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.

The interfacial behaviour of fibre-reinforced composites subjected to tension fatigue loading is studied based on the shear-lag model. The governing equations of this problem are obtained and solved. In order to describe the interfacial debonding, the Paris fatigue crack growth formula as well as a modified degradation model fo the coefficient of friction is adopted. Finally some important values related to interfacial debonding are obtained, In the present investigation, Poisson's contraction is considered

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.

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.

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.

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)

The bond decay at the bar–concrete interface under variable fatigue loads is investigated in this paper. Two kinds of loading paths are considered: low- and high-amplitude cycles. Based on the shear-lag model, the governing equations of the problem are established and solved with reference to three different interfacial degradation models. By the aid of Paris formula, the interfacial debonding rate, the debonded length, and the pull-out force are studied. The effect of the amplitude of the middle applied load and of several material parameters on bond decay is discussed. It is found that the power-degradation model is suitable for short embedment lengths, while both the linear-degradation model and the modified power-degradation model are advantageous in study of bond in long embedment length. It is also found that interfacial friction plays an important role in resisting interfacial debonding, in spite of the effects of Poisson's contraction.

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)

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.

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.