Axisymmetrical Analysis of Functionally Graded Circular Piezoelectric Plate by Graded Element Using MATLAB

Circular piezoelectric bimorph has been successfully used in numerous types of microdevices, such as actuators for flowcontrol applications, transducers for acoustic applications, and in locomotion of robotic systems, energy harvesting and active structural health monitoring applications. Recently, the concept of the functionally graded material (FGM) is introduced to improve properties and increase lifetime by selectively grading the elastic, piezoelectric, and/or dielectric properties along the thickness of a piezoceramic. However, even for the simple case of homogeneous circular piezoelectric geometry, analytical treatments are severely limited. This study established an axisymmetric and isoparametric graded element to model the functionally graded circular piezoelectric plates. All the material properties including elastic coefficients, piezoelectric coefficients, dielectric parameters and mass density are graded in the element and interpolated using the shape functions, which is also used to render the displacements and electric potential distribution in the element. Both static and dynamic cases can be considered in this element. MATLAB is used to implement the whole FEM code and gives some numerical examples to demonstrate the presented method.