对比,证明了结果可行性。该结果可为柔性管抗拉伸层结构设计提供快速的预估计方法。     

静水压力下具有轴对称初始缺陷圆柱壳承载能力研究

文章针对含有轴对称初始缺陷和局部轴对称凹陷的圆柱壳在静水压力下的稳定承载能力问题进行了研究。通过一种数值计算方法,给出了初始缺陷幅值、壳体半径与厚度比、壳体长度、局部凹陷长度及位置对静水压力下圆柱壳屈曲临界压力的影响。并针对不同缺陷幅值对圆柱壳的刚度进行折减,给出了初始缺陷幅值与刚度折减系数的关系。研究结果表明,对于轴对称初始缺陷对圆柱壳稳定承载能力的影响,本质上是降低圆柱壳轴向弯曲刚度和轴向的薄膜刚度从而造成圆柱壳稳定承载能力的下降,因此针对轴对称初始缺陷可以增加纵筋提高其弯曲刚度,增加稳定承载能力。     

缓波型非粘接柔性立管的干涉敏感性

针对非粘接柔性立管在波浪和海流作用下易发生立管干涉的问题,以我国南海某油田输油立管和相邻锚链为例,分别对拖曳力系数、管道单位长度质量、外径、内部介质密度、立管抗拉弯扭刚度和悬挂角度等参数进行敏感性分析,得出不同参数的敏感性情况,并在此基础上提出一些建议供实际工程设计参考.     

简支梁桥上CRTS Ⅱ型板式轨道墩台挠曲力研究

根据简支梁桥上CRTS Ⅱ型板式轨道的结构特点,运用有限元软件建立了墩台挠曲力的计算模型,分析了底座与桥梁间的滑动层摩擦系数、墩台水平线刚度、扣件纵向阻力和轨道板、底座刚度折减系数对墩台挠曲力的影响。计算结果表明,墩台挠曲力随墩台水平线刚度的增大而增大,基本成线形关系;滑动层摩擦系数、刚度折减系数对墩台挠曲力有较大影响,而扣件纵向阻力的影响可忽略不计。     

柔性立管阻力特性试验数据处理技术

本文提出3种数据处理方法分析均匀来流中柔性立管的初始阻力特性。首先通过分析柔性立管在均匀来流中的变形及振动情况,分离出立管流向的初始变形对应的弯曲应变。根据复杂梁的弯曲变形理论,建立起弯曲应变与平均阻力之间的微分方程。随后,针对试验中获取的立管轴向力及立管表面弯曲应变,提出计算平均阻力的数据处理方法,并进行算例验证与分析。最终使用提出的数据处理方法分析试验数据,得到立管表面各截面处的阻力分布。     

高桩墩台桩土共同作用对结构内力的影响*

根据广州某高桩墩台结构断面图和土层参数勘察报告,建立了包含墩台、桩基及土层的三维有限元模型。桩土界面采用面面接触模型,允许桩土分离及滑移,通过接触应力反映桩基土对桩的侧压力和摩阻力。分析得出了高桩墩台在多种荷载组合下的应力场和位移场,以及各桩的弯矩图和轴力图。并进一步将有限元结果与以丰海高桩墩台计算程序为代表的传统嵌固点法计算结果相比较,分析了2种方法单桩轴力图、弯矩图的差异及原因,同时分析了桩基土对结构内力的影响,得到桩排中的最大轴力弯矩桩的位置及单桩上轴力弯矩极值点的位置,为传统的嵌固点法计算结果提供了一些修改与补充,从而为高桩墩台结构设计提供参考。