Static behavior of functionally graded magneto-electro-elastic shells under electric displacement and magnetic flux

Three-dimensional (3D) static behavior of doubly curved functionally graded (FG) magneto-electro-elastic shells under the mechanical load, electric displacement and magnetic flux is studied by an asymptotic approach. Without loss of generality, the material properties of the shells are regarded as heterogeneous through the thickness coordinate. The edge boundary conditions are considered as the full simple supports. The basic equations of 3D magneto-electro-elasticity are firstly reduced to the state-space vector equations by means of direct elimination. By introducing a geometric perturbation parameter and following the regular asymptotic expansion, we finally decompose the 3D problem as recursive sets of two-dimensional (2D) problems with governing equations of the coupled classical shell theory (CCST). It is shown that the 3D solutions can be obtained by repeatedly solving the CCST-type equations order-by-order in view of the recursive property among various order problems. Parametric studies for both the coupling magneto-electro-elastic effect and the influence of the gradient index of material properties on the structural behavior of various FG shells under magneto-electro-mechanical loads are presented.