Static Analysis of Functionally Graded Piezoelectric Beams under Thermo-Electro-Mechanical Loads

This paper presents the analysis of static bending of beams made of functionally graded piezoelectric materials (FGPMs) under a combined thermo-electro-mechanical load. The Euler Bernoulli theory (EBT), first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT) were employed to compare the accuracy and the reliability of each theory in applications. The material properties vary continuously through the thickness direction. The material compositions were selected from the PZT family. The governing equations were derived from Hamilton's principle and solved using the finite element method and Fourier series method. Cubic Hermit interpolation shape function was used for estimating the transverse deflection, and the linear interpolation function was used for the axial displacement and the shear rotation as well. Fourier series expansion, based on the boundary conditions, were employed to solve the governing equations analytically. The accuracy of the method was validated by comparing the results with the previous studies. Finite element results were compared with the analytical results presented in this paper. A comprehensive parametric study is conducted to show the influence of the voltage, shear deformation, material composition, end supports, and the slenderness ratio on the thermo-electro-mechanical characteristic.