Mechanical behavior of functionally graded material plates under transverse load—Part II: Numerical results

Abstract

The formulations of the complete solutions to the rectangular simply supported plates with power-law, sigmoid, and exponential FGMs have been derived in Part I. In this part, we focus on the numerical solutions evaluated directly from theoretical formulations and calculated by finite element method using MARC program. The effects of loading conditions, the change of PoissonÕs ratio, and the aspect ratio on the mechanical behavior of an FGM plate are discussed. Besides, a comparison of the results of P-FGM, S-FGM, and E-FGM is investigated. Finite element modelsIn the numerical calculation, consider a square FGM plate with the ratio of width to thickness equal to 50, i.e., a = b = 100 cm, h = 2 cm. The plate is simply supported on its four sides and is subjected to the transverse load, as shown in Fig. 1. The PoissonÕs ratio of the FGM plate is assumed to be constant in the whole plate. Take m = 0.3. The YoungÕs moduli at the top and bottom surfaces of the FGM plate are assumed to be E 2 and E 1 , respectively. However, the YoungÕs modulus at any point on the FGM plate varies continuously in the thickness direction based on the volume fraction of the constituents. 0020-7683/$ -see front matter Ó

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

“…Lee et al 2009). Typically, FG shell structures were presented using: (i) Kirchhoff-Love theory, Chi and Chung (2006), where the shear strains are assumed zero, which is not acceptable for FG shell; (ii) the First-order Shear Deformation Theory (FSDT) (Praveen and Reddy 1998;Thai and Kim 2015), which gives a correct overall assessment. Notice that the shear correction factors should be incorporated to adjust the transverse shear stiffness; (iii) the High-order Shear Deformation Theory (HSDT) (Neves et al 2012;Wali et al 2014Wali et al , 2015Frikha et al 2016) in which the equations of motion are more complicated to obtain than those of the FSDT; among other theories.…”

Three-Dimensional Modeling of Functionally Graded Multiferroic Composites

“…There are mainly three types of functions defining the variation of material properties in the previous research: an exponential function called E-FGM [23, 26 and 28], a power-law function called P-FGM [29][30][31], and a sigmoid function composed of two power-law functions called S-FGM [32][33][34]. While all these grading variations can be easily included in our 3D FEM program, in this article, we focus on the E-FGM and P-FGM cases.…”

“…The layered plate has the geometric dimensions L x = L y = 1m and t 1 = t 2 = t 3 = 0.1m. A mechanical load 33 18.6 0 e 42 11.6 0 e 51 11.6 0 is applied on the top surface while all other extended traction components are zero. On the bottom surface, it is traction free (i.e., σ xz = σ yz = σ zz = D z = B z = 0).…”

A Theoretical Analysis of Functionally Graded Beam under Thermal Loading

“…The analytical solutions of the previous distributions FGM plates were proved by the numerical results of finite element method [14]. While in [15] they evaluated the numerical solutions directly from theoretical formulations and calculated by finite element method using MARC program. On the other hand, Sun et al [16] had numerically investigated the buckling and post-buckling thermo-mechanical deformations of a Functionally Graded Material (FGM) Timoshenko beam resting on a two-parameter nonlinear elastic foundation and subjected to only a temperature rise with the shooting method.…”