大挠度钻柱强度分析的平衡微分方程法

对小井眼、大曲率井中钻柱强度问题,以井轴为基准轴,在对井轴弯挠描述和钻柱微段三维受力变形分析的基础上,建立大位移钻柱平衡微分方程,采用Longe-Kutta法解之求内力,并依此求应力和建立强度条件.对H767侧钻水平井施工中钻柱应力计算分析,结果说明与有限元模型和弹性化软绳模型比较相吻合,该模型比有限元模型计算简捷方便;比弹性化软绳模型更完善可信;该井钻柱破坏事故愿因在于井眼曲率过大,兼有应力集中.     

以点的曲线运动为例研究空间曲线

空间曲线任一点处的自然坐标系(Frenet标架)以及曲线在该点的曲率和挠率列为高等师范院校物理专业的高等数学教学大纲所要求的内容。作为向量微分运算仅仅安排了两个学时,所以不能介绍微分几何中的有关严密推证。     

基于曲率插值的大变形梁单元

线性梁单元的形函数在单元大转动时会引起虚假应变,不适用于几何非线性分析．传统的几何非线性梁单元由于位移插值和转角插值的相干性,常常引起剪切闭锁等问题．该文 提出了一种平面大变形梁单元,通过单元域内的曲率插值以及曲率与节点位移之间的函数关系,将单元节点力和节点位移表示为节点曲率的函数．由于曲率插值本质上是对梁的应变进行插值,保证了单元任意刚体运动不会产生虚假的节点力;且将梁的截面形心位移表示为曲率的函数,避免了传统单元中的剪切闭锁问题．因而所提方法特别适用于梁的几何非线性分析．数值算例说明了所提方法的正确性和有效性.     

环空钻柱结构三维非线性分析

应用有限元理论和牛顿－拉裴逊法对弯曲井眼中环空钻柱结构进行非线性分析．根据变形特点，提出了对不同参量采用不同形式的单元的描述计算分析方法。采用罚函数法处理待定边界问题。计算表明了井眼曲率对钻头侧向力的非线性效应。     

基于改进位移模式的二维有限元线法超收敛算法

提出了基于改进位移模式的二维有限元线法超收敛算法．利用单元内部需满足平衡方程的条件,推导了超收敛计算的解析公式的显式,即将高阶有限元线法解的位移模式用常规有限元线法解的位移模式表示．用常规有限元线法解的位移模式与高阶有限元线法解的位移模式之和构造新的位移模式,基于线性形函数,采用变分形式推导了有限元线法求解的修正的常微分方程组．该算法在前和后处理同时使用超收敛计算公式,在原有试函数的基础上,增加了高阶试函数．使得单元内平衡方程的残差减少,从而达到提高精度的目标．对于二维Poisson方程问题,给出了有代表性的算例,结点和单元内的位移、导数的收敛精度得到了极大的提高．     

一种便于摄动分析的编队飞行卫星相对运动的描述

定义了一组参数来描述卫星编队飞行的相对运动,称为相对轨道要素．利用它可以方便地分析摄动对相对轨道构形的影响以及卫星编队队形的几何特点．首先,对相对轨道要素给予了详细的推导,指出当主星偏心率为小量时,在主星轨道坐标系中相对轨道是一椭圆柱和一平面相交所得的交线,用描述该椭圆柱和平面的参数即可确定相对轨道构形,进而提出了相对轨道要素．其次,利用相对轨道要素对相对轨道进行地球扁率摄动分析,指出相对轨道构形的变化由两部分组成:一是椭圆柱的漂移导致相对轨道中心的漂移,二是平面法线的章动和进动引起相对轨道平面转动,同时还给出了地球扁率摄动下相对轨道构形漂移率及转动率的解析公式．最后,针对J2摄动分析了卫星编队相对轨道构形的变化以及相对轨道构形的漂移量和转动量．     

管状曲面在曲线论中的应用

研究了围绕曲线的管状曲面上的曲率线,渐近线与测地线,给出它们的方程,揭示了这些曲线与Bertrand曲线或Mannheim曲线之间的关系,采用新的方法给出一条曲线是Bertrand曲线或Mannheim曲线的充要条件的另一种证明以及Mannheim侣线的曲率与挠率之间的关系．     

残余界面应力对粒子填充热弹性纳米复合材料有效热膨胀系数的影响

根据黄筑平等人提出的基于“3个构形”的表/界面能理论,研究了热弹性纳米复合材料的有效性质,重点讨论了残余界面应力对纳米尺度夹杂填充的热弹性复合材料有效热膨胀系数的影响．首先,给出了由第一类Piola-Kirchhoff界面应力表示的热弹性界面本构关系和Lagrange描述下的Young-Laplace方程;其次,采用Hashin复合球作为代表性体积单元,推导了在参考构形下复合球内部由残余界面应力诱导的残余弹性场,并进一步计算了从参考构形到当前构形的变形场;最后,基于以上计算得到了热弹性复合材料有效体积模量和有效热膨胀系数的解析表达式．研究表明,残余表/界面应力对复合材料的热膨胀系数有重要影响．     

类空和类时曲线的仿射性质研究

本文研究类空和类时曲线的中心仿射曲率,中心仿射挠率,曲线的曲率和挠率满足的关系以及两类曲线的正交标架和仿射标架之间的关系的问题.利用仿射空间和Minkowski空间中曲线的基本理论,讨论当类空和类时曲线的弧长与仿射弧长相同时,类空和类时曲线的仿射性质.根据得到的结论,通过变量代换讨论当类空和类时曲线的曲率κ(s)和挠率τ(s)满足τ(s)=aκ^λ(s)(a≠0,λ∈R)时,曲线的曲率所满足的特殊微分方程.     

关于两曲面交线的不变量

本文研究了R3中相交子流形的不变量.利用活动标架法,得出了一个类似的欧拉公式. 即两曲面交线的挠率可以用两曲面的测地挠率、法曲率及两曲面的夹角表示.     

The buckling of a drill string in a curvilinear borehole with axial line imperfections

The problem of the elastic buckling of drill strings in the channels of deep curved boreholes with geometric axial line imperfections is formulated. Imperfections in the form of localized helices are considered. The relation between the forces resisting the motion of the string and the amplitudes, pitches and sites of localization of the imperfections is analysed. The distributed forces of contact and friction interaction between the drill string and the borehole surface are found and the effects of seizure of the drill string are established. It is shown that the resistive forces and their moments increase as the amplitudes of the imperfections increase, and as their pitches and the displacement of the zones where they are relocated from the lower most distorted parts to the upper least distorted parts, decrease.     

井下钻柱纵向横向耦合振动模型建立与数值分析

针对井下钻柱运动的复杂性,基于动力学理论,建立了井下钻柱纵向和横向耦合振动的数学模型,并进行数值求解及分析.根据井下钻柱的实际工况,以整个井下钻柱为研究对象,提出了钻柱纵向和横向耦合振动的动力方程,并利用解析法和无量纲法分别求解出其动刚度和动阻尼的表达式,以及钻柱前两阶振动的固有频率.分析结果表明:当井下钻柱振动频率增大时,其动刚度呈幅值衰减的周期性变化,而其动阻尼呈幅值增强的周期性变化;井下钻柱长度和横截面面积越大,其动刚度和动阻尼的幅值越小;井下钻柱的Poisson(泊松)比对其振动的动刚度、动阻尼和前两阶固有频率没有影响;同时,井下钻柱的第二阶固有频率始终大于第一阶固有频率.该文的研究方法和模型为井下钻柱钻具分析和结果优化提供了理论参考和实际意义.     

A contribution to efficient calculation of complex drill string dynamics for deep hole drilling

This paper presents a hybrid model to describe drill string dynamics for deep hole drilling. Generally, a typical rotary drill string has a length of several kilometers, but the diameter is less than half a meter. Due to the large ratio of length to diameter, a drill string is a very flexible system. Consequently, an operating drill string is always affected by axial, torsional and lateral vibrations, which potentially induce serious failures. In order to avoid fatal defects, simulations to forecast vibrations are necessary. The simulation should be capable to exhibit the complex dynamical phenomena, e.g. sick-slip, forward whirl and backward whirl, and interactions between drill string and borehole. Usually, these simulations are very time-consuming. In this work, a hybrid model consisting of lumped masses connected with weightless beam elements representing the drill string is developed. The interaction between the drill string and the borehole is implemented by unilateral constraints to describe the nonlinear contact behavior. It was shown that accuracy and simulating time were improved by this model with respect to classical finite-element models. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

气体钻井钻柱气固耦合横向振动数学模型的建立与控制

根据钻柱力学和动量守恒基本理论,建立了考虑气体钻井液对钻柱内外耦合影响时的钻柱横向振动模型,此模型与一般的梁式结构的振动模型不同,它包含了钻柱轴力、钻柱内注入压力、环空压力和钻柱内气体对钻柱振动的影响.同时给出边界条件和初始条件.通过把系统外激励函数当作控制变量,利用Banach空间几何性质证明了此系统存在唯一最优控制元.     

On the Wellbore Contact of Drill Strings in a Finite Element Model

In drill string dynamics the Finite Element Method is usually applied to models of very long drill strings in a wellbore with arbitrary curvature. Taking account of geometrical constraint between the drill string and the wellbore, a high density of nodes is necessary. This density is much higher than the one needed to describe the natural vibrations properly, so this firstly leads to an extension of the computing time. A penalty function is frequently utilized to describe the contact problem between the drill string and the wellbore where the contact normal force acts only on the nodal points of the drill string. It was recognized that only node-to-surface contact models cannot fulfill this geometrical constraint, because the segment between two nodal points deeply penetrates the wellbore wall in some cases. A process with Gaussian points along the segment in time domain will be introduced, so that the drill string will be described according to this geometrical constraint with good accuracy but with a smaller density of nodes and less computing time. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear multivariable modeling and stability analysis of vibrations in horizontal drill string

Nowadays, economical extraction of the oil and gas, and their products is an important problem. Up to now, vertical wells have been used for oil extraction but some wells exist that they cannot be reached by using the vertical drilling. Horizontal and directional drillings are some techniques to reach these wells. In this article, dynamics of the horizontal drill string is studied. According to the forces that affect the dynamics of drilling, its longitudinal vibration is analyzed. After determination of the boundary conditions and normal modes of the system with using mode summation method, displacement of the bit is obtained. Finally, dynamics of the horizontal drill string is simulated and the effect of increasing the number of modes and the mode convergence phenomenon is discussed. Through this study, while it is shown that four modes are sufficient for a reliable prediction of the stable and unstable conditions; five modes are included for the system analysis. Then, the effects of other parameters such as the mud frequency and constants of bit/rock interaction model are studied. Through the proposed parametric study, the stability of the system is investigated. Moreover, the dominant modes which cause the instability of the horizontal drilling process are determined.     

Numerical study of linear and nonlinear string vibrations by means of physical discretization

To solve partial differential equations numerically, discretization of the continuous model is required and may be achieved either mathematically or physically. This paper illustrates how physical discretization of a continuous string may be accomplished by employing discrete model theory which has as its essential substance Newtonian mechanics.Typical examples of wave motion in discretized ‘linear’ and ‘non-linear’ strings are discussed. They include the transverse vibrations of a string after having been subjected to a given initial displacement, reflection and superposition of wave pulses in the string, and resonance of the string when coupled to a harmonic vibrator. The equations that arise after application of discrete model theory to these problems, describe the subsequent motion of the string, and are solved numerically by computer. In all cases the results obtained for the discrete linear string agree remarkably well with those for the corresponding continuous physical string. The stability of the solutions obtained by discretization are also investigated.     

不同模量横力弯曲梁的解析解

选择处于平面复杂应力状态下横力弯曲梁,对结构进行了中性层的判定,推导出中性轴、正应力、剪应力、位移的计算公式,得到如下结论:对于复杂应力状态下的不同模量弹性弯曲梁,其中性轴位置与剪应力无关,因此用正应力作为判据而得到解析解,改进了以往用主应力判定中性点的多次循环的计算方法．把解析解的结果与经典力学同模量理论,以及有限元数值解进行了比较,结果表明:解析解很好地考虑了拉压不同模量的效应．还提出了对不同模量结构的计算修正以及对结构优化的思想．