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

As the first endeavor, a combination of fast Fourier transform and p-version of finite element method is proposed for electro-thermo-elastic analysis of a thick hollow cylinder under asymmetric thermal loadings. Especially in shells of revolution, the proposed FFT-pFE method is accompanied by a significant decrease in the computational costs. Due to the problem periodicity in such structures, the fast Fourier transform technique is used to discretize the governing equations into a set of harmonics in circumferential direction. Each harmonic is then partitioned using higher order finite elements. Hierarchical finite 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 a FGP hollow cylinder are then discretized by using the higher-order Lagrangian finite elements. The effects of FFT grid-size as well as the order of the interpolation functions are investigated on convergence behavior of the proposed mixed FFT-pFE method. The piezoelectric material properties, with the exception of the Poisson’s ratio, are considered to vary along the radius of the cylinder and pursue the power function. The governing equations are derived using the principle of virtual displacements. For a 3D FGP hollow cylinder, the influence of ...