Porosity effect on the nonlinear deflection of functionally graded magneto-electro-elastic smart shells under combined loading

Abstract

This article presents a higher-order nonlinear finite element formulation to evaluate the nonlinear deformation of functionally graded magneto-electro-elastic porous (FG-MEEP) shells under the influence of electro-magnetic and mechanical loads. To derive the equations of motion, Donnell's shell theory with higher-order shear deformation theory and von-Karman's geometric nonlinearity is plugged into the principle of minimum potential energy. The credibility of the formulation is verified against published articles. The even or uneven distribution of porosity is implemented in the analysis. The coupled material properties are functionally graded according to modified power law. Two forms of material gradation such as ‘B’ rich bottom and ‘F’ rich bottom are considered. Several numerical examples are illustrated to demonstrate the influence of parameters such as shell geometry, porosity distribution, gradient index, porosity volume, functionally graded pattern, electro-magnetic loads on the nonlinear central deflection of FG-MEEP shells. Special attention has been paid to distinguish between the structural responses of FG-MEEP shells at fully coupled and uncoupled states.