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.     

Lateral buckling of subsea pipelines triggered by combined sleeper and distributed buoyancy section

In order to release the axial compressive force resulting from high-temperature conditions, sleepers or distributed buoyancy sections are usually installed along the route of the subsea pipeline as the buckle initiation facilities to trigger lateral buckles. DNV-RP-F110 suggests that the individual buckle initiators can be combined to further increase the reliability of buckle formation. In this study, an improved buckle initiation technique, called the combined sleeper and distributed buoyancy section, is investigated. A generalised mathematical model is proposed to simulate lateral buckling triggered by the combined sleeper and distributed buoyancy section, and it can also be applied to simulate lateral buckling triggered by an individual technique, such as triggered only by sleeper or only by distributed buoyancy section. The mathematical model is verified by comparing with the solutions in the literature. The parametric analysis shows that the buckle formation reliability can be improved when the combined sleeper and distributed buoyancy section is employed. Moreover, both the axial force and the maximum stress along the buckled pipeline in the post-buckling stage are at a lower level, so the pipeline will be safer when the combined sleeper and distributed buoyancy section is utilised as the triggers.     

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.     

Imperfection study on lateral thermal buckling of subsea pipeline triggered by a distributed buoyancy section

Controlled lateral buckling is triggered by distributed buoyancy section at predesigned sites to release the axial force induced by high temperature and high pressure in subsea pipelines. Due to the larger diameter and smaller submerged weight of distributed buoyancy section, compared to the normal pipe section, imperfections are more easily introduced at the location of distributed buoyancy section. In this study, an analytical model is proposed to simulate lateral buckling triggered by a distributed buoyancy section for an imperfect subsea pipeline, which is validated by test data. Semi-analytical solutions are derived. First, snap-through buckling behaviour is discussed. Then the influence of initial imperfections on buckled configurations, post-buckling behaviour, displacement amplitude and maximum stress is discussed in detail. The results show that there is no snap-through phenomenon for large amplitude of initial imperfections, which appears only when the amplitude of imperfection is small enough. The displacement amplitude increases with the amplitude of initial imperfections, and it first increases and then decreases with wavelength of initial imperfection. Compared to a perfect pipeline, the maximum stress amplifies for relative small wavelength of initial imperfections. Therefore, a large enough wavelength of initial imperfection should be introduced.     

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.     

Post-buckling behaviour and strength of multi-stiffened aluminium panels under combined axial compression and lateral pressure

This paper presents the results of complementary numerical study done in the continuation of the activities carried out by the Committee III.1 “Ultimate Strength” of ISSC'2003 (Ref. [28] ).The main focus of the paper concerns the post-buckling behaviour and strength characteristics of the aluminium multi-stiffened panels under combined axial compression and lateral pressure.The finite element model proposed by the Committee III.1 “Ultimate Strength” of ISSC'2003 is used in the present investigation. Material is aluminium alloy AA6082-T6 and the multi-stiffened panel is a triple-span structure. Stiffeners are of either extruded or non-extruded angle-bar profiles. An initial deflection is imposed on the model in a procedure similar to that applied by the Committee III.1. General purpose finite element code ANSYS is used for non-linear elastic–plastic analyses.Main objectives are to study the influence of initial deflections and also HAZ on the post-buckling behaviour and collapse characteristics of aluminium stiffened panels under combined axial compression and lateral pressure. Different values of lateral pressure are exerted on the model in a systematic manner to simulate various levels of lateral pressure loading on multi-stiffened aluminium panels used in the construction of high-speed crafts.     

Evaluation of ultimate strength of stiffened panels under longitudinal thrust

A series of collapse analyses is performed applying nonlinear FEM on stiffened panels subjected to longitudinal thrust. MSC.Marc is used. Numbers, types and sizes of stiffeners are varied and so slenderness ratio as well as aspect ratio of local panels partitioned by stiffeners keeping the spacing between adjacent longitudinal stiffeners the same. Initial deflection of a thin-horse mode is imposed on local panels and that of flexural buckling and tripping modes on stiffeners to represent actual initial deflection in stiffened panels in ship structures. On the basis of the calculated results, buckling/plastic collapse behaviour of stiffened panels under longitudinal thrust is investigated. The calculated ultimate strength are compared with those obtained by applying several existing methods such as CSR for bulk carriers and PULS. Simple formulas for stiffened panels, of which collapse is dominated fundamentally by the collapse of local panels between longitudinal stiffeners, are also examined if they accurately estimate the ultimate strength. Through comparison of the estimated results with the FEM results, it has been concluded that PULS and modified FYH formulas fundamentally give good estimation of the ultimate strength of stiffened panels under longitudinal thrust.     

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.     

高速船复合材料层合板非线性动力失稳分析

对高速船复合材料层合板在轴向线性增长载荷作用下的非线性动力失稳进行了研究。基于极的大挠度基本假设,导出四边简支矩形层合板的非线性动力方程及变形及协调方程;用级数展开把非线性偏微分方程组化为易于求解的Kronecker内积形式的二阶常微分方程组,并由四阶Runge-kutta法数值求解,讨论了加载速率对复合材料层合板动力失稳的影响。由于本文在方程求解中采用了Kronecker内积,故提高了解的精度及效率。     

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.     

加筋板格高级屈曲分析技术研究及软件开发

文章给出了基于弹性大挠度理论和刚塑性分析的加筋板格高级屈曲分析方法(EPM),该方法包括五种失效模式,即正交加筋板格整体屈曲、纵向加筋子板格整体屈曲、纵向加筋和带板的局部屈曲或屈服、纵向加筋的侧倾以及全部屈服,可以考虑初始挠度和残余应力的影响以及双向压缩和侧向载荷的联合作用。以EPM方法为核心开发了加筋板格高级屈曲分析软件系统,包括任务管理、数据输入、屈曲分析、结果查看、能力曲线和文件分析等六个模块。为验证EPM方法的精度进行了系列纵向加筋和正交加筋板格试验模型的比较计算,并计算了四种典型加筋板格的双向应力能力曲线,与板格极限状态分析（PULS）软件和协调共同结构规范（HCSR）方法进行了比较分析。结果表明EPM方法可以分析联合载荷等因素对加筋板格极限强度的影响,文中开发的软件系统可用于加筋板格高级屈曲分析。     

A computational investigation of the effects of both-sides general corrosion on the buckling/plastic collapse behaviour and strength of stiffened plates

This paper presents the results of an investigation into the post-buckling behaviour and ultimate strength of imperfect corroded stiffened steel plates used in ships and other marine-related structures. A series of elastic–plastic large deflection finite element analyses is performed on stiffened steel plates suffering general corrosion wastage with random distribution. General corrosion is introduced into the finite element models using a random thickness surface model. The effects of corroded stiffened plate parameters on the post-buckling and ultimate strengths are evaluated in detail. The stiffeners of different symmetrical or unsymmetrical cross-sections are introduced into the models for analysis. Some distinctions are explored and highlighted between the behaviours of steel plates suffering general corrosion in unstiffened and stiffened cases. Finally, a proposal is given in order to simulate the average stress–average strain relationship of stiffened steel plates having both-surface general corrosion wastage.     

肘板对肋骨侧向稳定性的影响

通过研究在环肋圆柱壳的肋骨周向均匀布置肘板,得到肘板能有效限制肋骨的侧向变形,改善肋骨的侧向稳定性,提高肋骨的临界失稳压力,通过对比分析半肋距肘板和整肋距肘板,得到整肋距肘板对肋骨的侧向约束效果更明显,更有利于提高肋骨的侧向稳定性,最后得出整肋距肘板能有效提高肋骨的侧向稳定性和圆柱壳的整体稳定性。     

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.     

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.     

Research on the dynamic buckling of a typical deck grillage structure subjected to in-plane impact Load

The dynamic buckling of the main deck grillage would result in the total collapse of the ship hull subjected to a far-filed underwater explosion. This dynamic buckling is mainly due to the dynamic moment of the ship hull when the ship hull experiences a sudden movement under impact load from the explosion. In order to investigate the ultimate strength of a typical deck grillage under quasi-static and dynamic in-plane compressive load, a structure model, in which the real constrained condition of the deck grillage was taken into consideration, was designed and manufactured. The quasi-static ultimate strength and damage mode of the deck grillage under in-plane compressive load was experimentally investigated. The Finite Element Method (FEM) was employed to predict the ultimate strength of the deck grillage subjected to quasi-static in-plane compressive load, and was validated by comparing the results from experimental tests and numerical simulations. In addition, the numerical simulations of dynamic buckling of the same model under in-plane impact load was performed, in which the influences of the load amplitude and the frequency of dynamic impact load, as well as the initial stress and deflection induced by wave load on the ultimate strength and failure mode were investigated. The results show that the dynamic buckling mode is quite different from the failure mode of the structure subjected to quasi-static in-plane compressive load. The displacements of deck edge in the vertical direction and the axial displacements are getting larger with the decrease of impact frequency. Besides, it is found that the dynamic buckling strength roughly linearly decreased with the increase of initial proportion of the static ultimate strength P₀. The conclusions drawn from the researches of this paper would help better designing of the ship structure under impact loads.     

Riks弧长法在压杆非线性屈曲分析中的应用

为了得到单轴压缩杆件考虑几何非线性时的后屈曲特性,介绍Riks弧长法的基本原理,并以工字钢为例,说明Riks弧长法在压杆非线性屈曲分析中的应用.结果表明,考虑初始缺陷后,压杆的屈曲强度大大减小,且屈曲强度对缺陷因子极为敏感.该研究可为单轴压缩杆件的非线性屈曲分析提供参考.     

均布外压下球形封头屈曲特性研究（英文）

This study aims to experimentally and numerically examine the buckling performances of stainless steel spherical caps under uniform external pressure. Three laboratory-scale caps were fabricated, measured, and tested. The buckling behaviors of these caps were investigated through experiments and three numerical methods, namely, nonlinear Riks algorithm, nonlinear bifurcation, and linear elastic analysis. The buckling of equal-radius caps was numerically analyzed with different methods to identify their applicability under different wall thicknesses. The results obtained from the nonlinear Riks algorithm are in good agreement with the experimental results, which means the nonlinear Riks algorithm can accurately predict the buckling performances of spherical caps, including the magnitude of critical buckling loads and the deformation of post-buckling modes. The nonlinear bifurcation algorithm is only suitable for predicting the buckling loads of ultra-thin or large-span caps, and the linear buckling method is inappropriate for predicting the buckling of metal spherical caps.     

Two- and three-dimensional hydroelastic modelling of a bulker in regular waves

The relatively high rates of bulk carrier casualties in recent years, as well as structural features such as large deck openings, make this vessel type a suitable example for investigating the influence of hydroelastic modelling on predicting wave-induced loads and responses. Two- and three-dimensional fluid–flexible structure interaction models, due to their different degree of complexity and associated data requirements, can be used at different stages of the design process when estimating wave-induced loads, namely preliminary and detailed design stages, respectively.

In this paper, therefore, two- and three-dimensional hydroelasticity theories are applied to predict and compare the dynamic behaviour of a bulk carrier hull, based on OBO MV Derbyshire, in waves. Both symmetric and antisymmetric motions and distortions are incorporated in these investigations. The three-dimensional structural model consists entirely of shell finite elements, representing all major external and internal structural components, whilst the two-dimensional model is generated using Timoshenko beam finite element and finite difference discretisations. Issues relevant to the structural modelling stage, for both idealisations, are discussed. The in vacuo dynamic characteristics are compared for all models, with particular emphasis on the influence of hatch openings, shear centre and warping on the antisymmetric dynamics of the structure. For the wet analysis the fluid–flexible structure interaction is carried out using two-dimensional (Timoshenko beam and strip theory) and three-dimensional (beam and shell finite element idealisations combined with potential flow analysis based on pulsating source distribution over the mean wetted surface) analyses. Comparisons are made between steady-state responses predicted by two- and three-dimensional models in bow quartering regular waves.

It is shown that whereas the predicted symmetric dynamic responses obtained from two- and three-dimensional models are in good agreement, differences are observed for the antisymmetric dynamic characteristics. It is thought that this may be due to inadequacies in the beam models employed when simulating the global dynamic behaviour of this highly non-prismatic hull girder whilst allowing for the effects of warping.     

小波加权残值法在固支矩形板后屈曲上的应用

根据Von Karman板大挠度方程,以小波函数作为试函数,采用小波加权残值法将四边固支矩形板的平衡控制方程和变形协调方程化解为两个非线性方程组,将后屈曲路径的求解转化为两个非线性方程组的求解问题.将载荷分为多个水平,利用Newton-Raphson迭代算法求得非线性方程组的解,从而得到四边固支矩形板的后屈曲平衡路径和四级渐进解.通过算例表明小波可以用于解决矩形板的后屈曲问题.