Static analysis of simply supported functionally graded and layered magneto-electro-elastic plates

Abstract

In this article, static analysis of functionally graded, anisotropic and linear magneto-electro-elastic plates have been carried out by semi-analytical finite element method. A series solution is assumed in the plane of the plate and finite element procedure is adopted across the thickness of the plate such a way that the three-dimensional character of the solution is preserved. The finite element model is derived based on constitutive equation of piezomagnetic material accounting for coupling between elasticity, electric and magnetic effect. The present finite element is modeled with displacement components, electric potential and magnetic potential as nodal degree of freedom. The other fields are calculated by post-computation through constitutive equation. The functionally graded material is assumed to be exponential in the thickness direction. The numerical results obtained by the present model are in good agreement with available functionally graded three-dimensional exact benchmark solutions given by Pan and Han [Pan, E., Han, F., in press. GreenÕs function for transversely isotropic piezoelectric functionally graded multilayered half spaces. Int. J. Solids Struct.]. Numerical study includes the influence of the different exponential factor, magneto-electro-elastic properties and effect of mechanical and electric type of loading on induced magneto-electro-elastic fields. In addition further study has been carried out on non-homogeneous transversely isotropic FGM magneto-electro-elastic plate available in the literature [Chen, W.Q., Lee, K.Y., Ding, H.J., 2005. On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates].

An Inhomogeneous Cell‐Based Smoothed Finite Element Method for Free Vibration Calculation of Functionally Graded Magnetoelectroelastic Structures

“…For FGMEE materials, we have (10) where u, Φ, and Ψ are the vectors of node displacement, node electrical potential, and node magnetic potential, respectively; N , N Φ , and N Ψ are displacement shape, electrical potential shape, and magnetic potential shape functions of ICS-FEM, respectively. N , N Φ , and N Ψ were expressed in similar shape functions.…”

“…Several computational techniques were proposed to investigate the electroelastic, magnetoelastic, and electromagnetic coupling effects of smart structures, such as finite element method (FEM), mesh-free method, and scaled boundary FEM [5][6][7][8][9][10]. Bhangale and Ganesan analyzed the static behaviors of linear anisotropic FGMEE plates using semianalytical FEM and investigated the free vibration of FGMEE plates and cylindrical shells [11,12].…”

Layerwise finite element piezoelasticity analysis of functionally graded shell panel integrated with piezoelectric actuator and sensor

“…Functionally graded shallow and non-shallow shell panels with piezoelectric layers were studied under mechanical loading and electrostatic excitation [28]. Functionally graded and layered magneto-electro-elastic plates and shells were studied [29] using a semi-finite element method so that a series solution was assumed in the plane of the plate and the finite element procedure was adopted across the thickness of the plate. Also, FG shells were analyzed using a layerwise model in which cylindrical shells were assumed to include many homogeneous sub cylinders [30].…”

On semi‐analytical probabilistic finite element method for homogenization of the periodic fiber‐reinforced composites

“…Homogenization method is still a very powerful hybrid technique enabling the analysis of multiscale problems [1,2] including the atomistic scale [3], functionally graded materials [4] as well as some nanocomposites [5]. There are various non-linear models [6,7] accounting for viscoelastic [8], elastoplastic [9], or viscoplastic [10] components, for the overall strength prediction [11] and for prediction of effective properties in really complex engineering systems [12]; the area of homogenized thermal (or electromagnetic) characteristics of composites has also been deeply explored [13,14].…”