Both multi-layer piezoelectric cantilevers and multi-layer piezoelectric composite cantilevers are studied based on 2D linear theory of elasticity and piezoelectricity. Both the piezoelectric coefficient and the thickness for different layers are taken as variables. As opposed to traditional investigations based on the elementary theory of elasticity, the present investigation gives exact solutions for the variation of these parameters by introducing several recurrence formulae. The solutions obtained in the present paper are compared with numerical results and the results obtained by other investigators; good agreement is found. (Some figures in this article are in colour only in the electronic version)

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.

Bending behaviors of both a piezoelectric curved bi-morph actuator and a functional gradient piezoelectric curved actuator are studied and compared. The exact solutions of both mechanical and electrical fields of the actuators are obtained based fully on the theory of elasticity. It is found that non-zero normal stresses exist in the gradient piezoelectric curved actuator when the actuator is subjected to an external voltage, which is different from the results obtained in our previous works on the gradient piezoelectric flat actuator. It is also proved that the internal stresses are drastically reduced although the deflection of the gradient curved actuator is quite small. The present analytical solutions are compared with the FEM results and a good agreement is found. (Some figures in this article are in colour only in the electronic version)

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.

Interfacial fatigue of reinforced concrete under tension fatigue loading is simulated based on the shear-lag model. The effects of degradation of concrete strength, the loading frequency and the stress ratio as well as corrosive environment on the interfacial fatigue are considered and discussed. It is found that: (1) degradation of concrete strength and corrosive environment result in opposite effects on interfacial fatigue. (2) Degradation of concrete strength will result in larger effects on interfacial damage in low stress ratio than that in high stress ratio. (3)With a decrease of loading frequency, interfacial corrosion damage will remarkably increase though loading frequency has a small effect on fatigue crack growth in inert media.