The behavior of a rotating exponentially graded hybrid cylindrical shell subjected to an axisymmetric thermoelectromechanical loading and placed in a constant magnetic field is investigated. The hybrid shell consists of a functionally graded material host layer embedded with functionally graded piezoelectric material layers as sensors and/or actuators that are perfectly bonded to inner and outer surfaces of a shell. The shell is simply supported and could be rested on an elastic foundation. The material properties of functionally graded material and functionally graded piezoelectric material are assumed to be exponentially graded in the radial direction. To solve governing differential equations, the Fourier series expansion method through the longitudinal direction and the differential quadrature method across the thickness direction are used. Numerical examples are given to demonstrate the effects of material inhomogeneity, magnetic field, elastic foundation, thermal loading, and angular velocity on the response of the hybrid shell.

Static behavior of a functionally graded magnetoelectroelastic hollow sphere subjected to hygrothermal loading in the spherically symmetric state is studied. The sphere could be rested on a Winkler elastic foundation on the inner and/or outer surfaces. It is assumed that the material properties obey a power law in the radial direction. Considering the axisymmetric heat conduction and moisture diffusion equations, temperature and moisture concentration distributions within the radius of the sphere are achieved. The governing coupled differential equations are exactly solved. Numerical examples are discussed in detail to show the significant influences of inhomogeneity index, hygrothermal loading, elastic foundation and electromagnetic boundary conditions on the static behavior of a functionally graded magnetoelectroelastic hollow sphere.

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The piezoelectric phenomenon has been exploited in science and engineering for decades. Recent advances in smart structures technology have led to a resurgence of interest in piezoelectricity, and in particular, in the solution of fundamental boundary value problems. In this paper, we develop an analytic solution to the axisymmetric problem of a radially polarized, spherically isotropic piezoelectric hollow sphere. The sphere is subjected to uniform internal pressure, or uniform external pressure, or both and thermal gradient. There is a constant thermal difference between its inner and outer surfaces. An analytic solution to the governing equilibrium equations (a coupled system of second-order ordinary differential equations) is obtained. On application of the boundary conditions, the problem is reduced to solving a system of linear algebraic equations. Finally, the stress distributions in the sphere are obtained numerically for two piezoceramics.

The coupling nature of piezoelectric materials has acquired wide applications in electric-mechanical and electric devices. Recent advances in smart structures technology have led to a resurgence of interest in piezoelectricity, and in particular, in the solution of fundamental boundary value problems. In this paper, an analytic solution to the axisymmetric problem of a radially polarized, radially orthotropic piezoelectric hollow cylinder with thermal gradient is developed. An analytic solution to the governing equilibrium equations (a coupled system of second-order ordinary differential equations) is obtained. On application of the boundary conditions, the problem is reduced to solving a system of linear algebraic equations. The stress and potential field distributions in the cylinder are obtained numerically for two piezoceramics. It is shown that the hoop stresses in a cylinder composed of these materials can be decreased throughout the cross-section by applying an appropriate set of boundary conditions.