Experimental study the collapse failure mechanism of cemented casing under non-uniform load

Under non-uniform in-situ stress, the casing collapse failure often happens easily, and especially in soft rock the problem is more serious. In addition, only the few scholars do some studies about failure mechanism of cemented casing under non-uniform in-situ stress which has a strong effect on collapse properties of cemented casing, especially testing investigation. Hence, the collapsing test was performed for cemented casing under non-uniform load (NFL) by adopting self-developed testing equipment, by which the radial deformation of cemented casing and damage rules of cement sheath have been measured and the stress-strain laws of cemented casing are obtained during the testing process by the electrical method. The initial yield load and plastic limit load of cemented casing as well as the subsequent yield load have been obtained. By analyzing testing data, the stress-hardening rate and strain-hardening rate after hardening have been determined. The effects of cement sheath on collapse properties of P110SS casing and strain and deformation laws of P110SS casing after hardening have been obtained. The hardening character and failure mechanism of cemented casing have been figured out under NFL.     

考虑温升梯度影响的表贴式高速永磁电机转子强度分析

针对非导磁金属护套表贴式高速永磁电机的转子强度分析问题,基于弹性力学的平面应力模型,采用极坐标下的位移法,推导了考虑静态过盈量、转速以及转子温升梯度影响的转子强度解析解,并通过有限元仿真和试验验证了解析解的有效性.在转子强度解析解的基础上,进一步研究了护套厚度、静态过盈量、转速及转子温度等参数对转子应力的影响.仿真及试...     

水平荷载作用下钢板深梁弹性力学解

通过建立力学模型, 应用弹性力学中的半逆解法对水平荷载作用下钢板深梁应力与位移进行计算。推导出钢板深梁有关的应力分量与位移分量的解析计算公式。结果表明:非加劲钢板深梁计算所得结果与试验结果对比, 能够满足精度要求。对于两侧加劲钢板深梁, 随加劲肋与钢板的面积比的改变, 钢板深梁应力分布也发生改变。当面积比为0时, 所得解与非加劲钢板深梁解一致;随面积比增大时, 钢板深梁正应力减小, 最终近似为纯剪受力状态。所得解为构件设计和稳定性分析提供理论基础。     

超声波检测套管井水泥环缺陷仿真模拟

针对固井过程中由于顶替效率过低、气窜等原因造成水泥环局部缺失的现象,基于超声脉冲反射原理,运用有限元方法建立不同大小、不同方位的水泥环缺失模型,数值模拟了超声波在套管井多层介质中的传播规律。通过提取回波首波幅度、首波的接收时间,对回波进行频谱分析,对比了胶结良好和水泥环缺失两种情况下的时域特征和频域特征。在研究不同方位缺失影响时,引入了缺陷敏感频率,发现在一定激发频率下,有缺陷的位置上敏感频率会出现极大值,不同方位的缺陷有不同的敏感频率,而且区别较为显著,以此可以判断缺失方位。     

考虑膨胀土地基膨胀率和刚度沿深度变化的桩-土共同作用解析解

膨胀土地基中,土的膨胀率和刚度沿深度变化明显:较深位置的膨胀土应力水平较高,一方面遇水的膨胀率较小,另一方面土的刚度较大。该文基于桩-土相互作用机理,利用荷载传递法推导了考虑膨胀土沿深度膨胀率减小、刚度增加的单桩理论求解方程,并得到了级数形式的解析解。理论解与现场和模型试验数据符合较好,尤其是轴力沿桩身发展的模式。之后该文在膨胀土层的平均膨胀率和平均模量不变的前提下,分析了不同膨胀位移分布模式和刚度分布模式对桩受力和变形的影响,发现若按传统的土沿深度膨胀率和刚度为常值计算,将过高地估计单桩的轴力和位移。利用此解析解还讨论了膨胀土中桩的临界压重。     

采用等效介质模型研究地应力场中套管井周波速的空间分布

在以往的工作中,利用弹性力学理论获得了地应力场中套管—水泥环—地层系统应力分布的解析表达式。在此基础之上,应用等效介质模型的速度—应力关系式,研究了地应力场中套管井周弹性波速的空间分布规律。分析结果表明,相对裸眼井,套管井应力集中的程度更加明显,由于套管和水泥环的存在,地层应力集中的范围明显缩小到井眼附近。应力集中将导致套管井周波速空间分布的各向异性,对应不同方位径向偏振的横波速度的交叉点明显向井孔附近移动,这意味着垂直偏振的两种弯曲波频散曲线的交点会向高频移动。这一结果表明,在高频情况下,在套管井中应用正交偶极子声测井检测应力导致的各向异性是可行的。     

Analytical expressions for stress and displacement fields in viscoelastic axisymmetric plane problem involving time-dependent boundary regions

An analytical solution is developed in this paper for viscoelastic axisymmetric plane problems under stress or displacement boundary condition involving time-dependent boundary regions using the Laplace transform. The explicit expressions are given for the radial and circumferential stresses under stress boundary condition and the radial displacement under displacement boundary condition. The results indicate that the two in-plane stress components and the displacement under corresponding boundary conditions have no relation with material constants. The general form of solutions for the remaining displacement or stress field is expressed by the inverse Laplace transform concerning two relaxation moduli. As an application to deep excavation of a circular tunnel or finite void growth, explicit solutions for the analysis of a deforming circular hole in both infinite and finite planes are given taking into account the rheological characteristics of the rock mass characterized by a Boltzmann or Maxwell viscoelastic model. Numerical examples are given to illustrate the displacement and stress response. The method proposed in this paper can be used for analysis of earth excavation and finite void growth.     

Closure of circular arc cracks under general loading: effects on stress intensity factors

The two-dimensional circular arc crack solution of Muskhelishvili (Some basic problems of the mathematical theory of elasticity, P. Noordhoff Ltd, Groningen, Holland, 1953) has been used widely to study curved crack behavior in an infinite, homogeneous and isotropic elastic material. However, for certain orientations and magnitudes of the remotely applied loads, portions of the crack will close. Since the analytical solution is incorrect once the crack walls come into contact, the displacement discontinuity method is combined with a complementarity algorithm to solve this problem. This study uses stress intensity factors (SIFs) and displacement discontinuities along the crack to define when the analytical solution is not applicable and to better understand the mechanism that causes partial closure under various loading conditions, including uniaxial tension and pure shear. Closure is mainly due to material from the concave side of the crack moving toward the outer crack surface. Solutions that allow interpenetration of the crack tips yield non-zero mode I SIFs, while crack tip closure under proper contact boundary conditions produce mode I SIFs that are identically zero. Partial closure of a circular arc crack will alter both mode I and II SIFs at the crack tips, regardless of the positioning or length of the closed section along the crack. Friction on the crack surfaces in contact changes the total length and positioning of closure, as well as generally decreases the magnitude of opening along the portions of the crack that are not closed.     

Out-of-plane stresses in composite shell panels: layerwise and elasticity solutions

Boundary-layer effects in lengthy cross-ply laminated circular cylindrical shell panels under uniform axial extension are investigated by two analytical solutions. First, Reddy??s layerwise theory with state-space approach is utilized to determine the local interlaminar stresses. In this method, the general displacement field is discretized through the shell thickness by a linear shape function. When the shell panel is subjected to an axial force, the axial strain is estimated by an equivalent single-layer theory. Second, the stress-function approach along with Fourier series expansion is applied to develop a novel elasticity solution. The elasticity solution, which is based on simply-support edge conditions, is presented to show the effectiveness of the first solution. The numerical results show good agreements. Interlaminar stresses within various symmetric and unsymmetric cross-ply composite shell panels are then calculated and discussed. It is shown that the normal out-of-plane stress can get high magnitudes along the physical interfaces.     

Nonlinear thermoelastic analysis of thick-walled functionally graded piezoelectric cylinder

This research addresses the nonlinear behavior of a functionally graded piezoelectric (FGP) cylinder under thermal, mechanical and electrical loads. Except the Poisson ratio, the other thermal, mechanical and electrical properties vary continuously along the thickness direction. The geometric nonlinearity was considered in strain–displacement relation. The present paper proposes a novel analytical method for estimating the response of the systems of nonlinear differential equations. The proposed method is modification and combination of Adomian’s decomposition and successive approximation methods. The governing nonlinear differential equations were solved using the proposed analytical method. The nonlinear solutions were presented for different values of nonhomogenous index. For validation of the results and justifying the necessity of the present study, the present results were compared with results obtained using the linear analysis. Due to using the functionally graded cylinder in serious environments such as chemical and weapon equipments or adjustable and precise condition, a nonlinear analysis for these materials is necessary. A nonlinear analysis improves the results significantly. A maximum of 5% improvement for electric potential and 9% for radial displacement were attained employing this nonlinear analysis rather than a linear analysis. These considerable improvements can present a confidence and adjustable tool for manufacturing and design of sensors and actuators with better accuracy.     

Analytical solution for a functionally graded beam with arbitrary graded material properties

The plane stress problem of an orthotropic functionally graded beam with arbitrary graded material properties along the thickness direction is investigated by the displacement function approach for the first time. A general two-dimensional solution is obtained for a functionally graded beam subjected to normal and shear tractions of arbitrary form on the top and bottom surfaces and under various end boundary conditions. For isotropic case explicit solutions are given to some specific through-the-thickness variations of Young’s modulus such as exponential model, linear model and reciprocal model. The influence of different grade models on the stress and displacement fields are illustrated in numerical examples. These analytical solutions can serve as a basis for establishing simplified theories and evaluating numerical solutions of functionally graded beams.     

基于荷载传递法的嵌岩桩负摩阻力计算研究

结合有效应力法及荷载传递法建立了嵌岩桩负摩阻力计算的分段模型。通过位移控制方程计算得到了桩身不同段位移及轴力的解析解及幂级数解,进一步得到了计算桩身轴力及负摩阻力中性点位置的迭代计算方法。在一工程实例分析时,采用线性拟合的方法准确拟合桩周土体沉降,所得的桩身轴力沿桩长范围内的变化曲线与实测曲线较为吻合,该法能较准确地描述桩身负摩阻力的传递过程及其沿桩身的分布。     

A mathematical model to approach the fracture process of overconsolidated clay

Some soil and most rock masses contained defects (joints, cracks, bedding planes, fissures in clay, etc.). Beyond the peak shear strength of a mass of soil or rock, the stress falls as the strain increases. In this paper, the plane strain problem with double edge-cracks under shear loads is analysed based on linear elastic fracture mechanics but with finite stress concentration concept. We assumed that the fissured clay is a kind of strain-softening material and the growth of slip surface is along the maximum shear stress plane. The growth of slip surfaces in the progressive failure is expressed by the shear loads and slip displacement curves, which are obtained under the crack tip opening displacement criteria (CTOD_c) or the energy release rate criteria (J_c). The residual slip displacements are also taken into account by cumulating the elastic ones.     

横观各向同性弹性地基塞露蒂问题的解析解

根据横观各向同性弹性体半空间问题的基本方程,利用Hankel变换和Bessel函数理论,基于位移法导出的横观各向同性地基空间问题的一般解,得到了材料特征根不相等情况下横观各向同性地基塞露蒂(Cerruti)半空间问题的基本解。该解答经过退化与各向同性Cerruti问题的经典解相吻合。通过算例对两种不同地基内部位移和应力分布进行了对比分析。结果表明,对于给定的算例,两种地基内部沿深度方向的位移分布基本相同,但两种地基内部应力场的差异比较显著。     

含界面边裂纹压电材料反平面问题的应力强度因子

研究了含界面边裂纹的不同压电介质组成的复合材料在反平面荷载和平面内电场作用下的电弹场,得到了级数形式的基本解和应力强度因子,最后用边界配置法求解了应力强度因子。结果表明,在外加剪切荷载的作用下,应力强度因子与外加电场无关。     

On the optimum shape of fillets in plates subjected to multiple in-plane loading cases

The shape of a plate in plane stress is determined, such that the maximum elastic stress corresponding to given loads is minimized. The shape of the boundary is approximated by a series and optimization is carried out by solving a sequence of linearized minimum–maximum problems using linear programming. The optimization problem is extended to include multiple loading cases and geometrical constraints. The stress derivatives are found using analytical expressions for stiffnesses and stiffness derivatives of the finite elements. For the optimum design of a hole in an infinite plate under biaxial stretching the numerical result is compared with an analytical solution. As another example the method is used to optimize the edge shape of a shape of a junction in a web frame.     

酸性油气田C110套管断裂失效分析

为查明酸性油气田某油井C110套管断裂失效原因,通过C110断裂失效套管断口宏观形貌、金相组织、化学成分、力学性能和腐蚀产物成分等综合分析,对酸性油气田某油井C110套管断裂原因进行了探讨。结果表明:套管不居中导致套管产生应力集中,并在套管与卡瓦咬合的第1个齿形成严重机械损伤;同时,地层运动、套压波动等因素导致套管在应力集中部位出现交变载荷。最终,在套管内壁处于高H2S、低p H值环境下,在内表面交变应力集中区域发生腐蚀疲劳开裂。     

非轴对称下隧道锚网喷支护结构的可靠度分析

以圆形隧洞围岩的弹塑性解析解为基础,建立非轴对称情况下锚网喷支护结构的可靠度分析模型。考虑功能函数的高度非线性,采用Monte-Carlo法和Rosenblueth法计算可靠度指标。计算结果表明:锚网喷支护结构的可靠性是围岩、锚杆、钢筋网和喷层共同作用的结果,其可靠指标随围岩地应力、粘聚力、内摩擦角、喷层厚度、喷层混凝土抗压强度、锚杆抗拉强度和锚固力的变异系数的增加而降低。可靠指标随侧压系数的增加而增加,随地应力的增加而迅速降低。     

含椭圆孔压电材料的电弹场

采用复变函数的方法,研究了含椭圆孔的压电材料在无限远处受力电荷载作用的平面问题。与已有文献不同,通过求解10元一次方程,得到了满足可导通和不可导通电边界条件,孔内和压电材料体内电弹场的通解。以PZT一4压电陶瓷为例,给出了孔内的电场、压电材料体内电弹场沿孔边和坐标轴向的分布情况。得出了以下新的结论:含椭圆孔压电材料的电弹场与边界条件、力电荷载的方向、椭圆孔的形状有关,但在水平方向的拉伸载荷和电位移的作用下,椭圆孔的形状对长半轴处的环向电位移和正应力的最大值没有影响。     

Acoustoelastic Effects on Borehole Flexural Waves in Anisotropic Formations under Horizontal Terrestrial Stress Field

Applying the Stroh theory and based on the works of Hwu and Ting (1989), the complex function solution of stress and displacement fields around an open borehole in intrinsic anisotropic formation under horizontal terrestrial stress field is obtained. For cross-dipole flexural wave propagation along borehole axis, using the perturbation method, the acoustoelastic equation describing the relation between the alteration in phase velocity and terrestrial stress as well as formation intrinsic anisotropy is derived. At last, the numerical examples are provided for both the cases of fast and slow formation where the symmetry axis of a transversely isotropic (TI) formation makes an angle with the borehole axis. The phase velocity dispersion curves of borehole flexural wave and the corresponding velocity-stress coefficient are investigated. Computational results indicate that different from the stressed intrinsic isotropic formation situation, the variation in the phase velocity of flexural wave in stressed intrinsic anisotropic formation is dominated by two factors, one is the intrinsic formation anisotropy itself and the other is the stress-induced anisotropy. The former factor merely causes the borehole flexural wave split while the latter factor induces the dispersion curves intersection for two flexural waves polarized orthogonally. The combined effect of the two factors could strengthen or weaken the phenomenon of crossover for flexural wave dispersion curves. Thus, the dispersion curves of flexural waves may not intersect even under the unequal horizontal terrestrial stress field, whereas it is still possible to observe the crossover of the flexural wave dispersion curves under the equal horizontal terrestrial stress field. The polarized direction of the low-frequency fast flexural wave is no longer consistent with the direction of the maximum horizontal terrestrial stress all the time. Therefore, the crossover of the borehole flexural wave dispersion curves means that the terrestrial stress must exist. On the other hand, we can't exclude the possibility of the existence of terrestrial stress even if the flexural wave dispersion curves do not intersect. Based on the above researches, the method for terrestrial stress inversion from borehole flexural wave dispersion curves obtained by cross-dipole sonic logging in stressed intrinsic anisotropic formation is simply discussed.