Non-axisymmetrical element for functionally graded piezoeletric structure of axial symmetry

Summary form only given. Many axisymmetric structures in engineering subjected to non-axisymmetric loads cannot be treated as an axisymmetric problem. However, they can be solved through a series of two-dimensional problem by expanding the load in terms of Fourier series in the circumferential direction based on the geometric symmetric of the structures. This work presents a harmonic element for transversely isotropic functionally graded piezoelectric structure of the axial symmetry. Finally, the whole FEM code the whole FEM code is implemented using MATLAB and some numerical examples including static and dynamic cases are given to demonstrate the proposed element and the results are compared with those from AYSYS.