Helical wire stress analysis of unbonded flexible riser under irregular response

A helical wire is a critical component of an unbonded flexible riser prone to fatigue failure. The helical wire has been the focus of much research work in recent years because of the complex multilayer construction of the flexible riser. The present study establishes an analytical model for the axisymmetric and bending analyses of an unbonded flexible riser. The interlayer contact under axisymmetric loads in this model is modeled by setting radial dummy springs between adjacent layers. The contact pressure is constant during the bending response and applied to determine the slipping friction force per unit helical wire. The model tracks the axial stress around the angular position at each time step to calculate the axial force gradient, then compares the axial force gradient with the slipping friction force to judge the helical wire slipping region, which would be applied to determine the bending stiffness for the next time step. The proposed model is verified against the experimental data in the literature. The bending moment–curvature relationship under irregular response is also qualitatively discussed. The stress at the critical point of the helical wire is investigated based on the model by considering the local flexure. The results indicate that the present model can well simulate the bending stiffness variation during irregular response, which has significant effect on the stress of helical wire.     

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.     

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。     

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.     

A study on scantling formulae of plate members due to lateral pressure under the effect of axial loads

Existing rule scantling formulae of plate members are based on conventional plastic design theory, and do not necessarily reflect complicated plate bending phenomena under axial loads. In this study, we first formulated the effect of axial load on the fully plastic moment based on the von Mises yield criterion for longitudinally stiffened plate in addition to the well-known formula for transversely stiffened plate. In addition, we derived a theoretical formulation of the lateral pressure corresponding to 2-point hinge and 3-point hinge formation taking account of the effect of the additional lateral force due to the axial loads on the deflected plating, using a simple plate strip bending model assuming a long plate with a large aspect ratio.Then, a series of elastic-plastic FE analyses was carried out to verify the structural behavior and the effect of axial load on the plate plastic bending strength. The plate strength was evaluated based on the residual deflection criteria of two cases (0.26 mm and 4.0 mm), and the results were compared with the theoretical derivation. As a result, it was found that assumption of linear strength reduction to the axial stress can cover the transversely stiffened plate under compressive axial stress conservatively. As to the transversely stiffened plate under tensile axial stress and the longitudinally stiffened plate, the strength reduction was in accordance with the reduction in the fully plastic moment based on the von Mises yield criterion in the conservative side. Finally, based on the findings, the required plate thickness coefficients were proposed on an empirical basis both for transversely and longitudinally stiffened plate under compressive and tensile axial loads.     

Experimental and finite element analysis of fatigue strength for 300 mm2 copper power conductor

The fatigue strength of a 300 mm² stranded copper conductor was investigated experimentally and by finite element (FE) analysis. An analytical model was also developed and validated. Wires taken from the outer layer of the conductor were fatigue tested in tension–tension loading and compared with similar data for wires taken from a 95 mm² conductor. The wire cross section was deformed due to the compacting process that was applied during fabrication. When corrected for stress concentrations due to the deformation the data for the two sets of wire fell within the same scatter-band. Full scale testing was carried out in a specially designed rig with constant tensile load and reversed displacement controlled bending with a fixed curvature variation. The loading is a simulation of the loading of a power cable hanging from a floating vessel through a bellmouth. Conductors were tested in two states; dry and lubricated. A finite element model was established for the copper conductor. The model was formulated by a combination of elastic beam and beam-contact elements that included the effects of friction. The effect of local bending due to contact forces was included in the model. Two contact conditions were investigated; the point (trellis) contact between adjacent layers of wire and the inline contact within each layer and between the first layer (centre wire) and the second layer. The FE model was validated by a calibration test of a full scale conductor, and by sensitivity studies varying the size and the number of elements of the model. Fatigue analysis of the conductor was carried out, based on the S–N curve for individual wires. Taking into account the effects of friction and local bending, agreement was obtained between predicted and experimental fatigue strength of the conductor, for the FE model as well as the analytical model.     

Analytical study on controlled lateral thermal buckling of antisymmetric mode for subsea pipelines triggered by sleepers

Subsea pipelines exposed to high temperature and high pressure (HTHP) conditions is susceptible to lateral buckling. In order to control lateral buckling, engineered buckle initiators, such as sleepers, are introduced to initiate planned lateral buckles along the pipeline at specific locations in order to ensure that the stress in each lateral buckle remains acceptable. In this study, taking the interaction of adjacent buckles into account, analytical solutions of antisymmetric lateral buckling mode triggered by sleepers are derived. With the proposed formulations, the method to obtain the accurate locations of lateral displacement amplitude and maxima of bending stress is presented and discussed. And a detailed comparison between symmetric and antisymmetric mode of lateral buckling triggered by single sleeper is presented. Moreover, the influence of the sleeper spacing on controlled lateral buckling behaviour with the consideration of axial interaction between adjacent buckles is conducted. Finally, a detailed analysis about the influence of the sleeper height, lateral frictional coefficient and submerged weight of the pipeline on the controlled post-buckling behaviour is presented. Our results show that, for smaller sleeper friction or smaller sleeper height, the symmetric mode is more likely to happen, while the antisymmetric mode is prone to occur for larger sleeper friction and larger sleeper height. One effective method to reduce displacement amplitude and maximum stress is to decrease the sleeper spacing. The minimum critical temperature difference decreases with increasing sleeper height and increases with increasing lateral friction coefficient or submerged weight of the pipeline. And an alternative way to reduce the maximum stress is to reduce the lateral friction coefficient or submerged weight of the pipeline even though the displacement amplitude increases.     

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.     

Numerical prediction and mitigation of out-of-plane welding distortion in ship panel structure by elastic FE analysis

As an application to predict and mitigate the out-of-plane welding distortion by elastic FE analysis based on the inherent deformation theory, a panel structure of a pure car carrier ship is considered. The inherent deformations of different types of welded joints included in this ship panel structure are evaluated beforehand using thermal elastic plastic FE analysis. Applying idealized boundary condition to focus on the local deformation, elastic FE analysis shows that the considered ship panel structure will buckle near the edge and only bending distortion is dominant in the internal region. In order to mitigate out-of-plane welding distortion such as buckling and bending, straightening using line heating is employed. In the internal region, only inherent bending with the same magnitude as welding induced inherent bending is applied on the opposite side of welded joints (fast moving torch). On the other hand, only in-plane inherent strain produced by line heating is introduced to the edge region to correct buckling distortion (slow moving torch). The magnitude of out-of-plane welding distortion in this ship panel structure can be minimized to an accepted level.     

Mode jumping in the lateral buckling of subsea pipelines

Unburied subsea pipelines under high-temperature conditions tend to relieve their axial compressive stress by forming localised lateral buckles. This phenomenon is traditionally studied under the assumption of a specific lateral deflection profile (mode) consisting of a fixed number of lobes. We study lateral thermal buckling as a genuinely localised buckling phenomenon by applying homoclinic (‘flat’) boundary conditions. By not having to assume a particular buckling mode we are in a position to study transitions between these traditional modes in typical loading sequences. For the lateral resistance we take a realistic nonlinear pipe-soil interaction model for partially embedded pipelines. We find that for soils with appreciable breakout resistance, i.e., nonmonotonicity of the lateral resistance characteristic, sudden jumps between modes may occur. We consider both symmetric and antisymmetric solutions. The latter turn out to require much higher temperature differences between pipe and environment for the jumps to be induced. We carry out a parameter study on the effect of various pipe-soil interaction parameters on this mode jumping. Away from the jumps post-buckling solutions are reasonably well described by the traditional modes whose analytical expressions may be used during preliminary design.     

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.     

Snap behaviour in the upheaval buckling of subsea pipelines under topographic step imperfection

Pipelines exposed to high temperature and high pressure with a topographic step imperfection are susceptible to the phenomenon of upheaval buckling potentially leading to a hazard for the structural integrity of the pipeline. To analyse this problem we derive analytical upheaval buckling solutions and obtain the locations of maximum displacement and maximum axial compressive stress. We also analyse the typical post-buckling behaviour and its dependence on step height, axial soil resistance and wall thickness. The difference in behaviour between a pipeline with step imperfection and one with a symmetric prop imperfection is discussed. Our results show that a pipeline with a step imperfection is more prone to upheaval buckling than a perfect pipeline. For sufficiently small step heights the pipeline may suffer a snap-back instability under decreasing thermal loading, raising the possibility of hysteretic snap behaviour under cyclic thermal loading (for instance caused by periodic start-ups and shut-downs). The snap-back buckling disappears for large enough step height and the minimum critical temperature difference decreases with increasing step height and wall thickness or with decreasing axial soil resistance. The maximum compressive stress decreases with increasing step height and axial soil resistance or with decreasing wall thickness. A pipeline with step imperfection is safer than one with a symmetric prop imperfection.     

Effect of pitting corrosion on local strength of hold frames of bulk carriers (2nd Report)—Lateral-distortional buckling and local face buckling

Pitting corrosion is typical corrosion observed on coated hold frames of bulk carriers which exclusively carry coal and iron ore. In order to secure the safety of these types of bulk carriers, it is important to understand the effect of pitting corrosion on local strength of hold frames.

In order to investigate this effect, a series of 4- and 3-point bend tests on structural models which consist of web, shell and face plates has been carried out. Artificial pitting was created on the web plate to simulate pitting. In the 4-point bend tests, two equal concentrated loads have been applied vertically at the one-third points of simply supported models so that compression load due to bending would act on the face plate. In this testing condition, lateral-distortional buckling occurred before reaching the ultimate strength and local buckling of the face plate was observed after reaching the ultimate strength. The effect of web plate pitting on the lateral-distortional buckling strength was found to be small but the ultimate strength decreases with increase in the degree of pitting intensity. In the 3-point bend tests, concentrated load has been applied vertically at the center of simply supported models so that compression load due to bending would act on the face plate. In this testing condition, local face buckling occurred just after reaching the ultimate strength. The ultimate strength is found to be decreasing with increase in the degree of pitting intensity.

A series of non-linear FE analyses has been performed to simulate the deformation behavior observed in the tests. It has been revealed that even in the case of randomly distributed pitting corrosion the ultimate strength of the structural models was almost the same as that of the structural models with uniform corrosion corresponding to the average thickness loss.     

Ultimate hull girder strength of a bulk carrier under combined global and local loads in the hogging and alternate hold loading condition using nonlinear finite element analysis

For bulk carriers in hogging, the most critical situation is the alternate hold loading (AHL) condition with odd numbered holds loaded with high density cargoes and even numbered holds empty. The effect of the local lateral pressure loads should be considered in the assessment of ultimate hull girder strength in the hogging and AHL conditions. In the present paper the ultimate strength of a Capesize bulk carrier hull girder under combined global and local loads in the hogging and AHL condition is extensively and systematically investigated using nonlinear finite element (FE) analysis with ABAQUS software. Since the bulk carrier used as a reference vessel in this study is an old design we also studied the effect of modified scantlings by multiplying the plate thickness in the bottom structure by a design modification factor (DMF). In particular, it should be noted that a DMF of 1.4 gives a design in accordance with the new CSR rules. Based on the results obtained by nonlinear FE analyses, a practical interaction equation is established between global hogging bending capacity and average external sea pressure over the bottom.     

Progressive collapse analysis of ship hull girders subjected to extreme cyclic bending

This paper introduces a novel analytical method to predict the buckling collapse behaviour of a ship hull girder subjected to several cycles of extreme load. This follows the general principles of the established simplified progressive collapse method with an extended capability to re-formulate the load-shortening curve of structural components to account for cyclic degradation. The method provides a framework for assessing residual hull girder strength following a complex series of unusually extreme load events where the wave induced bending moment rises close to, or even surpasses, the monotonic ultimate strength. These load events may be sequential, such as might be caused by a series of storm waves, or they may occur as a collection of discrete events occurring over a longer period. The extreme cyclic bending amplifies the distortion and residual stress initially induced by fabrication in the flanges of the girder, which results in a deterioration of the residual ultimate strength. Validation is firstly completed through a comparison with previously published experimental work and secondly via comparison with numerical simulation on four ship-type box girders using the nonlinear finite element method.     

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.     

A numerical investigation into strength and deformation characteristics of preloaded tubular members under lateral impact loads

This paper presents the results of a numerical investigation into the structural behaviour of preloaded tubular members under lateral impact loads by means of finite element method. The lateral load represents a statically modelled impact from collision between tubular member and a solid rectangular indenter. Three different kinds of end conditions have been applied to the model and the effects of boundary conditions are investigated. Also, the effect of preloading on the buckling strength as well as the ultimate strength for laterally impacted tubes is assessed and it will be shown that preloading and position of applying force directly affect these strengths. In other words, by increasing in the amount of preloading, ultimate strength reduces and member tends to collapse under lower amounts of loads. The influence of the position of applying lateral load has also been addressed and relevant results will be discussed. In order to verify the performance of numerical model, the results have been examined against an available experimental test.     

Ultimate collapse tests of stiffened-plate ship structural units

An increasingly popular approximate method for assessing ship hull girder ultimate strength is to combine the individual elasto-plastic load-carrying characteristics of each single stiffened-plate unit comprising the ship hull cross section. In order to evaluate methods (numerical and experimental) for developing the load-carrying characteristics (load–shortening curves), a full-scale testing system was designed and constructed to provide data for stiffened steel plate units under combined axial and lateral loads. The system included an assembly of discrete plate edge restraints that were developed to represent symmetric boundary conditions within a grillage system. Twelve full-scale panels including ‘as-built’, ‘deformed’ and ‘damaged’ specimens were tested in this set-up.

The specimens failed by combined plate and flexural buckling, stiffener tripping or local collapse, depending on the magnitude of lateral loads and local damage. Load-shortening curves associated with different failure modes were found to be distinctly different and it was found that a small lateral load could change the failure mode from flexural buckling to tripping. Current design criteria should directly consider effects of the lateral loads on the failure modes and the collapse loads of stiffened plates.     

Controlled pipeline lateral buckling by reeling induced curvature imperfections

Expansion of pipelines installed on the sea floor due to the passage of high temperature and pressure hydrocarbons leads to lateral buckling. Interaction with a frictional sea floor can result in localization of such buckles, which must be controlled to ensure that the local bending is within acceptable limits. Periodic geometric imperfections introduced to a pipeline installed by reeling using the Residual Curvature Method are modeled and their effectiveness as expansion loops is evaluated. The imperfections are generated by allowing chosen lengths of the line to retain a small curvature by judicious action at the straightener. The model properly accounts for the complex interactions between geometric and material nonlinearities with frictional forces. It is demonstrated that as the temperature increases, the line can buckle in a snap-through manner, or can grow stably usually causing plastic deformation in its crest. The behavior is governed by the length, curvature, amplitude and periodicity of the imperfection, and by the lateral and axial frictional forces that develop. The effect of each of these variables is studied parametrically. Overall, the Residual Curvature Method is found to be a viable and effective method of controlling lateral buckling. The results provide guidance on the optimal periodicity, how to avoid snap-through buckling, and how to simultaneously minimize plastic bending.     

带止屈器的复合材料圆柱壳结构屈曲分析及优化

针对海洋工程上的复合材料圆柱壳结构,基于有限元软件ABAQUS,利用Python语言编程实现参数化建模、屈曲分析以及在后处理中提取屈曲因子。研究复合材料圆柱壳结构在单独受到轴向压力、侧向压力以及两种压力组合作用下止屈器的位置对屈曲极限强度的影响,并利用遗传算法多参数优化的方法对止屈器的位置进行优化,最终找到最优解。研究结果可以为复合材料圆柱壳结构抵抗屈曲失效的优化设计提供参考。