The problem of a finitely long circular cylindrical shell of cylindrically orthotropic piezoelectric/piezomagnetic composite under pressuring loading and a uniform temperature change is analytically investigated in detail. The analytical solution is obtained through the power series expansion method and the Fourier series expansion method. Numerical results are presented and compared for two-layered piezoelectric/piezomagnetic composite circular cylindrical shells with different stacking sequences under inner pressuring loading.

In this paper we studied a finite crack in an infinite medium made of a functionally gradient piezoelectric material subjected to antiplane shear and inplane electric field. The material properties, including the elastic shear modulus, the piezoelectric modulus and the dielectric modulus are assumed to vary exponentially with spatial position. By means of Fourier transformation, the governing equations of the problem are firstly reduced to two pairs of dual integral equations and then to a Fredholm integral equation of second kind. The electroelastic fields are completely determined and the field intensity factors can be defined. It is found that the stress and the electric displacement have the inverse square-root singularity at the crack tip as that of homogeneous piezoelectric materials, and the stress intensity factor and the electric displacement intensity factor increase with the increase of the material gradient constant of functionally gradient piezoelectric materials.

In this paper, we give the elastic solution for a special type of microstructure-a circular cylindrical rod containing periodically distributed inclusions along its axial direction. Each inclusion has the same uniform axisymmetric transformation strain (eigenstrain). Analytical elastic solutions are obtained for the displacements, stresses and elastic strain energy of the rod. The effects of microstructure and its evolution (growth of inclusions) on the elastic stress and strain fields as well as the strain energy of the rod are quantitatively demonstrated. As a result of such microstructure evolution nominal stress-strain relation with strain softening is derived for a rod under uniaxial tension.

An exact three-dimensional analysis is presented for a functionally gradient piezoelectric material rectangular plate that is simply supported and grounded along its four edges. The state equations of the functionally gradient piezoelectric material are developed based on the state space approach. Assuming that the mechanical and electric properties of the material have the same exponent-law dependence on the thickness-coordinate, we obtain an exact threedimensional solution of the coupling electroelastic fields in the plate under mechanical, and electric loading on the upper and lower surfaces of the plate. The influences of the different functionally gradient material properties on the structural response of the plate to the mechanical and electric stimuli are then studied through examples.

A cylindrically anisotropic magnetoelectroelastic material is a special inhomogeneous anisotropic magnetoelectroelastic material. The constitutive law for any material point is the same when it is referred to a cylindrical coordinate system. An example of cylindrically anisotropic magnetoelectroelastic material is composite made of cylindrically anisotropic piezoelectric/piezomagnetic materials. In this paper an exact solution is derived for the two-dimensional problem of a circular tube or bar of cylindrically anisotropic magnetoelectroelastic material under pressuring loading by applying the Stroh formalism for a cylindrical coordinate system. The explicit expressions for the extended displacement vector and the extended traction vectors are presented. As encountered in the cases of elastic material and piezoelectric material, the stresses, electric fields, and magnetic fields at the axis of a circular rod may be infinite when the rod is subjected to a radial pressure. The existence of the singular stresses is also verified by our calculations for some magnetoelectroelastic materials.