扁化效应对弯曲段套管抗挤强度的影响对比分析

针对弯曲段套管抗挤强度随井眼曲率变化规律问题，利用材料力学理论将弯曲段套管等价为均布载荷作用下的弯曲梁模型，根据拉梅厚壁筒理论和强度理论得到套管抗挤强度公式．借鉴扁化变形在圆管类结构中的研究思路，将其拓展到套管抗挤强度分析，对比分析是否考虑扁化效应下四种规格套管不同井眼曲率下的抗外挤强度．研究表明，套管轴向应力随井眼曲率基本呈线性变化；套管抗挤强度随井眼曲率的增加非线性下降．井眼曲率为2o/30 m时，是否考虑套管扁化变形得到的5 1/2"×10.54 mm P110套管抗挤强度误差为12.8 %；井眼曲率为12o/30 m时，误差46.9 %．井眼曲率为2o/30 m时，4 1/2"×9.65 mm TP140V套管抗挤强度误差11.9 %；井眼曲率为12o/30 m时，误差44.7 %．可见，考虑扁化变形后套管抗挤强度小于未考虑扁化变形情况；井眼曲率不大时，两种算法的差距较小，随着井眼曲率的增加，套管扁化变形对套管抗挤强度的影响不能忽略．     

力-热载荷下双金属复合管的屈曲失效研究

采用有限元方法研究了力-热载荷下双金属复合管的屈曲失效行为,通过三维有限元建模考虑了双金属复合管的准静态复合成型制造过程中产生的残余应力,分析了温度及内压两个主要参数对双金属复合管屈曲失效的影响。结果表明,高温导致材料发生软化,抑制了双金属复合管的屈曲;弯矩、内压及热载荷联合作用下,复合管内介质温度降低,复合管弯矩达到最大值对应的曲率减小,而弯曲承载能力增大,外基管的椭圆率也增大;内压变化对复合管的弯曲承载能力和外基管的椭圆率影响较小。     

Localization and propagation of curvature under pure bending in steel tubes with Lüders bands

The paper examines the plastic bending of steel tubes exhibiting Lüders bands through a combination of experiments and analyses. In pure bending experiments on tubes with diameter-to-thickness ratio of 18.8 tested under end-rotation control, following the elastic regime the moment initially traced a somewhat ragged plateau. At the beginning of the plateau Lüders bands appeared on the tension and compression sides of the cross section and simultaneously the curvature localized in one or two short zones while the rest of the tube maintained a much lower curvature. As the rotation of the ends was increased, one of the higher curvature zones spread at a nearly steady rate, affecting an increasingly larger part of the tube. When the whole tube was deformed to the higher curvature, the moment started to gradually increase while the tube deformed uniformly. A moment maximum was eventually attained and the structure failed by localized diffuse ovalization without any apparent effect from the initial Lüders bands-induced propagating instability. The problem was analyzed using 3D finite elements with a fine mesh. The material was modeled as an elastic–plastic solid with an up–down–up response over the extent of the Lüders strain, followed by hardening. The calculated response reproduced all major structural events observed experimentally including the initiation of the Lüders deformation, the moment plateau that followed, its extent, and the curvature localization and propagation associated with it. As in the experiments, once the high curvature extended over the whole tube length, the response of the tube became stable and the curvature uniform. With further bending the increasing ovalization induced a limit moment at a very high curvature.     

Buckling and post-buckling of long pressurized elastic thin-walled tubes under in-plane bending

The present paper focuses on the structural stability of long uniformly pressurized thin elastic tubular shells subjected to in-plane bending. Using a special-purpose non-linear finite element technique, bifurcation on the pre-buckling ovalization equilibrium path is detected, and the post-buckling path is traced. Furthermore, the influence of pressure (internal and/or external) as well as the effects of radius-to-thickness ratio, initial curvature and initial ovality on the bifurcation moment, curvature and the corresponding wavelength, are examined. The local character of buckling in the circumferential direction is also demonstrated, especially for thin-walled tubes. This observation motivates the development of a simplified analytical formulation for tube bifurcation, which considers the presence of pressure, initial curvature and ovality, and results in closed-form expressions of very good accuracy, for tubes with relatively small initial curvature. Finally, aspects of tube bifurcation are illustrated using a simple mechanical model, which considers the ovalized pre-buckling state and the effects of pressure.     

Length dependence of critical measures in single-walled carbon nanotubes

This paper presents an investigation on the buckling behaviour of single-walled carbon nanotubes under various loading conditions (compression, bending and torsion) and unveils several aspects concerning the dependence of critical measures (axial strain, bending curvature and twisting angle) on the nanotube length. The buckling results are obtained by means of an atomistic-scale generalized beam theory (GBT) that incorporates local deformation of the nanotube cross-section by means of independent and orthogonal deformation modes. Moreover, some estimates are also obtained by means of non-linear shell finite element analyses using Abaqus code. After classifying the buckling modes of thin-walled tubes (global, local and distortional), the paper addresses the importance of the two-wave distortional mode (flattening or ovalization mode) in their structural behaviour. Then, the well known expression to determine the critical strain of compressed nanotubes, which is based on Donnell theory for shallow shells, is shown to be inadequate for moderately long tubes due to warping displacements appearing in the distortional buckling modes. After that, an in-depth study on the buckling behaviour of nanotubes under compression, bending and torsion is presented. The variation of the critical kinematic measures (axial strain, bending curvature and twisting angle) with the tube length is thoroughly investigated. Concerning this dependence, some uncertainties that exist in the specific literature are meticulously explained, a few useful expressions to determine critical measures of nanotubes are proposed and the results are compared with available data collected from several published works (most of them, obtained from molecular dynamics simulations).     

On the effect of Lüders bands on the bending of steel tubes. Part I: Experiments

In several practical applications hot-finished steel pipe that exhibits Lüders bands is bent to strains of 2–3%. Lüders banding is a material instability that leads to inhomogeneous plastic deformation in the range of 1–4%. This work investigates the influence of Lüders banding on the inelastic response and stability of tubes under rotation controlled pure bending. Part I presents the results of an experimental study involving tubes of several diameter-to-thickness ratios in the range of 33.2–14.7 and Lüders strains of 1.8–2.7%. In all cases the initial elastic regime terminates at a local moment maximum and the local nucleation of narrow angled Lüders bands of higher strain on the tension and compression sides of the tube. As the rotation continues the bands multiply and spread axially causing the affected zone to bend to a higher curvature while the rest of the tube is still at the curvature corresponding to the initial moment maximum. With further rotation of the ends the higher curvature zone(s) gradually spreads while the moment remains essentially unchanged. For relatively low D/t tubes and/or short Lüders strains, the whole tube eventually is deformed to the higher curvature entering the usual hardening regime. Subsequently it continues to deform uniformly until the usual limit moment instability is reached. For high D/t tubes and/or materials with longer Lüders strains, the propagation of the larger curvature is interrupted by collapse when a critical length is Lüders deformed leaving behind part of the structure essentially undeformed. The higher the D/t and/or the longer the Lüders strain is, the shorter the critical length. Part II presents a numerical modeling framework for simulating this behavior.     

On the effect of Lüders bands on the bending of steel tubes. Part II: Analysis

Part II of this study presents a modeling framework that is shown to successfully simulate all aspects of the inhomogeneous bending of tubes associated with Lüders banding reported in Part I. The structure is discretized with solid finite elements using a mesh that is fine enough for Lüders bands to develop and evolve. The material is modeled as a finitely deforming, J₂ type, elastic–plastic solid with an “up–down–up” response over the extent of the Lüders strain, followed by hardening. Regularization of the solution was accomplished by introducing a mild rate dependence of the material. Simulation of the rotation controlled bending experiments confirmed most of the experimental observations and revealed additional details of the localization. Thus, the initial uniform-curvature elastic regime terminates with the nucleation of localized banded deformation on the tensioned and compressed sides of the tube. The bands appear in pockets that propagate into the hitherto intact part of the structure while the moment remains essentially unchanged. The tube develops two curvature regimes; a relatively high curvature in the Lüders deformed section and a low curvature in the unaffected one. Simultaneously, the plasticized zone develops higher ovalization and wrinkles with a wavelength that corresponds to the periodicity of the banded pockets. For tubes with lower D/t and/or shorter Lüders strain the higher curvature eventually spreads to the whole structure at which point homogenous bending resumes. For tubes with higher D/t and/or longer Lüders strain the localized curvature, ovalization, and wrinkle amplitude are larger and cannot be sustained; the tube collapses prematurely leaving behind part of its length essentially undeformed. For every tube D/t there exists a threshold of Lüders strain separating the two types of behavior. This bounding value of Lüders strain was studied parametrically.     

Post-buckling behaviour of slender structures with a bi-linear bending moment-curvature relationship

Certain classes of slender structures of complex cross-section or fabricated from specialised materials can exhibit a bi-linear bending moment-curvature relationship that has a strong influence on their global structural behaviour. This condition may be encountered, for instance, in (a) non-linear elastic or inelastic post-buckling problems if the cross-section stiffness may be well approximated by a bi-linear model; (b) multi-layered structures such as stranded cables, power transmission lines, umbilical cables and flexible pipes where the drop in the bending stiffness is associated with an internal friction mechanism. This paper presents a mathematical formulation and an analytical solution for such slender structures with a bi-linear bending moment versus curvature constitutive behaviour and subjected to axial terminal forces. A set of five first-order non-linear ordinary differential equations are derived from considering geometrical compatibility, equilibrium of forces and moments and constitutive equations, with hinged boundary conditions prescribed at both ends, resulting a complex two-point boundary value problem. The variables are non-dimensionalised and solutions are developed for monotonic and unloading conditions. The results are presented in non-dimensional graphs for a range of critical curvatures and reductions in bending stiffness, and it is shown how these parameters affect the structure's post-buckling behaviour.     

Liner wrinkling and collapse of bi-material pipe under bending

Lining internally a carbon steel pipe with a thin layer of corrosion resistant material is an economical method for protecting offshore tubulars from the corrosive ingredients of hydrocarbons. In applications involving severe plastic bending, such as in the reeling installation process, the liner can detach from the outer pipe and develop large amplitude buckles that compromise the flow. This paper outlines a numerical framework for establishing the extent to which lined pipe can be bent before liner collapse. The modeling starts with the simulation of the inflation process through which the two tubes develop interference contact pressure. Bending the composite structure leads to differential ovalization and eventually separation of part of the liner from the outer pipe. The unsupported strip of the liner on the compressed side first wrinkles and at higher curvature buckles and collapses in a diamond shaped mode. The sensitivity of the collapse curvature to the various parameters of the problem is studied, and amongst other findings the onset of collapse is shown to be very sensitive to small geometric imperfections in the liner. It is also demonstrated that bending the pipe under modest amounts of internal pressure can delay liner collapse to curvatures that make it reelable.     

On the effect of corrosion defects on the collapse pressure of pipelines

The loss of metal in a pipeline due to corrosion usually results in localized pits with various depths and irregular shapes on its external and internal surfaces. The effect of corrosion defects on the collapse pressure of offshore pipelines was studied through the combination of small-scale experiments with nonlinear numerical analyses based on the finite element method. After calibrated based on the experimental results, the model was used to determine the collapse pressure as a function of material and geometric parameters of different pipes and defects. An extensive parametric study using 2-D and 3-D numerical models was carried out encompassing different defect geometries and their interaction with pipe ovalization.     

Bending instabilities of elastic tubes

The present paper examines instabilities of long thin elastic tubes. Both initially straight and initially bent tubes are analyzed under in-plane bending. Tube response, a combination of ovalization instability and bifurcation instability (buckling), is investigated using a nonlinear finite element (FE) technique, which employs polynomial functions in the longitudinal tube direction and trigonometric functions to describe cross-sectional deformation. It is demonstrated that the interaction between the two instability modes depends on the value and the sign of the initial tube curvature. The ovalization of initially bent tubes is examined in detail and, in particular, the case of opening moments. Furthermore, the paper emphasizes on bifurcation instability. It is shown that buckling may occur prior to or beyond the ovalization limit point, depending on the value of the initial curvature. Using the nonlinear FE formulation, the location of bifurcation on the primary path is detected, post-buckling equilibrium paths are traced, and the corresponding wavelengths of the buckled configurations are calculated. Moreover, results over a wide range of initial curvature values are presented, extending the findings of previous works. Finally, several analytical approaches, introduced in previous research works, are also employed to estimate the moments causing ovalization and bifurcation instability. These approaches are based on nonlinear flexible shell theory or simplified ring analysis. The efficiency and accuracy of those analytical methods with respect to the nonlinear FE formulation are examined.     

Elastic-plastic secondary indeterminate problem for thin-walled pipe through the inner-wall loading by three-point bending

The inner-wall loading by three-point bending about thin-walled pipe is an elastic-plastic secondary indeterminate problem in the symmetrical three-roller setting round process. In this study, the shifting of the tangent point between the pipe and lower roller is ignored. The bilinear hardening material model is adopted, and the static equilibrium condition, physical relationship of elastic-plastic deformation, and deformation compatibility condition are taken into account. Based on the geometrical discrete idea, a semi-circular pipe is meshed equably into N micro-pipe-wall elements with same geometric parameters along the circumferential direction. Deformation characteristics of each element are calculated, and then the deformation history response of the whole pipe is resolved by the load increment method. The finite element model of static bending in three-roller setting round process is established by using the software package ABAQUS. The theoretical and simulated results show that the cross section of pipe has two positive bending regions and two reverse bending regions; the maximum bending curvature appears in the bottom section of pipe, the minimum bending curvature appears in the section corresponding to the tangent point of the pipe and lower roller. The quantitative relationships between the upper roller load, maximum(minimum) bending curvature and reduction are given. Finally, the reliability of theoretical calculation is proved by numerical simulation.     

Effective bending modulus of carbon nanotubes with rippling deformation

This paper concerned with the relation of the bending moment to the bending curvature during bending of carbon nanotubes, and the relation between the rippling formation and the bending modulus. Based on the three-dimensional orthotropic theory of finite elasticity deformation, a non-linear bending moment–curvature relationship of carbon nanotubes which is the appearance of wavelike distortion on the inner arc of the bent nanotubes is simulated by using an advanced finite element analysis package, ABAQUS. Utilizing the non-linear bending moment–curvature relationship, the effective bending modulus of carbon nanotubes with different cross-sections are obtained by means of a bi-linear theory and a simplified vibration analysis method. The effective bending modulus of carbon nanotubes simulated in the paper is close to the measuring result presented in reference [Science 283 (1999) 1513].     

Nonlinear bending response and buckling of ring-stiffened cylindrical shells under pure bending

In this paper, the nonlinear bending response of finite length cylindrical shells with stiffening rings is investigated by using a modified Brazier approach. The basic assumptions for the present study are that the deformation of a shell subjected to pure bending can be simplified into a two-stage process. One is that the shell ovalizes but its axis remains straight; the other is that the bending of the shell is regarded as a beam with nonuniform ovalization. The nonlinear bending response is derived by applying the minimum potential energy principle and the corresponding critical moment, associated with local buckling, is determined by employing the Seide–Weingarten approximation. Numerical results are shown and compared with those obtained from other methods, which demonstrates that the assumptions used in the present study are reasonable.     

Eigenanalysis and continuum modelling of pre-twisted repetitive beam-like structures

A repetitive pin-jointed, pre-twisted structure is analysed using a state variable transfer matrix technique. Within a global coordinate system the transfer matrix is periodic, but introduction of a local coordinate system rotating with nodal cross-sections results in an autonomous transfer matrix for this Floquet system. Eigenanalysis reveals four real unity eigenvalues, indicating tension–torsion coupling, and equivalent continuum properties such as Poisson’s ratio, cross-sectional area, torsion constant and the tension–torsion coupling coefficient are determined. A variety of real and complex near diagonal Jordan decompositions are possible for the multiple (eight) complex unity eigenvalues and these are discussed in some detail. Analysis of the associated principal vectors shows that a bending moment produces curvature in the plane of the moment, together with shear deformation in the perpendicular plane, but no bending–bending coupling; the choice of a structure having an equilateral triangular cross-section is thought responsible for this unexpected behaviour, as the equivalent continuum second moments of area are equal about all cross-sectional axes. In addition, an asymmetric stiffness matrix is obtained for bending moment and shearing force coupling, and possible causes are discussed.     

基于均匀荷载面曲率的简支裂纹梁损伤识别

为了采用模态参数对结构裂纹进行定位与定量,基于集中柔度模型,采用无质量的扭转弹簧模拟裂纹,建立简支裂纹梁的振动微分方程。针对现有柔度曲率指标仅能判断裂纹的大致范围,基于线性插值理论,建立裂纹位置与相邻测点均匀荷载面曲率差的关系,提出裂纹进一步定位公式,实现裂纹位置的精确定位。针对现有大多数损伤识别方法无法实现裂纹的损伤定量,基于位移曲率与结构刚度和弯矩的关系,理论推导了均匀荷载面曲率的结构刚度损伤程度识别方法,基于弹簧串联原理和线刚度思想,首次提出串联等效线刚度模型,建立裂纹深度与均匀荷载面曲率的关系,实现裂纹深度的定量。通过简支裂纹梁数值算例,考虑多裂纹的损伤情况,验证了新方法对裂纹定位与定量的有效性。     

Wrinkling of tubes in bending from finite strain three-dimensional continuum theory

The problem of a tube under pure bending is first solved as a generalised plane strain problem. This then provides the prebifurcation solution, which is uniform along the length of the tube. The onset of wrinkling is then predicted by introducing buckling modes involving a sinusoidal variation of the displacements along the length of the tube. Both the prebuckling analysis and the bifurcation check require only a two-dimensional finite element discretisation of the cross-section with special elements. The formulation does not rely on any of the approximations of a shell theory, or small strains. The same elements can be used for pure bending and local buckling a prismatic beam of arbitrary cross-section. Here the flow theory of plasticity with isotropic hardening is used for the prebuckling solution, but the bifurcation check is based on the incremental moduli of a finite strain deformation theory of plasticity.For tubes under pure bending, the results for limit point collapse (due to ovalisation) and bifurcation buckling (wrinkling) are compared to existing analysis and test results, to see whether removing the approximations of a shell theory and small strains (used in the existing analyses) leads to a better prediction of the experimental results. The small strain analysis results depend on whether the true or nominal stress–strain curve is used. By comparing small and finite strain analysis results it is found that the small strain approximation is good if one uses (a) the nominal stress–strain curve in compression to predict bifurcation buckling (wrinkling), and (b) the true stress–strain curve to calculate the limit point collapse curvature.In regard to the shell theory approximations, it is found that the three-dimensional continuum theory predicts slightly shorter critical wrinkling wavelengths, especially for lower diameter-to-wall-thickness (D/t) ratios. However this difference is not sufficient to account for the significantly lower wavelengths observed in the tests.     

A Curvature-ovalization measurement apparatus for circular tubes under cyclic bending

In this paper, the authors report the design and construction of a new measurement apparatus, along with the result of its testing. This apparatus can be placed at the midspan of the circular tube specimen and is suitable for simultaneous experimental determinations of the tube curvature and ovalization of the tube cross section. For testing the newly designed apparatus, the tube specimen of AISI 304 stainless steel was bent cyclically. It has been shown that the actual curvature and ovalization of the circular tube subjected to bending can be directly measured by the apparatus.     

Mechanical behavior and wrinkling of lined pipes

The paper focuses on wrinkling of lined pipes (sometimes referred to as clad pipes) under bending loading, where a corrosion-resistant thin-walled liner is fitted inside a carbon–steel outer pipe. The problem is solved numerically, using nonlinear finite elements to simulate liner pipe deformation and its interaction with the outer pipe. Stresses and strains are monitored throughout the deformation stage, detecting possible detachment of the liner from the outer pipe and the formation of wrinkles. The wrinkling behavior of elastic and elastic–plastic (steel) lined pipes under bending is examined. The results indicate that the lateral confinement of the liner pipe due to the deformable outer pipe and its interaction with the outer pipe has a decisive influence on the wrinkling behavior of the lined pipe. It is also shown that the behavior is characterized by a first bifurcation in a uniform wrinkling pattern, followed by a secondary bifurcation. The values of corresponding buckling curvature are determined and comparison with available experimental results is conducted in terms of wrinkle height development and the corresponding buckling wavelength. The results of the present research can be used for safer design of lined pipes in pipeline applications.     

Curvature sensitive nonlinear turbulence model

By modifying the Rodi assumption to take account of the influence of flow curvature, a new curvature modified algebraic stress model (CMASM) is developed from the second moment closure in the generalized curvilinear coordinate system. And the explicit form of the ASM, a new curvature modified nonlineark-ε model (CMNKE), is derived in the orthogonal curvilinear coordinate system. This new nonlineark-ε model is further validated by a numerical simulation of a two-dimensional U-type turnaround duct flow. The results show that the CMNKE can effectively capture the main characteristic of this curvature flow and simulate the damping effect of the shear stress by a convex curvature and the enhancing effect by a concave curvature. So, this model is a rational and effective simplification to the second moment closure. The project supported by the National Natural Science Foundation of China (19725208) and the National Climbing project of China