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.     

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.     

A finite element methodology for birdcaging analysis of flexible pipes with damaged outer layers

Flexible pipes are commonly exposed to damages on the outer layers due to abrasion with seafloor or improper installation and operation, which may render them vulnerable to birdcaging failures. This paper presents a finite element model for the residual axial compressive strength evaluation of a flexible pipe with local damage on the outer layers. The elastoplastic nonlinearity of tensile armour steel layers and hyperelasticity of polymeric outer sheath are taken into account. This model is verified against existing test data. Parametric studies are then performed by varying the damage size in either the pipe axial or circumferential directions. The flexible pipe axial resistance, deformations, as well as the tensile armour wires layers stress states near the damaged section under different damage and axial compression conditions are discussed. The case studies show that damage on the outer layer, especially the anti-birdcage tape layer, is highly detrimental to flexible pipe residual strength against axial compression. The present results and discussions are instructive in understanding the flexible pipe birdcaging mechanism.     

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.     

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.     

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.     

二维有限元潮流数学模型及其应用

采用有限元Galerkin加权余量法对二维潮流控制方程进行求解,建立了二维有限元潮流数学模型,并将模型运用于计算区域较小、边界较为复杂的海安湾。对海安湾潮流数值模拟的结果如下:计算水位和流速的大小及过程均与实测情况极为吻合,流场的趋势也与以往研究较为一致。新模型能采用不同形式的非结构网格,对于边界和地形变化复杂的工程区域有较强的适应性。研究成果说明,对于计算区域较小且陆域边界变化复杂的工程问题,采用有限元方法离散潮流方程能提高计算精度。     

河口垂向二维悬沙输移数学模型

针对窄深的潮汐河口建立了沿宽度方向积分平均的垂向二维悬沙输移数学模型,潮流场的模拟采用三维MOHID模型,悬沙对流扩散方程采用Galerkin有限元法进行求解。利用该模型模拟了长江口北槽段潮流输沙过程,计算结果与实测资料较好吻合,表明了该模型能够模拟窄深的潮汐型河口地区悬沙输移过程。     

A finite element model for the Venice Lagoon. Development, set up, calibration and validation

The development, calibration and validation of a two-dimensional finite element model for the Venice Lagoon is described. The model uses a staggered grid for the spatial integration of the water levels and velocities. A semi-implicit numerical time stepping scheme is implemented, which guarantees unconditional stability for the gravity wave propagation. Because of the shallow depths in the lagoon, the model deals also with areas where flooding and drying occur.A first calibration of the model has been performed against harmonic constants of 12 tide gauges located in the lagoon. After this calibration, model output shows a good agreement with a set of water level data referring to a period of calm winds and to another data set of water level data measured in 38 stations during a period of strong winds.Meteorological data and river discharges are used to set up a 1-year long simulation that models the salinity and temperature fields. The temperature time evolution is well simulated. Comparison of model output to salinity data is not straightforward, since input data for the main rivers that discharge freshwater into the lagoon is not available for the year of reference. However, yearly averages of observed values of salinity are in a reasonable agreement with results of a climatological simulation.The presented model shows good propagation of the tidal wave and stability characteristics. It is the first step for a comprehensive model of the Venice Lagoon that deals not only with hydrodynamic variables, but also with sediment transport and ecological processes.     

Coarse mesh finite element model for cruise ship global and local vibration analysis

This paper presents a practical procedure for creating finite element (FE) model for vibration analysis of cruise ships. The most preferable FE modelling approaches are studied and discussed through case studies of common ship structures, which cover the range from low to high frequencies. The application of homogenized equivalent single layer (ESL) theory based equivalent element for stiffened panel is extended to local forced vibration analysis, where inertia induced interaction between plate and stiffener occurs. Modal method is used with an energy-based correction for accounting the plate-stiffener interaction into modal properties. Case study results reveal that mesh density of one 4-node element per web frame spacing is suitable for global FE-model when vibration analysis is limited to global hull girder modes. For such modes it is sufficient to only include the membrane stiffness of stiffened panels. For investigating the response at higher frequencies, bending properties of stiffened panel should be included and mesh density should be at least two elements per web frame spacing. Then forced vibration analysis can be performed with an excellent accuracy up to frequencies about one third of the local plate natural frequencies between the stiffeners. Beyond that, the influence of the local plate vibration becomes more significant in panel vibration, making the ESL-theory based element limited. With the applied correction method, the validity of the ESL-model can be extended to approximately two thirds of the local plate natural frequency.     

开口管桩承载力计算方法及桩基模型研究

比较了《港口工程桩基规范》以及API RP 2A WSD规范中对于开口管桩单桩承载力两种计算方法各自的优缺点,利用有限元软件ANSYS对目前普遍采用的传统模型和基于荷载传递法的双曲线模型分别建立三维桩基有限元模型进行计算和比较,分析表明后者更加准确合理、适用性更广泛。     

Ultimate strength of container ships subjected to combined hogging moment and bottom local loads part 1: Nonlinear finite element analysis

This paper is the first of two companion papers concerning the ultimate hull girder strength of container ships subjected to combined hogging moment and bottom local loads. In the midship part of container ships, upward bottom local loads are usually larger than the downward ones. This leads to the increase of biaxial compression in the outer bottom plating and the reduction of the ultimate hull girder strength in the hogging condition. In this Part 1, the collapse behavior and ultimate strength of container ships under combined hogging moment and bottom local loads are analyzed using nonlinear finite element method. Buckling collapse behavior of bottom stiffened panels during the progressive collapse of a hull girder is closely investigated. It has been found that major factors of the reduction of ultimate hogging strength due to bottom local loads are (1) the increase of the longitudinal compression in the outer bottom and (2) the reduction of the effectiveness of the inner bottom, which is on the tension side of local bending of the double bottom. The obtained results will be utilized in the Part 2 paper to develop a simplified method of progressive collapse analysis of container ships under combined hogging moment and bottom local loads.     

A regression and beam theory based approach for fatigue assessment of containership structures including bending and torsion contributions

Container shipping has been expanding dramatically during the last decade. Due to their special structural characteristics, such as the wide breadth and large hatch openings, horizontal bending and torsion play an important role to the fatigue safety of containerships. In this study the fatigue contributions from vertical bending, horizontal bending and torsion are investigated using full-scale measurements of strain records on two containerships. Further, these contributions are compared to results from direct calculations where a nonlinear 3D panel method is used to compute wave loads in time domain. It is concluded that both bending and torsion have significant impacts on the fatigue assessment of containerships. The stresses caused by these loads could be correctly computed by full-ship finite element analysis. However, this requires large computational effort, since for fatigue assessment purposes the FE analysis needs to be carried out for all encountered sea states and operational conditions with sufficient time steps for each condition. In this paper, a new procedure is proposed to run the structure finite element analysis under only one sea condition for only a few time steps. Then, these results are used to obtain a relationship between wave loads and structural stresses through a linear regression analysis. This relation can be further used to compute stresses for arbitrary sea states and operational conditions using the computed wave loads (bending and torsion moments) as input. Based on this proposed method for structure stress analysis, an efficient procedure is formulated and found to be in very good agreement with the full-ship finite element analysis. In addition it is several orders of magnitude more time efficient for fatigue assessment of containership structures.