A complete set of equations for piezo-magneto-elastic analysis of a functionally graded thick shell of revolution

Tensor analysis and an orthogonal curvilinear coordinate system have been used to derive a complete set of equations for piezo-magneto-elastic analysis of a functionally graded (FG) thick shell of revolution with variable thickness and curvature. The mentioned structure can be subjected to mechanical, electrical and magnetic fields. It was assumed that all material properties (mechanical, electrical and magnetic properties) change functionally throughout the three axis of employed coordinate system. Kinetic and potential energies of the system have been evaluated in order to constitute the functional of the system. Final partial differential equations of the system can be derived by using minimization of the energy functional with respect to five employed functions of the system. For validation, the obtained differential equations have been reduced to two previously studied problems i.e. functionally graded piezoelectric materials and functionally graded piezo-magnetic cylinders. Furthermore, numerical results are evaluated for a case study.