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

Abstract

Tensor analysis and an orthogonal curvilinear coordinate system have been used to derive a complete set of equations for piezomagneto-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 piezomagnetic cylinders. Furthermore, numerical results are evaluated for a case study.

Influence of magneto-electric environments on size-dependent bending results of three-layer piezomagnetic curved nanobeam based on sinusoidal shear deformation theory

“…The piezomagnetic face-sheets are subjected to electric and magnetic potentials. The constitutive relations for piezomagnetic face-sheets are defined as [6, 15, 19] in which Cijkl p are stiffness coefficients of elastic core. In addition, eijk p are the piezoelectric coefficients, qijk p are piezomagnetic coefficients, Ei and Hi are the components of electric and magnetic fields, respectively defined as [15–19] …”

“…The electric and magnetic fields are assumed as a combination of a cosine function along the thickness direction and an unknown function along the circumferential direction θ [15–19] in which ψ0,φ0 are applied electric and magnetic potentials, ρ=ζ±he2±hp2 for the top and bottom piezomagnetic face-sheets. Substitution of electric and magnetic potentials from equation (7) into equation (6) gives electric and magnetic fields as follows …”

“…The electric displacement and magnetic induction along the radial and circumferential directions are derived as [15–19] in which mij and μij are dielectric and electromagnetic coefficients. Substitution of strain, electric, and magnetic fields into constitutive relations leads to the following relations:…”

“…They mentioned that influence of some geometrical parameters and patterns of layers are important in behaviors of the structure. Authors of this paper have studied the effect of applied electric and magnetic potentials as well as Pasternak's foundation on the electro-magneto-thermo-elastic behaviors of the sandwich rod, beam, and plates [15–19].…”

Nonlinear Electromechanical Stability of a Functionally Graded Circular Plate Integrated With Functionally Graded Piezoelectric Layers

“…Arefi (2013) and Arefi and Nahas (2014) presented nonlinear analysis of the functionally graded piezoelectric cylinder and sphere, respectively. Three dimensional analysis of a functionally graded piezoelectric shell under multi fields has been studied by Arefi (2014).…”