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.     

On the effect of the ply stacking sequence on the failure of composite pipes under external pressure

The use of high performance structural composites has become very important over the last decades, especially where weight is an essential factor. Particularly in the oil and gas industry, several designs of composite pipes for deep water applications have been recently proposed as competitive solutions against traditional steel pipes. Thus, it is important to assess the performance of composite pipes under high external pressure in order to avoid pipe failure or overconservative designs. In this paper, experimental tests of different composite pipe configurations are performed and then compared to analytical and numerical predictions. Unlike the case of internal pressure loads, the collapse pressure of composite pipes depends on the initial ovality and on the ply stacking sequence. The collapse resistance of different composite pipes is firstly studied through simplified analytical equations combined with different failure criteria. Then, a finite element model is developed using a progressive failure criterion [1]. Both analytical and numerical failure predictions were compared to experimental tests carried out on four composite pipes produced with different ply stacking sequence by the filament winding method [2]. An experimental-numerical-analytical comparison shows that numerical and analytical models provide results in good agreement with those obtained experimentally. Finally, a parametric analysis is carried out to show the effect of ovality and ply stacking sequence on the failure pressure of composite pipes.     

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。     

Comparisons of calculations with experiments on the ultimate strength of wide stiffened panels

Five specimens of wide stiffened panel with four stiffeners under axial compression until collapse are studied with a nonlinear finite element analysis and Common Structural Rules to compare with the experimental results. The stiffened panel models have two longitudinal bays to produce reasonable boundary condition at the end of edges. Tension tests have been conducted to obtain the material properties of the steel that are used in the finite element analysis. Three boundary condition configurations are adopted to investigate their influence on the collapse behaviour of the stiffened panels. A displacement transducer was used to measure the initial geometrical imperfections of the stiffened plates. The collapse behaviour of the stiffened panels is analysed in finite element analysis with the measured initial imperfections and with nominal imperfections. An equivalent initial imperfection is validated for the ultimate strength of stiffened panel under compressive load until collapse for the panels under consideration. With the same imperfection amplitude, the shape of the column-type initial deflection of stiffeners affects significantly the collapse shape, but only slightly the ultimate strength and the mode of collapse of the stiffened panels. The 1/2 + 1 + 1/2 bays model with restrained boundary condition BC3 gives an adequate FE modelling and is possible to be fabricated in experiment.     

Accuracy of nonlinear finite element collapse predictions for submarine pressure hulls with and without artificial corrosion damage

Nonlinear finite element (FE) collapse pressure predictions are compared to experimental results for submarine pressure hull test specimens with and without artificial corrosion and tested to collapse under external hydrostatic pressure. The accuracy of FE models, and their sensitivity to modeling and solution procedures, are investigated by comparing FE simulations of the experiments using two different model generators and three solvers. The standard FE methodology includes the use of quadrilateral shell elements, nonlinear mapping of measured geometric imperfections, and quasi-static incremental analyses including nonlinear material and geometry. The FE models are found to be accurate to approximately 11%, with 95% confidence, regardless of the model generator and solver that is used. Collapse pressure predictions for identical FE models obtained using each of the three solvers agree within 2.8%, indicating that the choice of FE solver does not significantly affect the predicted collapse pressure. The FE predictions are found to be more accurate for corroded than for undamaged models, and neglecting the shell eccentricity that arises due to one-sided shell thinning is found to significantly decrease the resulting accuracy of the FE model.     

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.     

均匀外压下有几何缺陷球壳的破坏压力

将球壳缺陷部分看作受球壳其余部分弹性约束的独立扁球壳,提出了弹性屈曲压力的分析方法,并得出临界弧长的解析结果。还对非弹性屈曲破坏问题提出了工程实用的处理方法。共作十四个铝球壳和四个钢球壳模型试验。     

非粘合柔性管破段强度解析分析（英文）

This paper presents an analytical scheme for predicting the collapse strength of a flexible pipe, which considers the structural interaction between relevant layers. The analytical results were compared with a FEA model and a number of test data, and showed reasonably good agreement. The theoretical analysis showed that the pressure armor layer enhanced the strength of the carcass against buckling, though the barrier weakened this effect. The collapse strength of pipe was influenced by many factors such as the inner radius of the pipe, the thickness of the layers and the mechanical properties of the materials. For example, an increase in the thickness of the barrier will increase contact pressure and in turn reduce the critical pressure.     

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。     

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.     

Influence of residual stresses and geometric imperfections on the elastoplastic collapse of cylindrical tubes under external pressure

The buckling problem of a circular cylindrical shell has long been widely investigated due to its great importance in the design of aerospace and marine structures. Geometric imperfections and residual stresses are inevitable in practice and have been so far frequently considered in analytical and numerical predictions. But little attention has been paid until now on the combined influence of such initial defects on the critical and often unstable response of such elastoplastic structures. In this paper, a shell finite element is designed within the total Lagrangian formulation framework to deal with the elastoplastic buckling and post-buckling of thin cylindrical tubes under external pressure and axial compression. A specific experimental process will be introduced in order to measure residual stresses in the shell very accurately, so as to include them in the numerical calculations. The present formulation will enable us to describe the complete non-linear solutions, namely the critical pressures (bifurcation and limit (collapse) loads), the bifurcation modes and the bifurcated equilibrium branches up to advanced post-critical states. Comparisons will be made between numerical results and the experimental critical value and deformation patterns of a new generation profiler. Furthermore, the combined effects of geometric imperfections, residual stresses and plasticity will be analyzed.     

An expeditious algebraic formulation to the buckling critical load of risers under dynamic compression

Dynamic compression of risers can play an important role in the structural stability of submerged pipes in catenary-like configuration. In this paper, the analytical formulation for the buckling critical load, developed in the early 2000's, is revisited and extended to cover a wider range of practical cases. A purely algebraic expression for the critical load is provided, eliminating the original formulation requirement related to solving transcendental equations, for both free and anchored risers. The analytic formulations and respective algebraic approximations are compared with numerical simulations, presenting a fairly good agreement. A discussion on the differences and similarities of each formulation ends this paper, highlighting their range of validity. Also, from the comparison, the analytical formulation developed in this work was more suitable for precise and fast determination of the critical buckling load for both riser types, rigid and flexible, and for most typical operating conditions. The proposed algebraic expressions were highly accurate and may substitute the previous analytical formulations for critical load prediction.     

考虑内流和海床作用的柔性立管和钢悬链线立管非线性分析(英文)

Flexible risers and steel catenary risers often provide unique riser solutions for today’s deepwater field development. Accurate analysis of these slender structures, in which there are high-speed HP/HT internal flows, is critical to ensure personnel and asset safety. In this study, a special global coordinate-based FEM rod model was adopted to identify and quantify the effects of internal flow and hydrostatic pressure on both flexible and deepwater steel catenary risers, with emphasis on the latter. By incorporating internal flow induced forces into the model, it was found that the internal flow contributes a new term to the effective tension expression. For flexible risers in shallow water, internal flow and hydrostatic pressure made virtually no change to effective tension by merely altering the riser wall tension. In deep water the internal pressure wielded a dominant role in governing the riser effective tension and furthering the static configuration, while the effect of inflow velocity was negligible. With respect to the riser seabed interaction, both the seabed support and friction effect were considered, with the former modeled by a nonlinear quadratic spring, allowing for a consistent derivation of the tangent stiffness matrix. The presented application examples show that the nonlinear quadratic spring is, when using the catenary solution as an initial static profile, an efficient way to model the quasi-Winkler-type elastic seabed foundation in this finite element scheme.     

水下压缩空气储能系统柔性立管响应特性分析（英文）

With the rapid development of marine renewable energy technologies, the demand to mitigate the fluctuation of variable generators with energy storage technologies continues to increase. Offshore compressed air energy storage(OCAES) is a novel flexible-scale energy storage technology that is suitable for marine renewable energy storage in coastal cities, islands, offshore platforms, and offshore renewable energy farms. For deep-water applications, a marine riser is necessary for connecting floating platforms and subsea systems. Thus, the response characteristics of marine risers are of great importance for the stability and safety of the entire OCAES system. In this study, numerical models of two kinds of flexible risers, namely, catenary riser and lazy wave riser, are established in OrcaFlex software. The static and dynamic characteristics of the catenary and the lazy wave risers are analyzed under different environment conditions and internal pressure levels. A sensitivity analysis of the main parameters affecting the lazy wave riser is also conducted. Results show that the structure of the lazy wave riser is more complex than the catenary riser; nevertheless, the former presents better response performance.     

FEM-based evaluation of friction and initial imperfections effects on sandwich pipes local buckling

Sandwich pipes have been studied as one option to overcome the high pressure problems in deep and ultra-deep waters. They have become a possible alternative solution for submarine infrastructure due to its thermal insulation capacity. This contribute to preventing the pipeline from clogging due to the difference in temperature between reservoir fluids and water at the bottom of the sea. The pipelines in ultra-deepwater are continually exposed to severe operating conditions, such as the effect of high levels of external pressure that can cause local deformation or even collapse of the pipe. Thus, a greater understanding of the mechanical behavior of sandwich pipes is required. This paper presents a FEM-based evaluation of friction and initial imperfection effects on sandwich pipes local buckling. The non-linear evaluation was carried out in FEM of local buckling of two sandwich pipes, with polypropylene and cement as filled annular material. The influence of initial imperfections and the degree of friction, between the annular material and the steel pipes, as well as geometric variations of the pipe were considered. The numerical simulations results indicate a capacity to withstand ultra-deep waters collapsing pressures, around 3000 m, either for polypropylene or cement filled annular material model. In addition, the results indicate that the collapse pressure is inversely proportional to the increase in annular thickness and directly proportional to the decrease in friction which have an impact and contribution on the carrying capacity of the sandwich pipe. Further research will consider a design of experiments analysis of reported effects for different diameter-to-thickness ratios.     

T型扶强材在横向载荷作用下的侧向屈曲

考虑船舱进水导致船体梁的结构崩溃而发生沉没的事故中舱壁是一个关键的环节,通过能量法导出舱壁扶强材在侧向静水压力作用下的弹性屈曲的临界载荷公式,与有限元数值计算比较,证明文中计算公式的正确、简单、实用性。     

A computational investigation of the effects of localized corrosion on plates and stiffened panels

Structural components are prone to corrosion damage, especially when exposed to a sea environment. This article describes an investigation on the effects of local corrosion applied to plates and stiffened panels typically found in ship structures. Finite element investigations of initial buckling, ultimate collapse and post-ultimate responses are presented and described through the use of load-shortening collapse curves. Geometric imperfections and residual stresses were included in the model and results are compared to analytical calculations and available experimental measurements. This improved knowledge of the structural integrity of a damaged ship structure can be used to develop more efficient maintenance practices.     

半潜式平台极限状态评估

对某半潜式钻井平台,采用ANSYS建立有限元计算模型,进行了典型波浪荷载作用下平台非线性垮塌性分析,不考虑几何非线性和初始缺陷的影响。分析结果表明,平台最终的失效形式和水动力荷载作用形式十分相关,初始失效部位和最终失效状态各不相同。文中对ANSYS计算模型和SESAM计算模型进行了对比,在相同的荷载条件下分别计算了两个模型,比较ANSYS计算结果和SESAM计算结果及ABS和DNV规范理论结果,三者结果吻合较好。对非线性垮塌分析结果进行了讨论,通过对截面力作用形式的分析,建立了两类半潜式平台极限状态方程。文中半潜式平台非线性垮塌分析结果可以作为基于ABS和DNV规范的半潜式平台极限状态的基准性研究。     

Numerical investigation of the collapse pressure of concentric tubes with frictionless and tied interface

The understanding and study of the mechanical behavior of submarine pipes have significant relevance in ocean exploration, allowing the application of these structures in adverse conditions. In this sense, protecting the tube's internal surface is vital for the transportation of corrosive materials, threatening structural integrity. Usually, the external surface is at constant hydrostatic pressure, leading to possible structural failure if the project does not consider all failure modes. Within the framework of Metallurgically Cladded Pipes (MCP) and Mechanically Lined Pipes (MLP), Corrosion-Resistant Alloys (CRAs) are inserted in the internal surface of pipelines. However, they are not typically deemed in the structural analysis as an integrant part of the mechanical resistance for the external load. This work presents an initial analytical proposal to calculate the collapse pressure of concentric tubes incorporating the rigidity provided by the CRA. Tied or frictionless numerical models are assumed to describe the interaction between the two bodies at the interface region. These two scenarios establish the upper and lower boundaries for cases where friction is part of the problem. The methodology applies a least-square minimization function based on nonlinear finite element simulations to extract analytical expressions that estimate the collapse pressure. An effort is made to reduce the number of sensitive parameters involved in the analytical proposals and minimize the complexity of the formulation. This process allows the analyst to visualize which parameters are more relevant in various scenarios. Nevertheless, the main goal is to evaluate how the variables are coupled and develop a methodology that can be adapted to reproduce the analyst's necessities.     

LQR control on multimode vortex-induced vibration of flexible riser undergoing shear flow

Under the actions of ocean currents and/or waves, deep-sea flexible risers are often subject to vortex-induced vibration (VIV). The VIV can lead to severe fatigue and structural safety issues caused by oscillatory periodic stress and large-amplitude displacement. As flexible risers have natural modes with lower frequency and higher density, a multimode VIV is likely to occur in risers under the action of ocean currents, which is considered as shear flow. To decrease the response level of the VIV of the riser actively, a multimode control approach that uses a bending moment at the top end of the riser via an LQR optimal controller is developed in this study. The dynamic equations of a flexible riser including the control bending moment in shear flow are established both in the time and state-space domains. The LQR controllers are then designed to optimize the objective function, which indicates the minimum cost of the riser's VIV response and control input energy based on the Riccati equation of the closed-loop system under the assumption that the lift coefficient distribution is constant. Finally, the VIV responses of both the original and closed-loop systems under different flow velocities are examined through numerical simulations. The results demonstrate that the designed active control approaches can effectively reduce the riser displacement/angle by approximately 71%–89% compared with that of the original system. Further, for multimode control, the presented mode-weighted control is more effective than the mode-averaged control; the decrease in displacement is approximately 1.13 times than that of the mode-averaged control. Owing to the increase in flow velocity as more and higher-order modes are excited, the VIV response of the original system decreases slightly while the frequency response gradually increases. For the closed-loop system, the response becomes smaller and more complicated, and the efficiency of the controller becomes lower at a certain flow velocity.