Three-dimensional analytical solutions for the axisymmetric bending of functionally graded annular plates

• 3D analytical solutions for the axisymmetric bending of annular plates of FG magneto- electro-elastic were found.
• A new method was established to find 3D analytical solutions for annular plates.
• An isoparametric element was developed to calculate the axisymmetric behavior of FG magneto-electro-elasticity.

Based on the three-dimensional theory, the axisymmetric bending behavior of functionally graded annular plates made of magneto-electro-elastic, piezoelectric and elastic materials respectively, was investigated. The transverse loads were expanded in terms of a Fourier–Bessel series and the solutions corresponding to each item of the series were found by the direct displacement method. Then the superposition principle was utilized to determine the mechanical, electric and magnetic quantities of the annular plates subjected to the arbitrary transverse pressures. It was found that four unusual boundary conditions can be rigorously satisfied at the inner and outer circumferential edges by this method. Meanwhile, the common boundary conditions such as simply supported, clamped and free boundary conditions were approximately satisfied using the Saint-Venant's principle. An innovative isoparametric element was also developed to calculate the axisymmetric behavior of the functionally graded magneto-electro-elasticity for comparison. Numerical examples were finally given to validate the present method.