Semi-analytical three-dimensional solutions for static behavior of arbitrary functionally graded multilayered magneto-electro-elastic shells

In this paper, a three-dimensional (3D) solution of static behavior of simply supported doubly curved functionally graded multilayered (FGM) magneto-electro-elastic shells subjected to mechanical, electric displacement, magnetic flux, electric potential and magnetic potential loads is presented. A coupling procedure based on the state space and the Runge-Kutta methods is elaborated for the 3D magneto-electro-elastic governing equations. An efficient semi-analytical approach is resulted for arbitrary functionally graded shells in thickness direction. The proposed mathematical modeling has been validated by several numerical tests. The obtained results are in good agreement with the available ones given by the three-dimensional asymptotic approach, the state space approach and a meshless collocation method. It has been revealed that, the loading conditions, the materials properties gradient index, the span-to-thickness ratio and the radius-to-thickness ratio remarkably influence the static response of FGM shells.