Analytical solutions for plane problem of functionally graded magnetoelectric cantilever beam

Abstract

In this paper, an exact analytical solution is presented for a transversely isotropic functionally graded magneto-electro-elastic (FGMEE) cantilever beam, which is subjected to a uniform load on its upper surface, as well as the concentrated force and moment at the free end. This solution can be applied for any form of gradient distribution. For the basic equations of plane problem, all the partial differential equations governing the stress field, electric, and magnetic potentials are derived. Then, the expressions of Airy stress, electric, and magnetic potential functions are assumed as quadratic polynomials of the longitudinal coordinate. Based on all the boundary conditions, the exact expressions of the three functions can be determined. As numerical examples, the material parameters are set as exponential and linear distributions in the thickness direction. The effects of the material parameters on the mechanical, electric, and magnetic fields of the cantilever beam are analyzed in detail.

An effective cell-based smoothed finite element model for the transient responses of magneto-electro-elastic structures

“…Wang and Xu (2015) derived the state space equations of anisotropic MEE materials under orthogonal curvilinear coordinates in a Hamiltonian system. Then, an exact analytical solution for functionally graded MEE structures was presented (Wu et al, 2010; Yue et al, 2015). These analytical solutions are highly valuable for illustrating the complicated multi-physics nature of the coupled fields, but they are restricted to a few specific problems with idealized material characteristics, configurations, and boundary conditions.…”

Fonksiyonel derecelendirilmiş ortotropik bir kirişin statik ve titreşim davranışlarının incelenmesi

“…Yue vd. [24] fonksiyonel derecelendirilmiş elasto-manyetik konsol bir kirişin düzlem problem ile analitik olarak incelemiştir. Son yıllarda fonksiyonel derecelendirilmiş malzemelerin mekanik davranışları ile ilgili bir çok çalışma literatürde yer almıştır [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”