Unified layer-wise model for magneto-electric shells with complex geometry

Abstract

This paper presents a polynomial layer-wise model in the framework of Carrera's Unified Formulation for the bending analysis of a magneto-electric shells with variable radii of curvature. A parametric surface is used to model the middle surface of the shell. Lame Parameters and Radius of Curvature are calculated by using Differential Geometry. The mechanical displacement, along with the electric and magnetic scalar potential functions, are expressed and modeled using Chebyshev polynomials of the Second Kind. The shells are exposed to different mechanical, electrical and magnetic loads. The Principle of Virtual Displacement is employed for obtaining the governing equations which are discretized by Chebyshev-Gauss-Lobatto grid distribution and solved in semi-analytical manner by the so-called Differential Quadrature Method (DQM). The basis function selected is the Lagrange polynomial. The DQM is employed for its straightforwardness in tackling complex yet regular shell structures under various multiphysical loads. A simple stress recovery technique based on 3D equilibrium equations is introduced to obtain the out-of-plane shear and normal stresses, transverse electric, and magnetic induction. Close-to-3D solutions have been achieved for classical shell structures. Furthermore, benchmark solutions for complex smart shells featuring variable radii of curvature, such as parabolic and cycloidal shells, are introduced.