Concentration of Mechanical Stresses near a Hole in a Piezoceramic Layer

A new procedure for solving three-dimensional mixed antisymmetric problems of elasticity theory for a layer weakened by through tunnel holes is proposed. The boundary-value problem is reduced to a system of one-dimensional singular integral equations consisting of 3k (k = 1, 2, ...) equations. The calculation results for characteristic stresses are presented.     

Mixed Antiplane Problem of Electroelasticity for a Piezoceramic Half-Space with a Tunnel Hole

Harmonic vibrations of a piezoceramic half-space weakened by a tunnel hole with a system of active surface electrodes are investigated. Based on integral representations for solutions to two types of conditions on the boundary of the half-space, the boundary-value problem of electroelasticity is reduced to a system of singular integrodifferential equations of the second kind. The results of parametric investigations characterizing the behavior of the electroelastic field components on the boundary and in the region of a piecewise-homogeneous half-space are presented.     

Antiplane Problem of Electroelasticity for a Hollow Piezoceramic Cylinder Excited by a System of Surface Electrodes

An antiplane mixed boundary-value problem of electroelasticity is considered for a hollow piezoceramic cylinder with an arbitrary system of active surface electrodes generating its harmonic vibrations. The problem is solved using a method elaborated earlier for investigating vibrations of a solid piezoceramic cylinder with a system of active surface electrodes. The scheme of numerical solution of the obtained singular integro-differential equations of the boundary-value problem is based on the quadrature method. Calculation results are presented that describe the amplitude-frequency characteristics of a hollow cylinder and the behavior of some mechanical and electric quantities both within the cylinder and on its boundary.     

Fundamental Solutions of Electroelasticity Equations for a Piezoceramic Layer in R3

Coupled electroelastic fields in a piezoceramic layer under the action of force and electric sources are determined analytically. The Fourier coefficients of the displacement and electric potential vectors and of the stress tensor are expressed in terms of the Macdonald cylindrical functions in a closed form. The solutions obtained can be used to consider the boundary-value problems of electroelasticity for a piezoceramic layer with tunnel heterogeneities.     

Excitation of Shear Waves in a Piezoceramic Medium with Two Tunnel Holes by a System of Surface Electrodes

An antiplane mixed dynamic problem of electroelasticity for an infinite piezoceramic medium weakened by two tunnel holes is considered. The conjugated fields are excited by the difference of electric potentials applied to a system of electrodes located on the surfaces of the holes. The boundary-value problem is reduced to a system of singular integrodifferential equations with discontinuous kernels, which is solved numerically by quadratures. The results of parametric investigations, characterizing the behavior of the electric field components on the boundary and in the region of the piecewise-homogeneous space, are presented.     

Lamb Problem for a Half-Space Covered with a Two-Axially Prestretched Layer

Within the framework of a piecewise homogeneous body model, with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies, an approach for investigating the Lamb problem for a half-space covered with a layer is developed. It is assumed that the half-space and the cover layer have two-axial initial stresses operating parallel to the layer plane. To the free face of the layer, a normal point force changing harmonically with time is applied. For solving the corresponding boundary value problems, the double-exponential Fourier transformation is employed. An algorithm for obtaining numerical results is proposed, which is examined in particular cases. Numerical results for the influence of prestretching the cover layer on the interfacial stresses are presented.     

多椭圆孔有限大复合材料层板的热弹性分析

本文利用各向异性体平面热传导，热弹性理论中的复势方法，以保角映射，Ｆａｂｅｒ级数展开以及最小二乘边界配置技术为工具，导出了内边界条件精确满足，外边界条件近似满足的多椭圆孔复合材料层板的热传导以及热弹性问题的级数解，详细探讨了层板大小，孔径，相对孔距，孔的设置方式，椭圆度以及层板的铺层比例诸参数的影响规律，得到了一些有益结论。     

Investigation of coupled physical fields in a compound piezoceramic wedge

A composition consisting of two infinite wedges fastened together along their common side is considered. The outer surfaces of the wedges are fixed and coated with grounded electrodes, and an ideal mechanical and electrical contact is assumed along the interface of both wedges. At certain relations of the geometric and stiffness parameters of the wedge components, the coupled electroelastic fields have a power-type singularity (intensified by oscillations) at the wedge vertex as a result of action of mechanical or electrical loads on the compound wedge. Such an effect is not observed in the case of piezopassive compound wedges (under antiplane strain conditions). The present study is dedicated to the investigation of this phenomenon. Closed-form solutions of some electroelastic boundary-value problems are constructed for the case of action of point shearing forces or electric charges.Sumskii State University, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 777–784, November–December, 1999.     

半线性方程ROBIN问题的角层解(英文)

本文讨论了一类半线性方程Robin边值问题.利用微分不等式理论,研究了边值问题角层解的存在性和渐近性态.     

First Boundary Value Problem of Electroelasticity for a Transversally Isotropic Plane with Curvilinear Cuts

The first boundary value problem of electroelasticity for a transversally isotropic plane with curvilinear cuts is investigated. The solvability of a system of singular integral equations is proved by using the potential method and the theory of singular integral equations.     

奇摄动向量问题的边界层和内层现象

本文考虑非线性向量边值问题:εy″=f(x,y,z,y',ε), y(0)=A₁ y(1)=B₁ εz″=f(x,y,z,z',ε), z(0)=A₂ z(1)=B₂其中ε是正的小参数,0≤x≤1,f,g是R4中的连续函数。在适当的假设下,利用微分不等式理论,我们证明了上述问题的解的存在性,并得到包括边界层和内层在内的解的估计.     

皮肤层蠕变分析的混合解法

本文利用积分变换方法求解皮肤层在表面压力作用下的蠕变响应问题。使用数值方法分别求解了双积分逆变换和由表面应力边界条件所得的第一类Ｖｏｌｔｅｒｒａ积分方程。计算所得的加载瞬时和平衡状态时的位移结果分别与不可压缩和可压缩单相弹性体的应移值相同，证明了本文方法的正确性。文中还给出了皮肤层在压力作用下的蠕变响应曲线。     

The Interior Layer Problem for the Strongly Nonlinear Singularly Perturbed System

The nonlinear strongly singularly perturbed systemεyi" = fi(t, y,y'), a < t < b, i = 1, 2, …, n, yi(a,ε)-pily'i(a,ε) = Ai, yi(b,ε) pi2y'i(b,ε) = Biare considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of interior solution for the problems are studied.     

具有转向点的一类奇摄动边值问题解的多重边界层现象

本文讨论如下边值问题：x=0是转向点（c（0）=0），而在x=－1处出现多重边界层现象．对不同层次采用不同的伸长变量，构造具有不同量级的边界层校正项，得到关于解的一致有效的渐近展开式和有关的余项估计．