Magneto-electro-thermal bending of FG-graphene reinforced polymer doubly-curved shallow shells with piezoelectromagnetic faces

In this paper, an analytical treatment is developed for the magneto-electro-thermal bending of composite doubly-curved shallow shells reinforced by functionally graded graphene platelets (FGGPLs) surrounded by two piezoelectromagnetic (PEM) face sheets with various boundary conditions. According to new piece-wise mixture rules, four kinds of FGGPLs reinforced doubly-curved shells are considered. These shells are assumed to be exposed to thermal load, external electric voltage and magnetic potential. The material properties of FGGPLs multi-layered doubly-curved shallow shells are assumed to be varied in the shell thickness direction according to the suggested piece-wise distribution. Each layer of the composite shell is composed of polymer matrix reinforced with uniformly distributed graphene platelets. A four-variable shell theory is considered to describe the displacement field. In accordance with this theory, four equilibrium equations are derived from the virtual work principle. The governing equations are analytically solved to obtain the displacements, electric displacements, magnetic induction and stresses in the composite shells. A parametric study is presented to investigate the effects of the shell curvatures, boundary conditions, electric potential, magnetic potential, temperature rise and graphene platelets distribution type on the deflection, electric displacements, magnetic induction and stresses in FGGPLs reinforced laminated doubly-curved shells. It is found that the increment in the GPLs weight fraction and decrement in temperature increase the strength of the present structure.