Non-polynomial hybrid models for the bending of magneto-electro-elastic shells

Abstract

This paper presents different non-polynomial hybrid models in the framework of Carrera’s Unified Formulation for the bending of a magneto-electric shell with variable radii of curvature. The shell’s middle surface is graphed by a parametric surface. Differential Geometry is employed for evaluating the Lamé Parameters and Radius of Curvature. The mechanical displacements are modeled in the context of an equivalent single layer by sinusoidal, hyperbolic, and tangential models. The electrical and magnetic scalar potential functions are written by a polynomial thickness function in the framework of Layerwise theory. The shell panels are subjected to mechanical, electrical, and magnetic loads. The governing equations are obtained by the Principle of Virtual Displacement. The correspondent partial differential equations are discretized by Chebyshev-Gauss-Lobatto grid distribution and solved by the so-called Differential Quadrature Method. The classical Lagrange polynomial is employed as the basis function for the method. The stresses, electrical displacement, and magnetic induction are recovered by the three-dimensional (3D) equilibrium equations. A comparative analysis with 3D solutions provided in the literature is performed for a square plate and a doubly curved shallow shell panel and remarkable results are obtained. So, the validated models are further used to study shells with variable radii of curvature; specifically, for helicoid, ellipsoid, and catenoid panels.