Statics of FGM circular plate with magneto-electro-elastic coupling: axisymmetric solutions and their relations with those for corresponding rectangular beam

Abstract

This paper investigates the static behavior of a functionally graded circular plate made of magneto-electro-elastic (MEE) materials under tension and bending. The analysis is directly based on the three-dimensional governing equations for magnetoelectro-elasticity, with the boundary conditions on the upper and lower surfaces satisfied exactly and those on the cylindrical surface satisfied approximately (in the Saint Venant sense). The analytical solutions, derived with a direct displacement method, are valid for any functionally graded material (FGM) with its properties varying independently in a continuous manner along the thickness direction. For homogeneous materials, these solutions are degenerated to the ones available in the literature. Interesting relations are also found between the solutions for a functionally graded magneto-electro-elastic (FG-MEE) circular plate and those for an FGMEE rectangular beam, and even those for a functionally graded elastic beam when only the elastic displacements are considered. The beam solutions are also derived using a direct displacement method. Numerical examples are presented to verify the present analytical solutions, show the effects of material heterogeneity and multi-field coupling, and indicate the correspondence between the plate solutions and beam solutions.

Exact solutions for axisymmetric flexural free vibrations of inhomogeneous circular Mindlin plates with variable thickness

“…where α is a constant associated with the radially varying parameters D and M and Poisson's ratio ν, β is a constant reflecting the comprehensive effect of the rotatory inertia and shear deformation, and C + ω and C − ω are two distinct roots of the quadratic equation (11) with respect to C ω in view of Eqs. (12) and (13).…”

“…In practical applications, the thickness, modulus, and mass density of circular plates usually vary continuously or stepwisely, in one spatial dimension or more, to meet the requirement for optimizing the self-weight distribution, improving the local strength, or tailoring the dynamical properties. In recent years, it becomes very popular to use functionally graded structures [6][7][8][9][10][11] to avoid the interface mismatch on mechanical or thermal properties efficiently.…”

Effects of porosity, profile of thickness, and angular acceleration on the magneto-electro-elastic behavior of a porous FGMEE rotating disc placed in a constant magnetic field

“…A solution for the stresses and displacements of a FGMEE disk under tension and bending was presented by Wang et al. 32 Dai et al. 33 disclosed the elastic behavior of a rotating FGPM annular plate under hygrothermal loads.…”

“…Loghman et al 31 studied FGPM rotating disc and considered creep behavior. A solution for the stresses and displacements of a FGMEE disk under tension and bending was presented by Wang et al 32 Dai et al 33 disclosed the elastic behavior of a rotating FGPM annular plate under hygrothermal loads. The free vibration response of circular and annular MEE plates was investigated by Vinyas et al 34 Saadatfar 35 investigated the hygrothermal stress redistribution in an MEE rotating disk using an analytical method.…”

Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment

“…Li et al (2008) investigated the problem of a functionally graded, transversely isotropic, magnetoelectro-elastic circular plate acted on by a uniform load. Recently, static behavior of a MEE-FG circular plates under tension and bending is investigated by Wang et al (2015).…”