Hybrid integral transform and p-version FEM for thermo-mechanical analysis of a functionally graded piezoelectric hollow cylinder subjected to asymmetric loads

The value of this ingenious study is to be a pioneer in providing a combination of Fast Fourier Transform (FFT) and p-version of finite element method for the electrothermo- elastic analysis of a thick hollow cylinder under asymmetric thermal loadings. In shells of revolution, the proposed FFT-pFE method is accompanied by a signicant decrease in computational costs. Due to the problem periodicity of these types of structures, the FFT technique is used to discretize the governing equations into a set of harmonics. Each harmonic is then partitioned using higher-order nite elements. Hierarchical nite elements based on Legendre polynomial interpolation functions are utilized to discretize 2D governing equations of a Functionally Graded Piezoelectric (FGP) cylinder. 3D governing equations of an FGP hollow cylinder are then discretized by using the higher-order Lagrangian nite elements. The effects of FFT grid-size and the order of the interpolation functions on the convergence behavior of the proposed mixed FFT-pFE method are investigated. The material properties, except the Poisson's ratio, are considered to vary along the radius of the cylinder. The governing equations are derived using the principle of virtual displacements. For a 3D FGP hollow cylinder, the in uence of axially and circumferentially non-symmetric thermal loadings is presented in contour plots.