THREE-DIMENSIONAL INTERACTIONS OF A HALF-PLANE CRACK IN A TRANSVERSELY ISOTROPIC PIEZOELECTRIC SPACE WITH RESULTANT SOURCES

Exact solutions in elementary functions are derived for the stress and electric displacement intensity factors of a half-plane crack in a transversely isotropic piezoelectric space interacting with various resultant sources, including force dipole, electric dipole, moment, force dilatation and rotation. Such force and charge sources may model defects like vacancies, foreign particles and dislocations. The locations and orientations of the stress and charge sources with respect to the crack are arbitrary.

EXACT SOLUTION TO THE PROBLEM OF A HALF-PLANE CRACK IN A TRANSVERSELY ISOTROPIC PIEZOELECTRIC BODY SUBJECTED TO ANTISYMMETRIC TANGENTIAL POINT FORCES

An exact and complete solution of the problem of a half-planecrack in an infinite transversely isotropic piezoelectric body ispresented. The upper and lower crack faces are assumed to be loadedantisym- metrically by a couple of tangential point forces inopposite directions. The solution is derived through a lim- itingprocedure from that of a penny-shaped crack. The expressions for theelectroelastic field are given in terms of elementary functions.Finally, the numerical results of the second and third mode stressintensity factors k_2 and k_3 of piezoelectric materials and elasticmaterials are compared in figures.

Numerical solutions for cracks in an elastic half-plane

The behavior of the stress intensity factor at the tips of cracks subjected to uniaxial tension σχ^∞= p with traction-free boundary condition in half-plane elasticity is investigated. The problem is formulated into singular integral equations with the distribution dislocation function as unknown. In the formulation, we make used of a modified complex potential. Based on the appropriate quadrature formulas together with a suitable choice of collocation points, the singular integral equations are reduced to a system of linear equations for the unknown coefficients. Numerical examples show that the values of the stress intensity factor are influenced by the distance from the cracks to the boundary of the half-plane and the configuration of the cracks.

The Boundary Contour Method for Half-Plane Piezoelectric Media

This paper presents a further development of the Boundary Contour Method (BCM) for half-plane piezoelectric media. Firstly, the divergence free property of the integrand of the half-plane piezoelectric boundary element is proven. Secondly, the boundary contour method formulation is derived and potential functions are obtained by introducing linear shape functions and Green's functions[1] for half-plane piezoelectric media. Finally, numerical solutions for illustrative example are compared with exact ones and that of conventional boundary element method (BEM) ones. The numerical results of BCM coincide very well with exact solution, and the feasibility and efficiency of the method are verified.

Determination of stress intensity factors in half-plane containing several moving cracks

The dynamic stress intensity factors in a half-plane weakened by several finite moving cracks are investigated by employing the Fourier complex transformation. Stress analysis is performed in a half-plane containing a single dislocation and without dislocation. An exact solution in a closed form to the stress fields and displacement is ob- tained. The Galilean transformation is used to transform between coordinates connected to the cracks. The stress components are of the Cauchy singular kind at the location of dislocation and the point of application of the the influence of crack length and crack running force. Numerical examples demonstrate velocity on the stress intensity factor.

Half-plane diffraction of Gaussian beams carrying two vortices of equal charges

This paper derives explicit expressions for the propagation of Gaussian beams carrying two vortices of equal charges m = ±1diffracted at a half-plane screen, which enables the study of the dynamic evolution of vortices in the diffraction field. It shows that there may be no vortices, a pair or several pairs of vortices of opposite charges m -=±, -1 in the diffraction field. Pair creation, annihilation and motion of vortices may appear upon propagation. The off-axis distance additionally affects the evolutionary behaviour. In the process the total topological charge is equal to zero, which is unequal to that of the vortex beam at the source plane. A comparison with the free-space propagation of two vortices of equal charges and a further extension are made.

A CLASS OF MIXED-TYPE FUNDAMENTAL PROBLEMS ON ELASTIC HALF-PLANE

The problems of equilibrium of an elastic half-plane with loads on some intervals of the boundary and zero displacements on its other parts are discussed. The solutions of such problems are expressed in terms of integrals by reducing them to Riemann boundary value problems. The analytic expressions of the solutions are obtained in cases of uniform loads. In particular, the solution is written in detail for the important case when uniform pressure is given on a single interval or two equal intervals.

An Elasticity Solution of a Nonhomogeneous Half-Plane Problem

We employ fundamental equations of non-homogeneous elasticity and Fourierintegral transformations to obtain the general solutions of the stress function.On thebasis of these points of view and when the forces on the boundary are arbityary for nonhomogeneous half-plane problems with the Young’s modulus E(x)-E_0θxp[βx].accurate solutions are obtained At last with the degeneracy it is obtained that thefamous Boussnesq solution and this method is successful.

Cracking in orthotropic half-plane with a functionally graded coating under anti-plane loading

This investigation evaluates, by the dislocation method, the dynamic stress intensity factors of cracked orthotropic half-plane and functionally graded material coating of a coating- substrate material due to the action of anti-plane traction on the crack surfaces. First, by using the complex Fourier transform, the dislocation problem can be solved and the stress fields are obtained with Cauchy singularity at the location of dislocation. The dislocation solution is utilized to derive integral equations for multiple interacting cracks in the orthotropic half-plane with functionally graded orthotropic coating. Several examples are solved and dynamic stress intensity factors are obtained.

ELASTODYNAMIC ANALYSIS OF A FUNCTIONALLY GRADED HALF-PLANE WITH MULTIPLE SUB-SURFACE CRACKS

The stress fields are obtained for a functionally graded half-plane containing a Volterra screw dislocation.The elastic shear modulus of the medium is considered to vary ex-ponentially.The dislocation solution is utilized to formulate integral equations for the half-plane weakened by multiple smooth cracks under anti-plane deformation.The integral equations are of Cauchy singular type at the location of dislocation which are solved numerically.Several examples are solved and the stress intensity factors are obtained.

Green’s functions for infinite planes and half-planes consisting of quasicrystal bi-materials

This paper deals with the combination of point phonon and phason forces applied in the interior of infinite planes and half-planes of 1D quasicrystal bi-materials. Based on the general solution of quasicrystals, a series of displacement functions are adopted to obtain Green's functions for infinite planes and bi-material planes composed of two half-planes in the closed form, when the two half-planes are supposed to be ideally bonded or to be in smooth contact. Since the physical quantities can be readily calculated without the need of performing any transform operations, Green's functions are very convenient to be used in the study of point defects and inhomogeneities in the quasicrystal materials.

考虑右半平面极点的三相并网变换器小干扰稳定性分析

电力电子设备渗透率的不断提高使得电力系统转动惯量和阻尼水平下降,对新型电力系统安全稳定运行带来不可忽略的影响。目前并网变换器系统判稳方法常采用奈奎斯特判据和广义奈奎斯特判据,但这两种判据均适用于阻抗比中不含右半平面(right half plane, RHP)极点的场景。针对上述问题,基于考虑正负序耦合和源荷之间耦合的等效单输入单输出(single-input single-output, SISO)系统阻抗模型,提出了考虑RHP极点的三相变换器并网系统判稳方法。首先,对研究系统的RHP极点个数及奈奎斯特曲线包围点(-1, j0)的次数进行估算。然后,在奈奎斯特判据的基础上,利用SISO系统阻抗伯德图进行分析,在系统存在RHP极点的情况下对系统的稳定性进行判断。最后,基于Matlab/Simulink中搭建电磁暂态仿真模型,验证了在有无RHP极点的不同场景下,所提判稳方法均能对三相变换器并网系统的小干扰稳定性进行有效分析。

半盘位自由测站测量方法测设平面监测基准网应用研究

由于运营铁路路基和桥梁段周围往往存在建筑物或树木等障碍物,通视条件较差,以致于采用在固定基准点上架设全站仪进行导线边角测量以建立平面监测基准网的方法,已不能很好地适应铁路变形监测的复杂环境。因此,本文提出采用半盘位自由测站测量方法建立平面监测基准网,并对没有直接测量的相邻后视基准点间的方位角中误差、测边中误差和相对点位中误差计算公式进行了推导,接着对其自由网平差与约束平差的结果进行精度统计分析,最后进行自由设站测量及精度评定以估算水平位移监测点的点位中误差。研究和实测结果表明,该方法可以达到二等水平位移监测基准网以及监测点点位中误差的精度要求,值得在涉铁项目平面监测基准网测量中推广应用。

基于模糊PID的Z源逆变器直流链升压电路控制

提出一种模糊PID补偿器用以直接控制Z源逆变器直流链电压最大值。控制至直流链电压最大值传递函数有一左(左半平面)一右(右半平面)2个零点,同时零、极点位置相近且靠近虚轴,具有严重的非最小相位现象。该文在详细的分析了控制至直流链电压最大值传递函数的基础上,针对Z源逆变器应用场合(燃料电池或光伏发电)中,输入电压大范围波动的特点,设计了具有良好非线性控制性能的模糊PID控制器。应用相平面响应轨迹特征向量法修正了模糊规则库,使系统具有良好的动态响应,同时用相平面法对闭环控制器进行了稳定性分析。该控制器能够实现直流链电压最大值的直接控制,消除了2个靠近极点的零点(1个右半平面和1个左半平面)造成的影响。减少了非最小相位系统阶跃响应的超调和负调。控制器设计简单,鲁棒性好,对输入电压扰动和负载电流变化具有良好的抗扰能力,动态、静态性能有了明显的改善。通过仿真和实验结果验证了理论分析的正确性。

层间应力影响下近距离煤层工作面合理错距留设问题研究

采用传统矿压、弹性半平面体理论及现场实测相结合的研究方法,考虑层间应力分布因素的影响,对近距离煤层联合开采条件下工作面合理错距的留设问题进行研究。研究得出:(1)由矿压理论计算得出工作面错距留设距离应满足的基本条件;(2)在理论计算或实测分析的煤层工作面支承压力影响范围的基础上,采用半平面体理论分析计算层间应力影响区范围,得到工作面错距修正值;(3)将工作面错距修正值与矿压理论计算值作类比,取其中数值较大并满足工作面错距留设基本条件的距离作为联采工作面的合理错距。以石圪节煤矿生产实际为背景,分析工作面合理错距的留设过程,最终选定该矿联采工作面合理错距值为55 m。在此错距条件下,工作面的安全、高效生产得到保证。

有耗平面和三维目标复合散射的FDTD分析

采用FDTD方法计算了有耗地面与三维目标的复合散射 ,对吸收边界条件 ,连接边界条件和近远场变换作了细致讨论。吸收边界使用了广义PML吸收层 ,它对电磁波有较好的吸收效果。连接边界处则利用解析入射波和三波迭加技术 ,上半平面用入射波和反射波、下半平面用透射波作为对目标的外加场进行计算。得到近场数据后 ,为避免出现复杂的Sommerfeld积分 ,用互易原理简化了外推过程。FDTD算法与矩量法和快速多层多极子相比 ,具有节省内存 ,计算时间短等优点。通过地上物体和地下物体的计算验证了FDTD方法的精确性 。

基于RHP零点限制的VSC-HVDC不同控制回路稳定性及交互作用机理分析

该文推导了电压源换流器型高压直流输电系统(voltage source converter based high voltage direct current,VSC-HVDC)在频域下的多输入–多输出传递函数矩阵模型,通过分析逆变及整流工作模式下VSC不同控制回路被控对象传递函数的右半平面(righthalfplane,RHP)零点分布规律,分析研究RHP零点对VSC不同控制回路自身稳定性的影响;在此基础之上,基于单通道分析设计方法,定量评估逆变及整流工作模式下VSC不同控制回路之间交互作用的强度,对比分析不同控制回路间交互作用对VSC-HVDC系统稳定性的影响;仿真结果验证了理论分析结论的正确性。

任意形状隧道围岩应力与位移的解析延拓求解

考虑隧道断面开挖轮廓线为任意不规则形状的情况,基于复变函数方法中的解析延拓法对弹性半无限空间内隧道的围岩应力与位移进行求解,建立了任意形状隧道围岩中任意一点处的应力值和位移值的隐式解析表达式.然后以圆形断面隧道、马蹄形断面隧道作为特例,同时考虑隧道衬砌等内支撑法向反力作用的影响,求解出弹性半空间内任意一点处的应力值和位移值解析解的具体显式表达式,其中假设隧道埋深与隧道直径之比较大,从而不用考虑重力梯度的影响,将重力简化为作用在边界上的均布外荷载.最后与已有的解析解与数值解进行比较,证明了该方法的准确性.该求解方法拓展了解析延拓法的应用,并能快捷地评估任意断面形状隧道开挖中的围岩应力状态及位移变形情况.

复变函数分析盾构隧道施工引起的地基变形

半无限空间中孔洞受均布位移作用下的问题已由Verruijt采用复变函数解答,而本文中给定椭圆化位移边界条件下的解答尚无文献报导。本文应用Verruijt的基本解法,采用共形映射方法,把含括一个圆形孔洞的半无限空间区域映射为圆环域。然后把这个区域内的解析函数展成Laurent级数的形式。利用Muskhelishvili的复变函数解法,求得隧道洞周给定位移条件下的应力场和位移场。分析了不同埋深、不同泊松比对位移场的影响、不同埋深对应力场的影响。最后分析了5个盾构隧道实测数据与4种不同位移边界条件解的对比情况。分析结果表明:笔者给出的第三、四边界条件的精确解对盾构隧道的设计有重要的实践意义。

半无限平面问题的相对位移

通过Flamant和Melan的解析解答、Mindlin解答的积分蜕化公式以及有限元数值分析计算结果,展示了在半无限平面问题中线荷载作用方向位移解答的不确定性。线荷载作用方向没有绝对位移,只有相对位移,但相对位移会随着与位移约束参考点距离的增大而增大,或随着线荷载在垂直于半平面方向分布长度的增大而增大,不具收敛性。这意味着,在解析和数值分析中,纯粹的半平面问题的位移解答具有多值性,因此,将岩土工程问题作为半空间问题进行分析是必要的。