Haojiang Ding

The elastic and electric fields for three-dimensional contact for transversely isotropic piezoelectric materials

Firstly, the extended Boussinesq and Cerruti solutions for point forces and point charge acting on the surface of a transversely isotropic piezoelectric half-space are derived. Secondly, aiming at a series of common three-dimensional contact including spherical contact, a conical indentor and an upright circular flat punch on a transversely isotropic piezoelectric half-space, we solve for their elastic and electric fields in smooth and frictional cases by first evaluating the displacement functions and then differentiating. The displacement functions can be obtained by integrating the extended Boussinesq or Cerruti solutions in the contact region. Then, when only normal pressure is loaded, the stresses in the half-space of PZT-4 piezoelectric ceramic are compared in the figures with those of the transversely isotropic material which are assumed to have the same elastic constants as those of PZT-4. Meanwhile, the electric components in the half-space of PZT-4 piezoelectric ceramic are also shown in the same figures.

A general solution for piezothermoelasticity of transversely isotropic piezoelectric materials and its applications

In this paper, a general solution for dynamic piezothermoelastic problems of transversely isotropic piezoelectric materials is derived. The general solution reduces to solutions for quasi-static problems when inertia terms are disregarded. The present general solution is similar to that proposed by Ashida et al. in form. But, the derivation is more concise and rigorous without integration operation. Thus, it is more convenient for application. Applying this general solution, the static problem of a half-space subjected to axisymmetric heating and quasi-static problem of response of a rectangular plate are studied. Numerical results are presented.

Green's functions and boundary element method for transversely isotropic piezoelectric materials

This paper summarizes our work on Greens functions and boundary element method for transversely isotropic piezoelectric materials. These include the two-dimensional (2D) Greens functions of a two-phase infinite plane, from which the fundamental solutions of an infinite piezoelectric plane and an infinite half-pane can be easily derived, as well as their 3D counterparts. All the results are obtained in an exact and explicit way and hence are very convenient to be used in the associated computation with boundary element method. Numerical examples are also given.

Fundamental solutions for plane problem of piezoelectric materials

Based on the basic equations of two-dimensional, transversely isotropic, piezoelectric elasticity, a group of general solutions for body force problem is obtained. And by utilizing this group of general solutions and employing the body potential theory and the integral method, the closed-form solutions of displacements and electric potential for an infinite piezoelectric plane loaded by point forces and point charge are acquired. Therefore, the fundamental solutions, which are very important and useful in the boundary element method (BEM), are presented.

On exact analysis of free vibrations of embedded transversely isotropic cylindrical shells

Abstract This paper exactly studies the coupled free vibration of a transversely isotropic cylindrical shell embedded in an elastic medium. Response of the elastic medium is represented by Winkler/Pasternak models while the behavior of the cylindrical shell is analyzed based on the three dimensional elasticity. Three displacement functions are chosen to represent three displacement components to decouple the three-dimensional equations of motion of a transversely isotropic body. After expanding these functions with orthogonal series, the coupled free vibration problem of an embedded transversely isotropic shell with ends simply-supported can be readily dealt with. In particular, Bessel function solution which includes complex arguments is directly used for the case of complex eigenvalues. Numerical examples are presented and compared to the results of existent papers.

On the equilibrium of piezoelectric bodies of revolution

By means of the three-dimensional general solution in displacement functions (weighted harmonic functions) for piezoelectric materials, the general solution of stress components and electric displacements expressed by the displacement functions is derived by use of the constitutive relation and the equilibrium equations. Based on this general solution, a series of problems is solved by the trial-and-error method, including circular plate (or cylinder), annular plate (or hollow cylinder), cone and hollow cone. These problems are circular plates and cylinders under uniform radial or axial tension and electric displacements as well as pure bending, simply-supported circular plates subjected to uniformly distributed loads, rotating disks and circular shafts, cones or hollow cones subjected to concentrated forces plus charge and concentrated force couple at their apex, etc. Analytical solutions to various problems are obtained. When the cone apex angle 2α equals π, the solutions for the cases of concentrated forces plus point charges and torsion reduce to the simple and practical solutions of the half-space problem.

Analytical Modeling of Sandwich Beam for Piezoelectric Bender Elements

Piezoelectric bender elements are widely used as electromechanical sensors and actuators. An analytical sandwich beam model for piezoelectric bender elements was developed based on the first-order shear deformation theory (FSDT), which assumes a single rotation angle for the whole cross-section and a quadratic distribution function for coupled electric potential in piezoelectric layers, and corrects the effect of transverse shear strain on the electric displacement integration. Free vibration analysis of simply-supported bender elements was carried out and the numerical results showed that, solutions of the present model for various thickness-to-length ratios are compared well with the exact two-dimensional solutions, which presents an efficient and accurate model for analyzing dynamic electromechanical responses of bender elements.

Green's functions for a piezoelectric half plane

A general solution which can be expressed by three “harmonic functions” is derived. Then using this general solution as well as the trial-and-error method, the Greens functions for point forces and point charge acting in the interior of a piezoelectric half plane are obtained. The point force solutions of an infinite piezoelectric plane can be derived as a special case of the results presented in this paper.

Mechanical behavior of a fiber end in short fiber reinforced composites

Stress singularities, displacement and singular stress fields near a fiber end in short fiber reinforced composites are analyzed based on the isotropic elastic theory of the spatial axisymmetric problem. The singular problem of the fiber end can be divided into two fundamental models. The results obtained by this paper show that the stress singularities near the fiber end coincide with those of the corresponding models in the plane strain problem. The dependence of the singular stress fields on the material properties can be described by three composite parameters of the fiber and matrix materials. The results may be significant in the stress analysis of composites and can be used to discuss the appropriateness of the approximating fiber end to the plane strain state.

Analytical solutions for axisymmetric bending of functionally graded piezoelectric annular plates

The bending of piezoelectric annular plates is the classic problem in theory of piezoelectric elasticity. The solution of axisymmetric bending of FGPM annular plates subject to arbitrarily transverse loads is not available in the literatures though some solutions for special loads have been derived. For this purpose, this paper analytically studies the axisymmetric bending of functionally graded piezoelectric annular plates subjected to arbitrary transverse loads. Based on the three-dimensional theory of piezoelectricity, this work derives analytical solutions for the axisymmetric bending of piezoelectric annular plates. The transverse loads are expanded in terms of the Fourier-Bessel series, and the solutions corresponding to each item of the series are obtained by the semi-inverse method. The total solutions are then obtained through the superposition principle. The present solutions rigorously satisfies the governing equations when the material properties obey the exponential law along the thickness of the plates. The boundary conditions on the top and bottom surfaces are completely satisfied while the boundary conditions at the circumferential edges are approximately satisfied based on Saint-Venants principle.