MODEL ESTABLISHMENT AND LOAD TRANSFER OF SEMI ARTICULATED FLEXIBLE DRILLING TOOL1)

半铰接柔性钻具的载荷传递规律直接影响超短半径水平井钻进的成功率。为此,首先推导出半铰接柔性钻杆的单元刚度方程并揭示了半铰接柔性钻杆的弯矩传递规律;然后,采用理论分析与数值模拟相结合的方法,验证了半铰接柔性钻杆有限元模型的正确性;最后,建立造斜段半铰接柔性钻具力学模型,对不同井眼曲率半径下半铰接柔性钻具的载荷传递规律进行研究。结果表明：井深位置相同时,井底扭矩值随曲率半径的增加而增大;半铰接柔性钻杆未锁死时,柔性钻杆不传递弯矩且井底扭矩波动较大,相关研究成果为柔性钻具的设计提供理论依据。     

A quaternion-based formulation of Euler–Bernoulli beam without singularity

This paper proposes a singularity-free beam element with Euler–Bernoulli assumption, i.e., the cross section remains rigid and perpendicular to the tangent of the centerline during deformation. Each node of this two-nodal beam element has eight nodal coordinates, including three global positions and one normal strain to describe the rigid translation and flexible deformation of the centerline, respectively, four Euler parameters or quaternion to represent the attitude of cross section. Adopting quaternion instead of Eulerian angles as nodal variables avoids the traditionally encountered singularity problem. The rigid cross section assumption is automatically satisfied. To guarantee the perpendicularity of cross section to the deformed neutral axes, the position and orientation coordinates are coupled interpolated by a special method developed here. The proposed beam element allows arbitrary spatial rigid motion, and large bending, extension, and torsion deformation. The resulting governing equations include normalization constraint equations for each quaternion of the beam nodes, and can be directly solved by the available differential algebraic equation (DAE) solvers. Finally, several numerical examples are presented to verify the large deformation, natural frequencies and dynamic behavior of the proposed beam element.     

三维轮轨法向接触力学行为弹塑性理论分析

基于Hertz接触理论和双线性强化模型,建立了轮轨法向接触弹塑性理论分析模型,分析了轮轨法向接触力学响应特征,讨论了轴重对接触压力和接触变形的影响规律。同时,基于三维轮轨接触有限元模型模拟了轮轨接触力学行为,并引入理论误差系数分析了弹性模型和双线性强化模型对轮轨接触力学响应预测结果的差异性。结果表明,轮轨最大接触压力和接触变形量均随轴重的增大而增大;双线性强化模型的理论误差系数较小,采用双线性强化分析模型能较准确地预测轮轨接触弹塑性力学行为。研究结果可为轮轨系统安全服役和损伤评估提供理论和技术支持。     

Atomistic–continuum coupled model for nonlinear analysis of single layer graphene sheets

In this paper, atomistic–continuum coupled model for nonlinear flexural response of single layer graphene sheet is presented considering von-Karman geometric nonlinearity and material nonlinearity due to atomic interactions. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that of at atomic level through Cauchy–Born rule. Strain and curvature dependent tangent in-plane extensional, bending–extension coupling, bending stiffness matrices are derived from strain energy density function constructed through Tersoff–Brenner potential. The finite element method is used to discretize the graphene sheet at continuum level and nonlinear bending response with and without material nonlinearity is studied. The present results are also compared with Kirchhoff plate model and significant differences at higher load are observed. The effects of other parameters like number of atoms in the graphene sheet, boundary conditions on the central/maximum deflection of graphene sheet are investigated. It is also brought out that the occurrence of bond length exceeding cutoff distance initiates at corners for CFCC, CFCF, SFSS, SFSF graphene sheets and near center for SSSS and CCCC graphene sheets.     

Effects of boundary conditions and anisotropy on elastically bent silicon

In four-point bending, the rollers that are used for load application impose additional constraints on the specimen that affect the anticlastic specimen curvature and cause the specimen displacement and stress profiles to deviate from the pure beam bending case. In this study, x-ray microdiffraction is used to map both the principal and anticlastic curvatures of elastically bent, rectangular (100)-type Si strips possessing width:thickness ratios of 40:1. We quantify the amount of roller constraint and show that the region over which the anticlastic specimen curvature is affected away from the roller is approximately five times the roller diameter. Consequently, for bending tests used to determine Poisson's ratio, if a region on the sample that is free from roller effects is not chosen, measurement errors as high as 46% can occur. Furthermore, we show that, due to the anisotropy of single crystal Si, this roller-constraining effect depends on crystallographic orientation and is more pronounced when the principal bending axis lies along the <100> direction as compared with the <100> direction.     

Effects of partial crack–face contact for the bending of thin shell structures

The physical occurrence that crack surfaces are in contact at the compressive edges when a flat or a shell is subjected to a bending load has been recognized. This article presents a theoretical analysis of crack–face contact effect on the stress intensity factor of various shell structures such as spherical shell, cylindrical shell containing an axial crack, cylindrical shell containing a circumferential crack and shell with two non-zero curvatures, under a bending load. The formulation of the problem is based on the shear deformation theory, incorporating crack–face contact by introducing distributed force at the compressive edge. Material orthotropy is concerned in this analysis. Three-dimensional finite element analysis (FEA) is conduced to compare with the theoretical solution. It is found that due to curvature effect crack–face contact behavior in shells differs from that in flat plates, in that partial contact of crack surfaces may occur in shells, depending on the shell curvature and the nature of the bending load. Crack–face contact has significant influence on the stress intensity factor and it increases the membrane component but decreases the bending component.     

预应力混凝土平面杆系结构的有限元方法

建立了基于有限元方法的考虑材料和几何非线性的任意截面预应力混凝土平面杆系结构的数值分析模型,可用于模拟预应力混凝土大跨度梁、单向偏压细长柱等的非线性全过程结构响应。引入修正的Rodriguez截面模型确定截面切线刚度,其中混凝土的贡献通过截面边界顶点定义的梯形单元来实现;在此基础上利用传统的平面非线性杆单元导出了标准有限元公式。通过两个算例验证了该模型的可靠性和适用性。     

NONLINEAR LARGE DEFORMATION BENDING PROPERTIES OF THE TRACHEA1)

研究了人工气管和生物气管拉伸和弯曲的力学性能及仿真方法。根据气管拉伸实验数据,拟合建立了人工气管的线弹性和生物气管的非线性幂函数本构模型,其与实验的最大误差为18.8%。根据非线性弯曲理论,建立了气管大变形的弯曲变形方程,并得到了其解析解,计算的弯曲载荷与实验的最大误差为8.7%。基于显式有限元法提出了气管弯曲变形的有限元仿真方法,犬气管的弯曲角度的有限元计算结果与实验的误差为3%。     

管线上卷极限弯矩分析

利用弹塑性理论对卷管施加弯矩载荷时的截面屈服过程进行了理论分析,得出了卷管上卷时卷管所能承受的极限弯矩;通过实例分析得出X65钢在发生塑性应变为2.5%时的卷管两端截面夹角为1.98rad、滚筒直径为5.05m、极限弯矩为99.2kN m。根据DNV-OS-F101和API-RP-1111的相关规定,可将99.2kN m界定为对卷管施加弯矩的上限值;卷管弯矩上限值对应卷管上卷时的滚筒直径上限值,表明卷管上卷时可通过滚筒直径来限制卷管弯矩值。本文结果可为深水管线卷轴铺设的应用提供理论依据。     

Anomalous behavior revisited: Dynamic response of elastic-plastic structures

Based on the minimum principle of acceleration in the elastic-plastic continua under finite deformation, the dynamic response of an elastic-perfectly plastic pin-ended beam subjected to rectangular impulse loading is studied with the help of a numerical approach. The calculated results once again show the anomalous behavior of the beam during its response process, which was previously found in [1]. By carefully analyzing the instantaneous distribution of the bending moment, the membrane force, the curvature and displacement during the response process, it is concluded that the interactive effect between the geometry and materials nonlinearities of the structure is the key reason for leading to the anomalous behavior. This will be helpful for clarifying some misunderstandings in explaining the problem before. Project supported by the National Natural Science Foundation of China.     

含腐蚀缺陷的管道静力性能试验测试研究

为研究腐蚀缺陷对管道承载力的影响,本文分别进行了含腐蚀缺陷管道在轴压载荷、弯曲载荷以及轴压和弯曲复合载荷作用下的静力失效过程测试。通过不同载荷作用下管道的荷载-位移曲线以及荷载-应变曲线来分析管道的失效模式和失效机理;通过有限元分析结果与试验测试结果验证其准确性。结果表明:腐蚀缺陷使管道在三种不同荷载作用下的极限承载力均有所下降;针对文中所研究的管道及其腐蚀缺陷,在轴压载荷作用下管道承载力下降了18.4%,在弯曲载荷作用下管道承载力下降了20.96%,在轴压和弯曲复合载荷作用下管道承载力下降了13.3%;管道中腐蚀缺陷位置的管壁厚度减小,该位置应变发展迅速,首先进入塑性屈服状态,最终导致该腐蚀位置发生弹塑性屈曲失效。     

超静定连续梁弹塑性过程分析的单位荷载法

讨论了分析超静定连续梁弹塑性受力和变形全过程的单位荷载法,运用该方法分析了集中荷载作用下一次超静定两跨连续梁的弹塑性加载和变形全过程．根据受力变形的特点,集中荷载作用下两跨连续梁的弹塑性加载过程可分为四个阶段,分别是弹性阶段、集中荷载作用点附近塑性区扩展阶段、集中荷载作用点保持为塑性铰而附近区域线性卸载阶段、两跨连接点附近塑性区扩展直至形成第二个塑性铰阶段．给出了加载过程中各阶段的弯矩内力和竖向位移随外荷载而变化的解析公式．研究结果表明：在相同的单跨荷载工况下,连续梁的变形过程不同于单跨一次超静定梁,其塑性铰形成顺序不同,静定结构形成顺序不同,但塑性极限破坏荷载相同．     

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].     

5-1/2 FH钻杆接头极限承载能力研究

随着超深井、定向井、水平井、大位移井及大斜度井在石油钻井工程中的广泛应用,由井下复杂工况引起的钻杆接头过早失效问题日益突出,导致钻井周期增长,成本增加,成为制约钻井工程效益的主要因素之一.近年来,不少学者对钻杆接头进行了大量研究,多数采用二维轴对称模型,少数采用三维力学模型,但并未同时考虑螺纹升角和井眼弯曲作用等因素的影响,而钻杆接头的极限承载能力研究更是鲜见报道.针对上述问题,基于虚功原理、von Mises屈服原则及接触非线性理论,同时考虑螺纹升角和井眼弯曲作用,建立了钻杆接头的三维数值仿真模型与井眼曲率到加载弯矩的转换模型,研究了钻杆接头的上扣特性、井眼曲率对连接强度和密封性能的影响,考虑预紧力、弯曲载荷及动载安全系数,计算了钻杆接头的极限工作拉力和极限工作扭矩.研究结果表明:上扣扭矩使钻杆接头产生一定的初始接触压力,保证钻杆接头井下作业过程中的连接强度与密封性能;井眼曲率对钻杆接头井下作业过程中的连接强度与密封性能影响极大,常见的某些工况会导致钻杆接头的连接强度和密封性能丧失,考虑服役时的随机振动与冲击,常规的超深井、水平井、定向井、大位移井及大斜度井弯曲段钻杆接头的设计和选型应着重考虑井眼曲率的影响;针对设计的每种钻杆接头,都应考虑常见的井眼曲率和轴向拉伸载荷进行极限工作拉力和极限工作扭矩的精细化数值计算,以确保其安全工作.     

Analysis of curved beams using a new differential transformation based curved beam element

Differential transformation method is used to obtain the shape functions for nodal variables of an arbitrarily non-uniform curved beam element including the effects of shear deformation considering axially functionally graded material. The proposed shape functions depend on the variations in cross-sectional area, moment of inertia, curvature and material properties along the axis of the curved beam element. The static and free vibration of axially functionally graded tapered curved beams including shear deformation and rotary inertia are studied through solving several examples. Numerical results are presented for circular, parabolic, catenary, elliptic and sinusoidal beams (both forms—prime and quadratic) with hinged-hinged, hinged-clamped and clamped-clamped and clamped-free end restraints. Three general taper types (depth taper, breadth taper and square taper) for rectangular cross section are studied. Out of plane vibration is studied and the lowest natural frequencies are calculated and compared with the published results. Out of plane buckling is investigated for circular beams due to radial load.     

一种提高四边形四节点平面壳单元计算精度的新方法

平面壳单元是由平面应力单元和平板弯曲单元叠加组合而成,具有简单的理论表达,但是它在计算曲面壳体结构时误差较大。为了进一步提高平面壳单元的计算精度,本文提出了一种计算平面壳单元刚度矩阵的新方法。通过该方法在高斯积分点建立多个单元局部坐标系,并保证每个局部坐标系都位于单元在高斯点处的切平面上,从而可以有效适应曲面壳体形状,达到进一步提高平面壳单元计算精度的目的。为了在这种新坐标系下计算单元刚度矩阵,给出了求解形函数对局部坐标的导数、局部到自然坐标系积分转换的雅可比、以及局部到整体坐标系的转换矩阵的新型计算方法。通过将这些新坐标系以及新计算方法运用到平面壳单元DKQ24中,可以有效提高平面壳单元尤其是在计算曲面壳体时的精度。计算结果表明,本文方法和平面壳单元相结合,不仅具有平面壳单元简单的理论表达式,还能得到满意的精度。另外,本文方法还可以应用到其他类型的平面壳单元,为提高其他类型平面壳单元的计算精度提供了一种新的途径和思路,具有广阔的应用前景。     

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.     

基于初弯曲单元的某弦支穹顶非线性稳定承载力分析

在单元的随动坐标系下,建立了初始弯曲对杆单元轴向刚度影响的计算公式,导出了考虑初始弯曲的非线性杆单元刚度矩阵;从经典的梁-柱理论出发,给出了考虑初始弯曲的非线性空间梁单元切线刚度矩阵推导过程。将建立的初始弯曲单元应用于弦支穹顶结构算例的非线性稳定承载力分析,研究了杆件初始弯曲对结构整体非线性稳定性能的影响,结果表明,杆件初始弯曲的存在会降低结构的整体刚度和极限承载力,而在不同的初始预应力状态下,极限荷载随初始弯曲增加都基本呈线性下降,并且其关系曲线基本平行。本文建立的基于初弯曲单元的非线性分析方法,可推广应用于各种类型空间网格结构的非线性分析,为结构设计方案的选择提供更为科学的依据。     

弯曲及拉伸荷载作用下的钢管抗压溃性能研究

钢管在海洋油气资源开发中应用广泛,一般依据在位应用时的荷载进行设计,设计理论较为成熟。但在某些安装工况中的拉伸和弯曲荷载与在位荷载具有相同的量级,此时钢管的设计需要考虑安装荷载的影响。本文针对钢管在承受拉伸和弯曲荷载下的抗外压压溃性能开展研究。基于商业软件ABAQUS建立有限元模型,开展钢管压溃实验与带有弯曲荷载下的钢管压溃实验验证有限元模型的正确性,进而利用验证后的数值模型讨论拉伸、弯曲荷载和两者联合作用下对管道抗外压压溃性能的影响。结果表明,弯曲荷载是影响抗压溃性能的重要因素,弯曲荷载的增加都会使极限压溃值显著下降。管道所受拉伸荷载对抗压溃性能有一定的影响,但影响很小,在两者共同作用下极限压溃值随弯曲荷载的增加都出现先增大后减小的现象,而且极值的位置与拉伸荷载的大小和弯曲荷载有关。因此,在抗压溃设计中应重点考虑弯曲荷载对压溃的影响,可忽略拉伸荷载的影响。本文可为海洋管道的安装起到指导作用。     

任意挠曲输液管道瞬时变分原理

给出了弹性系统瞬时势能泛函的一般表达式，得到了其关于任意挠曲输液管道的具体表达式，根据瞬时最小势能原理建立了该结构的有限元动力方程，并首次推导出其离心力载荷公式，讨论了管道结构静平衡位置的发散流速的确定，最后，用简单的实验结果对理论分析作了验证。