Exact solution of transient thermal stress problem of a multilayered magneto-electro-thermoelastic hollow sphere

This paper presents the theoretical analysis of a multilayered magneto-electro-thermoelastic hollow sphere under unsteady and uniform surface heating. We obtain the exact solution of the transient thermal stress problem of the multilayered magneto-electro-thermoelastic hollow sphere in the spherically symmetric state. As an illustration, we perform numerical calculations of a two-layered composite hollow sphere made of piezoelectric and magnetostrictive materials and investigate the numerical results for temperature change, displacement, stress, and electric and magnetic potential distributions in the transient state are shown in figures.     

Analytical solution for electromagnetothermoelastic behaviors of a functionally graded piezoelectric hollow cylinder

Analytical study for electromagnetothermoelastic behaviors of a hollow cylinder composed of functionally graded piezoelectric material (FGPM), placed in a uniform magnetic field, subjected to electric, thermal and mechanical loads are presented. For the case that the electric, magnetic, thermal and mechanical properties of the material obey an identical power law in the radial direction, exact solutions for electric displacement, stresses, electric potential and perturbation of magnetic field vector in the FGPM hollow cylinder are determined by using the infinitesimal theory of electromagnetothermoelasticity. Some useful discussions and numerical examples are presented to show the significant influence of material inhomogeneity, and adopting a certain value of the inhomogeneity parameter β and applying suitable electric, thermal and mechanical loads can optimize the FGPM hollow cylindrical structures. This will be of particular importance in modern engineering design.     

Two-dimensional solution for electro-mechanical behavior of functionally graded piezoelectric hollow cylinder

In this paper, the general theoretical analysis for a hollow cylinder made of functionally graded piezoelectric material subjected to two-dimensional electromechanical load, is developed. The material properties, except the Poisson’s ratio, are assumed to vary with the power law function through the thickness of the cylinder. The mechanical and electrical displacements are assumed to be a function of radial and circumferential directions. By using the separation of variables method and complex Fourier series, the Navier equations in terms of displacements are derived and solved.     

Analysis and numerical solution of a piezoelectric frictional contact problem

We consider a mathematical model which describes the frictional contact between an electro-elastic–visco-plastic body and a conductive foundation. The contact is modelled with normal compliance and a version of Coulomb’s law of dry friction, in which the stiffness and the friction coefficients depend on the electric potential. We derive a variational formulation of the problem and we prove an existence and uniqueness result. The proof is based on a recent existence and uniqueness result on history-dependent quasivariational inequalities obtained in [15]. Then we introduce a fully discrete scheme for solving the problem and, under certain solution regularity assumptions, we derive an optimal order error estimate. Finally, we present some numerical results in the study of a two-dimensional test problem which describes the process of contact in a microelectromechanical switch.     

Numerical solution of the propagation problem of longitudinal elastic waves in an orthotropic hollow cylinder

Wave processes in an orthotropic cylinder are analyzed. Harmonic oscillations are considered for which the original problem is reduced to a system of ordinary differential equations. This system is solved by the numerically stable discrete-orthogonalization method. Discrete curves for specific problems are given.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 75–78, 1985.     

Analytical solution in transient thermo‐elasticity of functionally graded thick hollow cylinders (Pseudo‐dynamic analysis)

This work studies transient thermal stresses in a thick hollow cylinder made of a functionally graded material (FGM). Material properties are considered to be nonlinear with a power law distribution through the thickness. The cylinder is assumed to be of infinite length, and the plane strain condition is supposed. The displacement and the distribution of stresses are obtained by analytical solution of governing differential equations of the Navier type. The transient dynamic behavior of thermal stresses is determined and discussed for various power law exponents appearing in functions determining mechanical properties of FGMs. Copyright © 2009 John Wiley & Sons, Ltd.     

Solvability of a dynamic contact problem between a piezoelectric body and a conductive foundation

We consider a mathematical model which describes the dynamic process of contact between a piezoelectric body and an electrically conductive foundation. We model the material’s behavior with a nonlinear electro-viscoelastic constitutive law; the contact is frictionless and is described with the normal compliance condition and a regularized electrical conductivity condition. We derive a variational formulation for the problem and then, under a smallness assumption on the data, we prove the existence of a unique weak solution to the model. We also investigate the behavior of the solution with respect the electric data on the contact surface and prove a continuous dependence result. Then, we introduce a fully discrete scheme, based on the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives. We treat the contact by using a penalized approach and a version of Newton’s method. We implement this scheme in a numerical code and, in order to verify its accuracy, we present numerical simulations in the study of two-dimensional test problems. These simulations provide a numerical validation of our continuous dependence result and illustrate the effects of the conductivity of the foundation, as well.     

Analytical solution of the quasi-static thermoelasticity problem in a pressurized thick-walled cylinder subjected to transient thermal loading

Thermoelasticity problem in a thick-walled cylinder is solved analytically using the finite Hankel transform. Time-dependent thermal boundary conditions are assumed to act on the inner surface of the cylinder. For the mechanical boundary conditions two different cases are assumed: Traction–displacement problem (traction is prescribed on the inner surface and the fixed displacement boundary condition on the outer one) and Traction–Traction problem (tractions are prescribed on both the inner and outer surfaces of the hollow cylinder). The quasi-static solution of the thermoelasticity problem is derived analytically, i.e., the transient thermal response of the cylinder is derived and then, quasi-static structural problem is solved and closed form relations are extracted for the thermal stresses in the two problems. The results show to be in accordance with that cited in the literature in the special cases.