Nonstationary axisymmetric electroelasticity problem for an anisotropic piezoceramic radially polarized cylinder

We consider an axisymmetric nonstationary electroelasticity problem for an anisotropic piezoceramic radially polarized cylinder of finite size whose lateral surface is subjected to an electric voltage that is an arbitrary function of the axial coordinate and time. A new closed-form solution is constructed by the vector eigenfunction expansion method in the form of a structural finite transform algorithm. This solution permits determining the natural vibration frequencies, the stress-strain state of an element, and the electric field potential and intensity. The results permit analyzing and optimizing the operation of inverse piezoelectric effect devices with cylindrical transducers.     

On one skew-symmetric problem of electroelasticity for inhomogeneous cylinder of finite length

In the present paper, static bending problem of the electroelasticity for an inhomogeneous cylinder of finite length with sliding fixed end-supports is investigated. The given boundary value problem is reduced to a system of 12 k (k = 1, 2, …) integro-differential equations. Expressions for the components characterizing the state of stress for the inhomogeneous cylinder are presented. Based on the developed analytical algorithm, extensive numerical investigations associated with the stress analysis of an inhomogeneous piezoceramic cylinder have been conducted. The results of these investigations are illustrated graphically, demonstrating the stress distributions in piezoceramic circular and elliptical cylinders with inclusions of various geometries.     

An elasticity solution for axisymmetric problem of finite circular cylinder

In this paper,the complete double-series in the closed region expressing the double-variable functions and their partial derivatives are derived by the H-transformation and Stockes’transformation.Using the double-series,a series solution for the axisymmetric boundary value problem of the elastic circular cylinder with finite length is presented.In a numerical example,the cylinder subjected to the axisymmetric tra(?)s with various loaded regions is investigated and the distributions of the displacements and stresses are obtained.It is possible to solve the axisymmetric boundary value problems in the cylinderical coordinates for other scientific fields by use of the method presented in this paper.     

Dynamic axisymmetric problem of the direct piezoeffect for a radially polarized anisotropic piezoceramic cylinder

An unsteady problem of electroelasticity for a long radially polarized anisotropic piezoceramic cylinder with normal stresses that are arbitrary functions of time applied to the radial surfaces is considered. A closed solution is constructed by the method of expansion with respect to eigen vector-functions. This solution allows determining the frequencies of natural oscillations, the stress-strain state of the element, and the potential and intensity of the induced electric field.     

The axisymmetric problem of the theory of elasticity for a thick-walled cylinder of finite length

International Applied Mechanics -     

Thermoelastic axisymmetric problem for a two-layer cylinder

The majority of devices and units of microelectronics are multilayer structures made of materials with differing coefficients of thermal expansion and elastic constants. Thermal stresses which arise in such systems due to temperature changes when manufactured or in operation may result in a breakdown, or plastic deformation or in a change of the physical properties of materials. At the same time, due to adopted assumptions the existing design models do not describe the stressed states in real systems of finite dimensions. The designs in [1–3] are obtained on the basis of the engineering theory of beams, and in [4, 5] the obtained solution was for the infinite strip in a half-space. In the present article a right circular cylinder of radius R was used as a mathematical model which was cut by the plane z = 0 into two layers of thickness H or H* (Fig. 1). In our considerations the quantities referring to the layer 2 are distinguished by an asterisk. The cylinder deformation problem due to the temperature lowering from t₁ to T₂ was solved within the framework of the linear theory of thermoelasticity. It was assumed that the material of each layer is homogeneous and isotropic, that the temperature is independent of the coordinates, and that the coefficients of thermal expansion and * are independent of T. Two formulations are analyzed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 132–138, January–February, 1978.     

Saint-Venant's problem for inhomogeneous and anisotropic elastic bodies

A method of solving Saint-Venant's problem for inhomogeneous and anisotropic elastic bodies is presented.     

Regular integral equations for the second boundary-value problem of the bending of an anisotropic elastic plate

Two systems of Fredholm equations of the second kind are constructed for the solution of the second boundary-value problem of the bending of an anisotropic plate (a normal bending moment and a generalized shear force are specified on the boundary of the simply-connected domain) under the assumption of validity of the Kirchhoff-Love hypotheses. Correct equilibrium conditions are specified for the examined boundary-value problem. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 108–119, May–June, 2005.     

On an inverse problem for inhomogeneous thermoelastic rod

In recent years, different fields of engineering have been increasingly incorporating functionally graded materials with variable physical properties that significantly improve a quality of elements of designs. The efficiency of practical application of thermoelastic inhomogeneous materials depends on knowledge of exact laws of heterogeneity, and to define them it is necessary to solve coefficient inverse problems of thermoelasticity.In the present research a scheme of solving the inverse problem for an inhomogeneous thermoelastic rod is presented. Two statements of the inverse problem are considered: in the Laplace transform space and in the actual space. The direct problem solving is reduced to a system of the Fredholm integral equations of the 2nd kind in the Laplace transform space and an inversion of the solutions obtained on the basis of the theory of residues. The inverse problem solving is reduced to an iterative procedure, at its each step it is necessary to solve the Fredholm integral equation of the 1st kind; to solve it the Tikhonov method is used. Specific examples of a reconstruction of variable characteristics required are given.     

Some axisymmetric problems for an elastic inhomogeneous thick-walled tube

An equilibrium differential equation for an axisymmetric problem is reduced to an integrable form under the assumption that the shear modulus is continuously differentiable and Poisson’s ratio is constant. A procedure of successive approximations is proposed for the case of a compressible material, and the Lamé problem is solved exactly for the case of an incompressible material. A piecewise continuous variation of the Lamé parameter as a function of radius is considered. Several examples of determining the stress-tensor components are given for various cases of inhomogeneity.