Summary In the present paper, the problem of a functionally graded piezoelectric cantilever beam subjected to different loadings is studied. The piezoelectric beam is characterized by continuously graded properties for one elastic parameter and the material density. A pair of stress and induction functions in the form of polynomials is proposed and determined. Based on these functions, a set of analytical solutions for the beam subjected to different loadings is obtained. As particular cases, series of solutions for some canonical problems can be directly obtained from the solutions of the present paper, such as for the problems of a piezoelectric cantilever beam with constant body force or without body forces, etc.

Two different kinds of heterogeneous elastic hollow cylinders are studied herein. One is a cylinder with multi-layers and another is a cylinder with continuously graded properties. A simple and convenient method is obtained to find the exact solutions of a N-layered elastic hollow cylinder submitted to uniform pressures on the inner and outer surfaces. For the hollow cylinder with continuously graded properties, the displacement method is used. A hyper-geometric equation is derived and solved, and then the exact solutions are found. The results obtained in the present paper are compared with both the numerical solutions and other findings provided by some references and good agreements are found. At the end of the present paper, some inherent properties of these two different kinds of heterogeneous graded hollow cylinders are presented and discussed.

Micromechanical damage of fiber/matrix interface under cyclic loading is simulated. The effects of loading conditions and shear deformation of matrix on interfacial debonding are considered and discussed. It is found that: (1) the force of interfacial fraction plays an important role in resisting interfacial debonding; (2) no matter what kind of the commonly considered loading conditions is, interfacial debonding always undergoes three stages though the damage degree is not the same; (3) the shear deformation of matrix has the ability to slow down the interfacial debonding rate.

We have used the plane strain theory of transversely isotropic bodies to study a piezoelectric cantilever. In order to find the general solution of a density functionally gradient piezoelectric cantilever, we have used the inverse method (i.e. the Airy stress function method). We have obtained the stress and induction functions in the form of polynomials as well as the general solution of the beam. Based on this general solution, we have deduced the solutions of the cantilever under different loading conditions. Furthermore, as applications of this general solution in engineering, we have studied the tip deflection and blocking force of a piezoelectric cantilever actuator. Finally, we have addressed a method to determine the density distribution profile for a given piezoelectric material.

Based on the general theory of elasticity, the static behavior of 2-2 multi-layered piezoelectric curved composites is investigated. The exact solutions of the mechanical and electrical fields of the curved composites are obtained by utilizing Airy stress function method. Both the piezoelectric coefficient and the thickness for different layers are taken as variables. Different from other investigations based on the elementary theory of elasticity, the present investigation gives exact solutions for these variables by introducing several recurrence formulas, which make the present results very useful. The theoretical results obtained in the present paper are compared with the numerical results and good agreements are found.