An orthotropic piezoelectric ellipsoid in a centrifugal field

A rotating ellipsoid composed of an orthotropic piezoelectric material (2mm) are considered, and the stress and electric displacement fields in this rotating ellipsoid are obtained exactly and completely. The solutions of the same problem for transversely isotropic piezoelectric material (6 mm) are also given by degenerating above results. At last, numerical examples for four kinds of media are illustrated in figures for comparison. Supported by the National Natural Science Foundation of China (No. 19872060).     

Indentation of a transversely isotropic piezoelectric half-space by a rigid sphere

This paper exactly analyzes the problem of a rigid sphere indenting a transversely isotropic piezoelectric half-space. The potential theory method is employed and generalized to include the piezoelectric effect. By using the previous results of elasticity, an exact solution is derived. It is found that all the elastoelectric variables can be expressed in terms of elementary functions. The work was partly supported by the National Natural Science Foundation of China (No. 19872060).     

用“调和函数”表示的压电介质平面问题的通解

本文首先从压电介质平面问题基本方程出发，引入一个位移函数，导出其通解，然后利用推广的Almansi定理，将通解化为简单形式，即通过三个“调和函数”来表示所有的物理量，其次，推导了楔形体顶端受集中力和点电荷作用时有限形式的解，退化可得半无限平面直线边界受集中力和点电荷的解。     

Exact solutions for free vibration of transversely isotropic piezoelectric circular plates

By employing the general solution for coupled three-dimensional equations of a transversely isotropic piezoelectric body, this paper investigates the free vibration of a circular plate made of piezoelectric material. Three-dimensional exact solutions are then obtained under two specified boundary conditions, which can be used for both axisymmetric and non-axisymmetric cases. Numerical results are finally presented. The project supported by the National Natural Science Foundation of China (No. 19872060)     

Axisymmetric bending of functionally graded circular magneto-electro-elastic plates

Axisymmetric bending of functionally graded circular magneto-electro-elastic plates of transversely isotropic materials is analyzed based on linear three-dimensional theory of elasticity coupled with magnetic and electric fields. The transverse loads are expanded in Fourier-Bessel series and therefore can be arbitrarily distributed along the radial direction. The radial distributions of the displacements are assumed in combination of Fourier-Bessel series and polynomials as well as the electric potential and magnetic potential. If the material properties obey the exponential law along the thickness of the plate, two three-dimensional exact solutions for two unusual boundary conditions can be derived since they satisfy the governing equations and specified boundary conditions point by point. For simply supported or clamped boundary, the obtained solutions satisfy the governing equations exactly and the boundary conditions approximately. A layer wise model is also introduced to treat with the plates whose material property components vary independently and arbitrarily along the thickness of the plates. The numerical results are finally tabulated and plotted to demonstrate the presented method and agree well with those from finite element methods.     

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

I. INTRODUCTIONBecause of the widespread application and intrinsic brittleness of piezoelectric ceramics, significantattention is being paid to the crack problems of piezoelectric ceramics. The last decade has seen a lotof three-dimensional studies of crack in piezoelectric ceramics[1??9]. In addition, the electroelastic fieldin a transversely isotropic piezoelectric space with a half-plane crack subjected to symmetric normalpoint forces, antisymmetric tangential point forces and point ch…     

The method of weighted residuals for transversely isotropic axisymmetric problems and its applications to engineering

A method with two harmonic functions is proposed for solving transversely isotropic axisymmetric problems by applying the theorems of Refs. [1] and [5]. A series of simple formulas of the boundary least square collocation method is derived. Two engineering examples show that the present method is much more convenient than Lekhniskii's with biharmonic functions. Some useful conclusions are finally obtained.     

GENERAL SOLUTION OF PLANE PROBLEM OF PIEZOELECTRIC MEDIA EXPRESSED BY “HARMONIC FUNCTIONS”

First, based on the basic equations of two-dimensional piezoelectroelasticity, a displacement function is introduced and the general solution is then derived. Utilizing the generalized Almansi's theorem, the general solution is so simplified that all physical quantities can be expressed by three harmonic functions. Second, solutions of problems of a wedge loaded by point forces and point charge at the apex are also obtained in the paper. These solutions can be degenerated to those of problems of point forces and point charge acting on the line boundary of a piezoelectric half-plane.Project supported by the National Natural Science Foundation of China     

Elasticity solutions of spherically isotropic cones under concentrated loads at apex

Based on the Ref. [9], the displacement and stress distributions in a spherically isotropic cone subjected to concentrated loads at apex are studied. The displacement and stresses are given explicily for the cone in compression torsion and bending cases, respectively, based on the situation of the concentrated forces and moments. Finally, the hollow cone problems are discussed. Project supported by National Natural Science Foundation of China     

The curved bar subjected to an arbitrarily distributed loading: Another paradox in the two-dimensional theory of elasticity

The problem of the curved bar subjected to an arbitrarily distributed loading on the surfacesr=a andr=b is solved by using the method of complex functions and expanding the boundary conditions atr=a andr=b into Fourier series. Then another paradox in the two-dimensional theory of elasticity is discovered, i. e., the classical solution becomes infinite when the curved bar is subjected to a uniform loading or when the angle included between the two ends of the curved bar 2 is equal to 2 and the curved bar is subjected to a sine or cosine loading. In this paper the paradox is resolved successfully and the solutions for the paradox are obtained. Moreover, the modified classical solution which remains bounded as 2 approaches 2 is provided.