Dynamic and static analysis of FGM skew plates with 3D elasticity based graded finite element modeling

Abstract

The present article deals with static and dynamic behavior of functionally graded skew plates based on the three-dimensional theory of elasticity. On the basis of the principle of minimum potential energy and the Rayleigh Ritz method, the equations of motion are derived in conjunction with the graded finite element approach. Solution of the resulted system of equations in time domain is carried out via Newmark's time integration method. Calculations are applied for fully clamped boundary condition. In the present paper, two different sets of distributions for material properties are considered. For the static analysis, material properties are considered to vary through the thickness direction according to an exponential law. In the case of dynamic analysis, variations of the volume fractions through the thickness are assumed to obey a power law function. Thus, the effective material properties at each point are determined by the Mori-Tanaka scheme. In case of dynamic analysis, the results are obtained for uniform step loadings. The effects of material gradient index and skew angle on displacement components and stress response are studied. Results of present formulations are verified by available results of a functionally graded rectangular plate for different boundary conditions and also compared with result of a homogenous skew plate by commercial FEM software.

Numerical Analysis of Geometrically Non-Linear Behavior of Functionally Graded Shells

“…Hence, most of reference solutions are previously reported numerical solutions. Particularly, for FE geometric nonlinear analysis of FG shells, several research papers are surveyed (Praveen and Reddy 1998;Reddy 2000;Kattimani and Ray 2015;Duc et al 2017; Reddy 2007a, 2007b;Alinia and Ghannadpour 2009;Phung-Van et al 2014;Kim et al 2008;Hajlaoui et al 2017;Frikha and Dammak 2017;Asemi et al 2014 andAnsari et al 2016). In these references, a number of theoretical formulation and finite element models based on von Karman, Kirchhoff-Love, FSDT and HSDT theories were proposed to study the geometrically non-linear behavior of FGMs Structures.…”

Quadratic Solid–Shell Finite Elements for Geometrically Nonlinear Analysis of Functionally Graded Material Plates

“…The second approach is based on a 3D formulation of solid elements, in which a fully 3D elastic behavior for FGMs is adopted. In such an approach, some specific kinematic assumptions for thin plates, such as the classical Kirchhoff plate theory and the von Karman theory, are also adopted in the FE formulation (see, e.g., [ 16 , 17 , 18 ]). The third approach is based on the concept of solid–shell elements, which are combined with FGM behavior.…”

Dynamic analysis of FGM rhombic plates with a variation in the mass

“…The bending behaviour of an FGM plate using a higherorder shear-deformation theory was studied by Taj et al 7 The finite-element formulation based on a third-order shear-deformation theory was used by Taj and Chakrabarti 8 to analyse the static and dynamic behaviour of skew plates from functionally graded material. Asemi et al 9 utilized the principle of minimum energy and Rayleigh-Ritz energy method for static and dynamic analyses of FGM skew plates. Most of the earlier dynamic analyses of the plates with cutouts were limited to isotropic plates [10][11] and Reddy 12 reported on a laminated composite plate with a cutout.…”