An antisymmetric problem of a penny-shaped crack in a piezoelectric medium

Summary  An exact, three-dimensional analysis is developed for a penny-shaped crack in an infinite transversely isotropic piezoelectric medium. The crack is assumed to be parallel to the plane of isotropy, with its faces subjected to a couple of concentrated normal forces and a couple of point electric charges that are antisymmetric with respect to the crack plane. The fundamental solution of a concentrated force and a point charge acting on the surface of a piezoelectric half-space is employed to derive the integral equations for the general boundary value problem. For the above antisymmetric crack problem, complete expressions for the elastoelectric field are obtained. A numerical calculation is finally performed to show the piezoelectric effect in piezoelectric materials. It is noted here that the present analysis is an extension of Fabrikant's theory for elasticity. Received 30 August 1999; accepted for publication 1 March 2000     

Inclined circular flat punch on a transversely isotropic piezoelectric half-space

Summary Utilizing the general solution of transversely isotropic piezoelectricity, the paper analyzes the problem of an inclined rigid circular flat punch indenting a transversely isotropic piezoelectric half-space. The potential theory method is employed and generalized to take into account the effect of the electric field in piezoelectric materials. Assuming that the punch is maintained at a constant electric potential, exact expressions for the elastoelectric field are derived in terms of elementary functions. It is noted that the solution corresponding to a flat circular punch centrally loaded by a concentrated force can be obtained as a special case. Received 15 December 1998; accepted for publication 9 March 1999     

Nonlinear inversion of strong scatterer of elastic wave for two parameters in half-space

The inversion of strong scatterer embedded in the half-space is an important problem in engineering and a very difficult nonlinear problem in mathematics, for which the Born iterative method is of no effect. In this paper the moment method is used in the discretization procedure. A numerical approach is presented by employing the regularization technique and DBI (distorted Born iterative) method. The simulation results show that the approach presented is efficient. Project supported by the Research Fund for the Doctoral Program of Higher Education (RFDP: 98048705).     

THE ELASTIC FIELD INDUCED BY A HEMISPHERICAL INCLUSION IN THE HALF—SPACE

The elastic field induced by a hemispherical inclusion with uniform eigeustralns in asemi-infinite elastic medium is solved by using the Green‘s function method and series expansion tech-nique. The exact solutions axe presented for the displacement and stress fields which can be expressedby complete elliptic integrals of the first, second, and third kinds and hypergeometric functions. Thepresent method can be used to determine the corresponding elastic fields when the shape of the inclusionis a spherical crown or a spherical segment. Finally, numerical results axe given for the displacementand stress fields along the axis of symmetry (x3-axis).     

弹性半空间二维出平面自由波场的一维化时域算法

提出了一种计算出平面SH波斜入射时弹性半空间自由波场时域计算的一维化有限元方法。首先利用Snell定律确定平面波沿水平方向的传播规律,在用有限元法对弹性半空间进行离散化时,竖向单元尺寸根据波动有限元模拟精度要求确定,而水平向有限元网格尺寸根据水平向波的传播规律和采用的离散时间步长确定,使得有限元离散模型中任意节点的运动可以用水平向相邻节点的运动表示,从而将二维有限元节点运动方程组化为一维的形式。求解此一维方程组,可得到弹性半空间中一列节点的运动,再根据行波的传播规律,可确定全空间自由波场。理论分析和数值算例表明,该方法具有较高的精度和良好的稳定性。     

Plasma in a high-frequency electric field with a reflective condition on the boundary

An analytical solution is obtained for the linearized problem of the behavior of a collisional gas plasma in a half-space in an external alternating electric field. It is assumed that the electrons are mirror-reflected from the plasma boundary. The solution is used for finding the screened field. The case of an external field frequency close to the plasma frequency is investigated separately.     

Dynamic analysis of interacting coplanar cracks in a half space with a clamped boundary condition using boundary integral equations

The three-dimensional dynamic problem of coplanar circular cracks in an elastic half-space with a clamped boundary condition is considered. The crack faces are subjected to harmonic loads. The problem is reduced to a system of two-dimensional boundary integral equations of the type of the Helmholtz potential for unknown discontinuities in the displacements of the opposite faces of the cracks. The stress intensity factors at the crack contours are obtained and discussed.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 153–159, January–February, 2005     

3-D DYNAMIC RESPONSE OF TRANSVERSELY ISOTROPIC SATURATED SOILS

Introduction Thedynamicanalysisofsaturatedporoelasticmediaisofbroadmeaninginmanyaspectssuchasseismology,earthquakeengineering,soilmechanicsandgeophysics,etc.Thetransverselyisotropicsaturatedsoilsissolid fluidcoupledtwophasemediainwhichthe soilskeletondisp…     

高速移动荷载下黏弹性半空间体的动力响应

分别以移动荷载和黏弹性半空间体模拟运动列车荷载和地基,分析了地基在运动列车作用下的动力响应.首先采用Green函数法求解黏弹性半空间体在各种移动荷载模式作用下的动力响应的解析解,包括恒常和简谐移动点源、线源和面源荷载.然后采用IFFT算法和自适应数值积分算法计算解析解中的二维积分,得到了包括低音速、跨音速和超音速移动荷载作用下位移的数值结果.最后分析了速度对位移的分布和最大值的影响,发现当速度大于Rayleigh波速时,位移发生显著变化.     

Contact interaction of an elastic punch and an elastic half-space with initial (residual) stresses

The contact interaction of an elastic punch of arbitrary cross-section and an elastic semi-space with initial (residual) stresses is studied. A general method to solve the problem is proposed. It allows solving contact problems for bodies with initial (residual) stresses when the solution of the corresponding elastic problem is known __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 28–40, December 2007.