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.     

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.     

Predicting the wet collapse pressure for flexible risers with initial ovalization and gap: An analytical solution

As offshore hydrocarbon production moves towards ultra-deep water, flexible risers have to withstand the huge hydro-static pressure without collapse. They are designed with strong collapse capacities, allowing them to operate under the condition where their annuli are flooded by the seawater. However, initial imperfections can weaken the collapse capacity under such a flooded condition, triggering the so-called “wet collapse”. Two common initial imperfections, the carcass ovality and the radial gap between the carcass and pressure armor, would reduce the collapse strength of flexible risers significantly. Mostly, collapse analyses are performed through numerical simulations, which are less feasible for the design stage of flexible risers comparing with analytical models. To date, there are few analytical models available in public literature to predict the wet collapse pressure of flexible risers accounting for initial ovality and gap. To meet this demand, an analytical model is established in this paper to address these issues. This model is developed as a spring-supported arch, solving the collapse pressure with stability theories of ring and arched structures. This analytical model is verified by numerical simulations, which gives prediction results that correlate well with the numerical ones.     

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。     

合拢弯矩作用下复合材料曲梁突变屈曲的研究

研究了复合材料曲梁在受到合拢弯矩作用下发生的屈曲情况,并给出一种理论解析方法来分析这种很可能发生在复合材料弯曲结构中的脱层耦合屈曲问题.该方法是基于曲梁大变形理论及断裂力学而提出来的.文中并用该解析方法分析了一个特定的常见的情况,在该题例中脱层发生在非常靠近内表面处并且突变屈曲就发生在该薄脱层.在文中也对脱层裂纹的弧角对极限载荷的影响进行了研究.     

实肋板式耐压液舱结构计算方法研究

应用弹性力学经典理论和求解环肋柱壳的传统方法,将耐压液舱结构的几种结构形式综合成统一的力学模型,进行整体求解,获得各应力解析表达式;提出了液舱区耐压船体壳板极限承载能力及波舱壳板失稳压力的计算方法。力学模型清晰合理,求解简便,计算结果符合实际,可应用于工程设计。     

Dynamic analysis of risers using a novel multilayered pipe beam element model

In this paper a recently proposed formulation for the multilayered pipe beam element is extended to dynamic analysis of risers. Derivations of hydrostatic and hydrodynamic loadings due to internal and external fluid acting on each element layer are presented. Mass and damping matrices, associated to each element layer, are properly derived by adding their respective contributions to the expression of the virtual work due to external loading. The finite element implementation allows for the numerical representation of either bonded or unbonded multilayered risers, including small slip effects between layers. A number of numerical examples have been carried out and the results show the accuracy and efficiency of the new element formulation, even in large scale riser analysis. Moreover, we establish a few benchmarks using multilayered pipes and risers.     

Investigation into non-linear bending of elastic bars with application to design of bend stiffeners

The objective of this paper is to examine non-linear bending of a flexible elastic bar near fixed termination and to develop analytical solutions that can be used in the design of bend stiffeners. The non-linear bending of prismatic bars of finite and se-infinite lengths is solved analytically, and results are employed to re-visit the problem of the “ideal” bend stiffener, which provides a constant curvature over its entire length. A complete solution is derived for all properties of the ideal bend stiffener, which is not limited by any assumptions on the system geometry and provides an improvement over known formulations. Other features of the non-linear bending of elastic bars are examined and examples are given to demonstrate application of the present theory to sizing bend stiffeners for flexible risers.     

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.     

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.     

Three-dimensional pipeline element formulation for global buckling analysis of submarine pipelines with sleeper

Submarine pipelines can utilize sleepers to control global buckling location, which mitigates potential risks under high temperature and pressure. However, pipelines with sleepers require execution in three-dimensional space and experience lateral buckling modes. As such, this paper proposes a 3D pipeline element for lateral buckling analysis, building on previous 2D element formulations. This new element considers non-linear pipe-soil interactions, thermal expansion, axial load, initial imperfections, large deflection, and other major factors that affect lateral buckling. The derivations of the 3D pipeline element are provided in detail, and the numerical analysis procedure is elaborated. To validate the accuracy and efficiency of the proposed 3D pipeline element, several examples are presented.     

Stability of submarine bi-material pipeline-liner system with novel polyhedral composites subjected to thermal and mechanical loading fields

This study is concerned with the thermal and mechanical instability behaviors of composite novel liners encased in deteriorated pipelines. A liner may contain many connected segments, and two adjacent segments may become disconnected after long years of service. In such a case, the single disconnected segment may reduce to a ring. An innovative polyhedral configuration is introduced to improve the bending stiffness of the composite ring that is confined by the pipeline. The radius and bending rigidity of the ring are simplified analytically to facilitate the derivation of the critical buckling load. By employing the classical shell criteria, and defining an admissible displacement function, the expression of the potential energy function is obtained with only two unknown parameters. Taking the first derivative of the energy function to the two unknowns respectively generates two equilibrium equations. By solving the two equations, the analytical buckling load is obtained for a composite polyhedral ring in a thermal variational field. Then, two comparisons are taken between the present analytical predictions and results from elsewhere, and good agreements are obtained. An amplification coefficient is defined as the ratio between the buckling load of the polyhedral and circular rings. Finally, parametric evaluations indicate the amplification coefficient reduces with the increase of thickness-to-radius ratio, the increase of the number of sides, and the increase of the temperature variation, respectively. Therefore, a polyhedral ring with a low thickness-to-radius ratio is recommended in engineering applications.     

含缺陷海底管道横向屈曲理论研究

考虑了初始几何缺陷对管道屈曲临界载荷的影响,基于经典热屈曲理论,推导了平坦海床上裸铺管道横向屈曲临界载荷的理论公式,给出了无限远处管道轴向力的计算公式及临界温度的计算公式。建立了平坦海床上裸铺管道的非线性有限元模型,并将有限元结果与解析结果进行了对比,验证了解析公式的合理性。     

考虑筋/板相互作用的环肋圆柱壳屈曲强度分析

环肋圆柱壳是潜艇耐压壳体的一种主要结构形式.环肋圆柱壳的失稳破坏主要表现在肋骨间的壳板失稳和总体失稳.在计算肋骨间的壳板失稳时,传统方法认为肋骨为壳板提供简支边界,忽略了在边界上肋骨和壳板的相互影响.在实际结构中,由于肋骨提供扭转刚度,壳板在与肋骨相交的边界上将存在弯矩,并非自由支持边界.因而,壳板失稳时,筋/板产生相互影响,提高了壳板的屈曲强度.本文的主要目的是,推导考虑筋/板相互影响的环肋圆柱壳壳板屈曲强度的理论计算方法,分析筋/板的相互关系.通过本文的算例表明,本文推导的计算方法以及所编制的计算程序是可靠的,可以用于工程设计.     

An integrated methodology for the design of mooring systems and risers

Traditionally, the design of mooring lines and risers of floating production systems (FPS) has been performed separately, by different teams, employing uncoupled analysis tools that do not consider the nonlinear interaction between the platform hull and the mooring lines and risers. Design processes have been focused on fulfilling the design criteria of the respective component (mooring/riser) alone, with few or no consideration to the other component, and little interaction between the design teams. Nowadays the importance of employing analysis tools based on coupled formulations is widely recognized, and analysis strategies have been proposed to consider feedback between mooring lines and risers within their respective design processes.In this context, this work details a proposal of one single and fully integrated design methodology for mooring systems and risers for deep-water FPS. In this methodology, the design stages of both risers and mooring lines are incorporated in a single spiral, allowing the full interaction of different teams; mooring design implicitly considers the riser integrity, and vice-versa, leading to gains in efficiency and cost reduction.Different analysis strategies are employed, taking advantage of uncoupled and coupled numerical models. The models generated at the initial/intermediate design stages can be reused in subsequent stages: simpler models are used in the initial stages, and more refined models are gradually introduced, to reach an ideal balance between computational cost and accuracy of results. In the advanced stages, the exchange of information between mooring/riser also allows the definition of criteria for the selection of governing/critical loading cases to be revised and verified in detail. This leads to the reduction of the original loading case matrix, allowing a feasible use of time-consuming fully coupled analysis.Results of a case study illustrating the application of some of the main processes of the methodology are included.     

Assessment of IACS-CSR implicit safety levels for buckling strength of stiffened panels for double hull tankers

The present study aims at applying structural reliability methods to assess the implicit safety levels of the buckling strength requirements for longitudinal stiffened panels implemented in the IACS Common Structural Rules (CSR) for double hull oil tankers. The buckling strength requirements considered are used in the initial stage of the hull girder scantlings’ design to control the buckling capacity of longitudinal stiffened panels subjected to the compressive loads induced by the hull girder vertical bending. The following buckling collapse failure modes are explicitly considered in the design formulation: uniaxial buckling of the plating between stiffeners, column buckling of stiffeners with attached plating and lateral-torsional buckling or tripping of stiffeners.The paper presents the procedure used to assess the implicit safety levels of the strength requirements for the three buckling collapse failure modes above mentioned, which includes the optimization of the scantlings of the plate panels and longitudinal stiffeners in order to reflect the minimum strength required by the formulation. A first order reliability formulation is adopted, and stochastic models proposed in the literature are used to quantify the uncertainty in the relevant design variables. A sample of five oil tankers representative of the range of application of the IACS-CSR design rules is considered. The effect of corrosion in the implicit safety levels is quantified based on the three corrosion levels of the Net Thickness Approach (NTA) adopted in the design rules. Sensitivity analyses are also performed to quantify the relative contribution or importance of each design random variable to the implicit safety levels.     

深水导管架桩腿制造误差与抗屈曲特性研究

文章通过典型算例详细阐述了具有制造误差的深水导管架桩腿屈曲分析方法,将线性扰动加载的特征值届曲预测算法和描述几何非线性屈曲过程的改进的Riks算法应用于导管架桩腿的详细设计校核,对比研究了模态扰动模拟制造误差和直接模拟制造误差模型的分析结果,并对典型桩腿结构在静水外压下的弹塑性屈曲响应特性进行了研究.分析结果表明,随着制造误差的增加,导管架桩腿抗静外压的临界屈曲载荷在下降,而且制造误差大的桩腿的极限承载能力较低.     

特征载荷下海工管状结构屈曲临界载荷分析

圆柱形管状结构在海洋工程领域中应用较多,在进行结构设计时,需重点关注其侧向受载时的屈曲强度问题。通过理论分析和数值模拟,对比研究径向线性载荷变化下圆柱壳的屈曲行为,以经典的Donnell壳体理论为基础,得到圆柱壳的屈曲控制方程,并通过本征值分析方法得到结构屈曲的临界条件。采用有限元软件ABAQUS对线性变化径压下圆柱壳的屈曲进行数值仿真。分析得出径厚比是径向线性分布载荷下圆柱壳屈曲临界载荷的主要影响因素,三角形径压下屈曲临界载荷值约为均布径压下屈曲临界载荷值的2倍。     

基于改进的屈曲模态阵型的锥形连续柱体结构屈曲分析（英文）

Elastic critical buckling load of a column depends on various parameters, such as boundary conditions, material, and crosssection geometry. The main purpose of this work is to present a new method for investigating the buckling load of tapered columns subjected to axial force. The proposed method is based on modified buckling mode shape of tapered structure and perturbation theory. The mode shape of the damaged structure can be expressed as a linear combination of mode shapes of the intact structure. Variations in length in piecewise form can be positive or negative. The method can be used for single-span and continuous columns. Comparison of results with those of finite element and Timoshenko methods shows the high accuracy and efficiency of the proposed method for detecting buckling load.     

深海复合材料悬链线立管基于可靠度的优化设计

研究基于可靠度的方法,对深海复合材料悬链线立管进行优化设计分析。对于正交各向异性层合复合材料结构而言,叠层顺序不同、各层铺角变化以及层间厚度差异等都会影响到结构的承载能力,因此,有必要引进可靠度作为优化设计指标。首先,根据经典层合板理论计算整体模型的等效属性,建立悬链线立管整体分析模型,得到关键截面响应,以此作为局部分析模型的约束;然后,运用试验设计方法构建Kriging近似模型;最后,利用蒙特卡罗撒点方法对比分析确定性优化与可靠性优化的结果。研究表明：优化后的深海复合材料立管在满足应力强度设计的要求下可有效降低结构重量,所提出的基于可靠度的优化设计复合材料悬链线立管具有可行性。