Three-dimensional analysis of doubly curved functionally graded magneto-electro-elastic shells

Three-dimensional (3D) solutions for the static analysis of doubly curved functionally graded (FG) magneto-electro-elastic shells are presented by an asymptotic approach. In the present formulation, the twenty-nine basic equations are firstly reduced to ten differential equations in terms of ten primary variables of elastic, electric and magnetic fields. After performing through the mathematical manipulation of nondimensionalization, asymptotic expansion and successive integration, we finally obtain recurrent sets of two-dimensional (2D) governing equations for various order problems. These 2D governing equations are merely those derived in the classical shell theory (CST) based on the extended Love–Kirchhoffsʹ assumptions. Hence, the CST-type governing equations are derived as a first-order approximation to the 3D magneto-electro-elasticity. The leading-order solutions and higher-order corrections can be determined by treating the CST-type governing equations in a systematic and consistent way. The 3D solutions for the static analysis of doubly curved multilayered and FG magneto-electro-elastic shells are presented to demonstrate the performance of the present asymptotic formulation. The coupling magneto-electro-elastic effect on the structural behavior of the shells is studied.