Thermoelastic analysis of a thick walled cylinder made of functionally graded piezoelectricmaterial

Abstract

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