Thermal bending response of functionally graded magneto-electric–elastic shell employing non-polynomial model

Abstract

The present mathematical model for complex shells is given in the framework of Carrera unified formulation. The mechanical, electrical, and magnetic equations are derived in terms of the principle of virtual displacement, Maxwell’s equations and Gauss equations. Fourier’s heat conduction equation is used. The governing equations are discretized by the Chebyshev–Gauss–Lobatto and solved with the differential quadrature method. The three-dimensional (3D) equilibrium for mechanical, electrical, and magnetic equations are employed for recovering the transverse stresses, electrical displacement and magnetic induction. Finally, quasi-3D solutions for cycloidal shell of revolution and a funnel panel are introduced in this paper.

Keywords:

• Magneto-electro–elastic material
• functionally graded material
• shell
• Carrera’s unified formulation
• differential quadrature
• heat conduction

Acknowledgments

This paper was written in the context of the project: “Desarrollo de materiales avanzados para el diseño de nuevos productos y servicios tecnológicos para la minería Peruana” founded by CONCYTEC (FONDECYT and GRUPO BANCO MUNDIAL) under the contract number N° 032-2019-FONDECYT-BM-INC.INV. The authors of this manuscript appreciate the financial support from the Peruvian Government.