Electro elastic analysis of a pressurized thick-walled functionally graded piezoelectric cylinder using the first order shear deformation theory and energy method

Shear deformation theory is employed for electro elastic analysis of a functionally graded piezoelectric cylinder as a physical sensor for estimation and controlling the internal pressure. Except Poisson ratio, all mechanical and electrical properties are graded along the radial coordinate system. The present paper develops the previous study using the shear deformation theory as a capable and advantageous theory instead of plane elasticity theory. Two radial and axial deformations are simulated using the first order shear deformation theory. Electric potential is supposed as a quadratic function along the thickness direction and as an unknown function along the longitudinal direction. Comparison between the present results at the regions that are adequate far from two ends of the cylinder with the results of plane elasticity theory justifies accuracy and capability of the present method. Some useful graphical and numerical results are presented in this study. The discussed problem in this paper has many advantageous properties and application in measurement and controlling of the mechanical and electrical components because of using the functionally graded materials instead of an isotropic material.