Thermoelastic analysis of a thick walled cylinder made of functionally graded piezoelectric material

In this paper, the thermopiezoelectric behavior of a thick walled cylinder with functionally graded materials is studied. The cylinder is loaded under the temperature gradient and inner and outer pressures. All the mechanical, thermal and piezoelectric properties except the Poisson ratio can be expressed as a power function in the radial direction. In the first step, with the solution of the heat transfer equation, a symmetric distribution of temperature is obtained. The stresses and electric displacement relations can be derived in terms of the temperature, electric field and strain. Substituting the resultant relations into the mechanical and electrical equilibrium equations yields the system of nonhomogeneous differential equations with two unknown variables (the mechanical displacement and the electrical potential). Solving the system of nonhomogeneous differential equations yields other mechanical and thermal terms such as the stress, displacement, electric field and electric displacement. The main result of the present study is that, by applying a proper distribution of mechanical and thermal properties in the functionally graded piezoelectric material (FGPM) solid structures, the distributions of stresses, electric potential and electric field in the FGPM can be controlled. Hence, the FGPM can be used in sensors or actuators.