Discussion on electromagnetic crack face boundary conditions for the fracture mechanics of magneto-electro-elastic materials

This paper discusses electromagnetic boundary conditions on crack faces in magneto- electroelastic materials, where piezoelectric, piezomagnetic and magnetoelectric effects are coupled. A notch of finite thickness in these materials is also addressed. Four idealized electromagnetic boundary conditions assumed for the crack-faces are separately investigated, i.e. （a） electrically and magnetically impermeable （crack-face）, （b） electrically impermeable and magnetically permeable, （c） electrically permeable and magnetically impermeable, and （d） electrically and magnetically permeable. The influence of the notch thickness on important parameters, such as the field intensity factors, the energy release rate at the notch tips and the electromagnetic fields inside the notch, are studied and the results are obtained in closed-form. Results under different idealized electromagnetic boundary conditions on the crack-face are compared, and the applicability of these idealized assumptions is discussed.

Shape factor for regular and irregular matrix blocks in fractured porous media

Describing matrix–fracture interaction is one of the most important factors for modeling natural fractured reservoirs.A common approach for simulation of naturally fractured reservoirs is dual-porosity modeling where the degree of communication between the low-permeability medium(matrix)and high-permeability medium(fracture)is usually determined by a transfer function.Most of the proposed matrix–fracture functions depend on the geometry of the matrix and fractures that are lumped to a factor called shape factor.Unfortunately,there is no unique solution for calculating the shape factor even for symmetric cases.Conducting fine-scale modeling is a tool for calculating the shape factor and validating the current solutions in the literature.In this study,the shape factor is calculated based on the numerical simulation of fine-grid simulations for single-phase flow using finite element method.To the best of the author’s knowledge,this is the first study to calculate the shape factors for multidimensional irregular bodies in a systematic approach.Several models were used,and shape factors were calculated for both transient and pseudo-steady-state(PSS)cases,although in some cases they were not clarified and assumptions were not clear.The boundary condition dependency of the shape factor was also investigated,and the obtained results were compared with the results of other studies.Results show that some of the most popular formulas cannot capture the exact physics of matrix–fracture interaction.The obtained results also show that both PSS and transient approaches for describing matrix–fracture transfer lead to constant shape factors that are not unique and depend on the fracture pressure(boundary condition)and how it changes with time.

Dynamic stiffness method for free vibration of an axially moving beam with generalized boundary conditions

Axially moving beams are often discussed with several classic boundary conditions, such as simply-supported ends, fixed ends, and free ends. Here, axially moving beams with generalized boundary conditions are discussed for the first time. The beam is supported by torsional springs and vertical springs at both ends. By modifying the stiffness of the springs, generalized boundaries can replace those classical boundaries. Dynamic stiffness matrices are, respectively, established for axially moving Timoshenko beams and Euler-Bernoulli (EB) beams with generalized boundaries. In order to verify the applicability of the EB model, the natural frequencies of the axially moving Timoshenko beam and EB beam are compared. Furthermore, the effects of constrained spring stiffness on the vibration frequencies of the axially moving beam are studied. Interestingly, it can be found that the critical speed of the axially moving beam does not change with the vertical spring stiffness. In addition, both the moving speed and elastic boundaries make the Timoshenko beam theory more needed. The validity of the dynamic stiffness method is demonstrated by using numerical simulation.

APPLICABILITY OF THE CRACK FACE ELECTRICAL BOUNDARY CONDITIONS IN PIEZOELECTRIC MECHANICS

The electrical boundary conditions on the crack faces and their applicability in piezoelectric materials are discussed. A slit crack and a notch of ?nite thickness in piezoelectric materials subjected to combined mechanical and electrical loads is considered. Here, a crack is de?ned as a notch without thickness, which is ?lled with air or vacuum. The crack or notch is perpendicular to the poling direction of the medium. The ideal crack face electrical boundary conditions, i.e., the electrically permeable crack and the electrically impermeable crack, are in- vestigated ?rst. Then dependence of the ?eld intensity factors on notch thickness at the notch tips is analyzed to obtain a closed-form. The results are compared with the ideal crack solutions. Some useful results are found.

DRIVING FORCE AND DEFORMATION ANALYSIS FOR DYNAMIC CRACK PROPAGATION IN GAS PIPELINES UNDER DIFFERENT BOUNDARY CONDITIONS

In the light of a growing need for fracture control of rapid crack propagation (RCP) in gas pipelines, a program PFRAC(Pipeline FRacture Analysis Code) has been developed((1)) to analyse the various events. In this paper, by using PFRAC for the simulation of axial crack propagation in gas pipelines, a number of dynamic analysis issues relating to boundary effects for uncracked and cracked pipes are investigated. This indicates that the boundary conditions along the length of the pipe play an important role for fracture analysis in the pipe. In contrast, the boundary conditions at the ends of a long pipeline have little effect on the dynamic fracture events.

A Split-Step Predictor-Corrector Method for Space-Fractional Reaction-Diffusion Equations with Nonhomogeneous Boundary Conditions

A split-step second-order predictor-corrector method for space-fractional reaction-diffusion equations with nonhomogeneous boundary conditions is presented and analyzed for the stability and convergence.The matrix transfer technique is used for spatial discretization of the problem.The method is shown to be unconditionally stable and second-order convergent.Numerical experiments are performed to confirm the stability and secondorder convergence of the method.The split-step predictor-corrector method is also compared with an IMEX predictor-corrector method which is found to incur oscillatory behavior for some time steps.Our method is seen to produce reliable and oscillatioresults for any time step when implemented on numerical examples with nonsmooth initial data.We also present a priori reliability constraint for the IMEX predictor-corrector method to avoid unwanted oscillations and show its validity numerically.

黏弹性Pasternak地基上修正Timoshenko梁横向自振特性分析

基于修正Timoshenko梁理论,建立黏弹性Pasternak地基上修正Timoshenko梁的横向振动控制方程,运用回传射线矩阵法推导出黏弹性Pasternak地基上两端简支修正Timoshenko梁自振频率和衰减系数的解析解,结合二分法和黄金分割法计算了经典边界条件下黏弹性Pasternak地基上修正Timoshenko梁的自振特性,对比分析了考虑剪切变形引起的转动惯量、梁长及不同的边界条件对结构自振特性的影响。研究表明:黏弹性Pasternak地基上修正Timoshenko梁的各阶自振频率和衰减系数小于经典Timoshenko梁的各阶自振频率和衰减系数;梁越短,剪切变形引起的转动惯量对结构自振频率和衰减系数的影响越大,且对高阶的影响明显大于低阶;边界约束条件越强,振动能量衰减越明显。

Recursion-transform approach to compute the resistance of a resistor network with an arbitrary boundary

We consider a profound problem of two-point resistance in the resistor network with a null resistor edge and an arbitrary boundary,which has not been solved before because the Green＇s function technique and the Laplacian matrix approach are invalid in this case.Looking for the exact solutions of resistance is important but difficult in the case of the arbitrary boundary since the boundary is a wall or trap which affects the behavior of a finite network.In this paper,we give a general resistance formula that is composed of a single summation by using the recursion-transform method.Meanwhile,several interesting results are derived by the general formula.Further,the current distribution is given explicitly as a byproduct of the method.

叶巴滩水电站坝址区挤压破裂带发育分布特征

勘探表明,在叶巴滩水电站坝址区岸坡石英闪长岩内广泛发育具有一定厚度和延伸长度的碎粒状岩屑条带——“挤压破裂带”,不仅使岩体完整性降低,而且劣化建基岩体质量。为了研究其发育特征、分布规律,基于野外调查、精细测量等方法,对施工期新揭露的典型挤压破裂带进行详细描述,揭示其发育特征、分布规律等。研究表明:叶巴滩水电站坝址区挤压破裂带在强弱卸荷带及以里均有发育,且空间分布不均匀,主要集中在左岸中高程;表现为有明显边界且具有一定厚度和延伸长度的碎粒状岩屑条带,一般发育在新鲜、完整的坚硬岩体内;可能为构造成因常依附于断层(或长度较大的结构面),范围有限,产状不稳定;带内大多劈理岩化,部分可见颗粒定向排列,具有分带性,无明显错距,表现出高地应力下的挤压变形特征;易受后期改造影响,局部可见风化加剧、锈染和泥质条带;主要分布于断层(长大结构面)夹持或围限区、断层(长大结构面)的端部、长大结构面的一侧。

古构造应力量值确定及其在构造地质建模中的应用

在对地质构造及构造应力场数值模拟分析过程中,关键问题是在地质建模时如何确定模型边界条件的应力量值大小。以塔里木盆地塔中 I#断裂带构造数值模拟的建模过程为例,应用岩石 Kaiser 效应与方解石晶体晶格位错的测试结果,结合构造特征和构造演化的解析进行综合分析,确定了研究区域目的层位在不同构造运动时期古构造应力场应力量值的大小,并成功地建立了研究区域构造地质模型。

小波有限元的研究及其工程应用

研究了一类新的有限元空间,它以小波尺度函数作为插值函数,从而构造出了小波有限元.利用小波的两尺度方程,很好地解决了因Daubechies小波尺度函数无明确解析表达式造成的积分困难,推导出了小波有限元常用刚度矩阵及载荷列阵积分公式,并给出了小波有限元用于薄板弯曲的分析列式.通过薄板弯曲及办公纸张温度场的数值分析,表明小波有限元具有满意的分析精度,可消除由于温度梯度变化而引起的0 5%左右的数值失真,并在处理变边界条件等大梯度问题方面,优于传统的小波有限元.

气体运移导致煤体结构变形演化特征研究--以注入氦气为例

气体运移引起煤体变形是研究煤层气抽采、预防瓦斯突出与温室气体的地质封存的核心问题。一般认为,有效应力变化是控制岩土类材料骨架变形的关键因素。但大量测试结果表明,煤的渗透率与有效应力(或者孔隙压力)表现出非线性关系。为此,应实时观测在静孔隙压力与三轴应力状态下氦气流动导致原煤变形演化全过程。在静孔隙压力状态下煤体积经历从收缩到回弹过程。注气压力越大,煤的收缩与回弹量越大,且收缩量总是大于回弹量。在三轴应力状态下注气初期煤样迅速膨胀。随着注气达到平衡状态,煤变形过程与约束条件表现出紧密相关性,即在应力约束下煤的膨胀率相比注气初期明显减缓;在位移约束下煤由膨胀转向收缩。上述试验结果表明,仅有孔隙压力作用下,煤基质与裂隙之间孔隙压力差可以压缩煤体,随着气体扩散的进行,可恢复煤的部分压缩变形量。在三轴应力状态下,煤的总体变形是裂隙与基质两者变形共同作用的结果。在应力约束下煤基质与裂隙可以自由膨胀。而煤体在位移约束下,因气体扩散导致煤基质膨胀只能挤压裂隙。根据上述实测结果探讨注气导致煤骨架变形演化机制,为深入理解煤裂隙与基质相互作用对煤渗透率演化提供试验依据。

考虑降雨入渗影响的非饱和土边坡瞬态安全系数研究

以土壤体积含水率作为控制变量 ,应用非饱和土水分运动基本理论建立了降雨入渗过程中土体瞬态含水率的计算模型并且编制了计算程序 ,在计算模型中通过改变边界条件考虑了降雨过程中土壤入渗能力的变化 ,采用非饱和土强度理论和极限平衡方法 ,得出了可以考虑基质吸力影响的边坡安全系数计算公式 ,编制了计算程序 ,最后通过具体的算例 ,讨论了降雨入渗对土质边坡稳定性的影响。

单裂缝多孔介质渗透特性研究

单裂缝多孔介质渗透特性的研究是裂缝性介质渗流分析的基础。针对含单裂缝的多孔介质,分别利用Darcy方程和Stokes方程描述基岩和裂缝中的流动,采用连续边界条件、Bea-vers-Joseph边界条件和Beavers-Joseph-Saffm an边界条件,得到考虑基岩渗透率的广义立方定律和分别满足3种边界条件的单裂缝介质的等效渗透率理论计算公式。参数分析表明,由3种边界条件所得到的单裂缝介质的等效渗透率较为一致(尤其当α>1时),因此应用经典的连续边界条件可简化问题,提高计算效率。研究结果为含裂缝多孔介质流动分析的参数确定提供了理论依据。

用传输矩阵法(TMM)研究二维光子晶体传输特性

将传输矩阵法 (TMM )用于光子晶体传输特性的理论研究 ,采用Mur近似吸收边界和周期边界来截断计算区域 ,研究了以TM模正入射时 ,二维方格子光子晶体在完整周期结构下和有缺陷结构下的透过率谱 ;在微波波段制作了光子晶体模型 ,并设计了实验装置 ;实验与数值模拟计算取得了基本一致的结果。

裂缝性油藏等效渗透率张量的边界元求解方法

等效渗透率张量是裂缝性油藏渗流分析的重要参数,应用边界元算法可计算裂缝性油藏的等效渗透率张量。根据流量等效原理,考虑每条裂缝的空间分布和属性参数对流动的影响,建立了求解裂缝性多孔介质等效渗透率张量的数学模型,并给出了数学模型的边界元求解方法。实例研究表明,边界元法数值计算结果与解析结果较为一致;裂缝对介质的渗透能力有重要影响,忽略渗透率张量的非对角线元素将产生较大误差;等效渗透率张量能够反映裂缝性多孔介质的非均质性和各向异性。

由统计规律模拟生成的岩体裂隙网络的非稳定渗流数值分析

研究裂隙岩体中渗透水流随时间、边界条件的变化规律,从而客观反映渗透水流情况,具有重要的意义.利用MonteCarlo模拟岩体中裂隙网络分布情况,基于裂隙岩体网络非稳定渗流数学模型,编制相应的程序,并通过算例进行验证,进而对工程实例进行分析.结论表明:运用MonteCarlo方法模拟岩体中裂隙网络分布状况并进行渗流分析是一种较好的分析方法;当边界条件发生变化时,裂隙岩体中水头分布变化存在一定的滞后性,并且当边界条件变化一定时,岩体中水头分布受时间变化影响不大.

楞古水电站碎裂岩质边坡变形破坏模式研究

碎裂结构岩质边坡是地质工程中遇到的一种最不稳定边坡,其原岩松弛,结构面普遍张开,围岩自稳能力差,碎裂结构岩体出露不连续,空间分布存在差异,导致边坡破坏边界不明显,变形破坏机制很难确定。本文以雅砻江楞古水电站碎裂结构岩质边坡为例,在地质环境调查和平硐勘测的基础上,系统研究了碎裂岩体结构特征,分析了控制边坡变形破坏的边界条件和变形破坏模式,并运用UDEC离散元程序模拟验证。研究结果表明:碎裂岩质边坡的变形破坏主要受自身结构及内部相对长大结构面控制,变形演化过程依循应力调整、时效变形和局部失稳3个阶段,变形破坏模式分为断层主控底滑型和裂隙切割破坏型。目前针对碎裂结构岩质边坡研究相对较少,缺乏大型工程实例支撑,该研究成果为水利工程中这类边坡的研究提供了参考。

断裂物理力学性质对其附近地应力场的影响

应用离散元方法,分别研究了断裂刚度、内摩擦角、内聚力和几何形态等对其附近地应力场的影响。结果表明:这些因素对断裂附近的地应力场均有不同程度的影响,能造成主应力方位和量值发生变化;这种变化主要限于断裂附近一定距离内,远离断裂,逐渐趋于与区域应力场一致;断层附近应力方位变化的幅度和发生变化的范围,是因断层的力学性质及几何形态等的不同而不同。认为断层的内摩擦角(φ)对断层附近应力方位变化的范围和幅度影响最大。

高速旋转薄壁圆柱壳的行波共振特性研究

基于传递矩阵法研究了不同边界条件下高速旋转薄壁圆柱壳的行波共振特性。首先,基于Love壳体理论,考虑离心力、科氏力和惯性力的影响,建立了旋转态薄壁圆柱壳的振动微分方程;然后,引入传递矩阵方法,根据壳体子段间的状态向量表达式,推导了结构的整体传递矩阵;最后,通过高精度的精细积分法进行求解,得到了两端简支、两端固支和固支-自由边界条件下的共振特性。算例结果表明,传递矩阵方法适合于求解高速旋转薄壁圆柱壳的行波共振特性,在三种边界条件下以周向模态的振动为主;在工作转速和1倍频激振力作用下,共振裕度小于10%的共振转速点仅有一个,而在其他倍频激振下的共振转速点不在安全裕值范围内。