Treffer: Static analysis of FGM plates using layer wise finite element

In limit state design, one of the limit states needed to provide structural safety under the design loads is the Ultimate Limit State (ULS). In ULS, as a computational condition, the strength or stresses field have to fulfil relevant design criteria, defined in the National Building Codes. Thus, the computation of stress as well as displacement field of plate structures, under static loading conditions, is the aim of this paper. After establishing the accuracy of the present layer wise (LW) model for linear and geometrically nonlinear bending, vibration and buckling analysis of laminated composite and sandwich plates subjected to mechanical and thermal load, as well as buckling and free vibrations of Functionally Graded Material (FGM) plates, in this paper, mechanical bending of FGM plates is presented. The mathematical model based on LW theory of Reddy, assumes layer wise variation of in plane displacements and constant transverse displacement through the thickness, linear strain displacement relations and linear orthotropic material properties. The properties of FGMs are assumed to be constant in xy plane and vary through thickness by power law function in terms of volume fraction of the constituent materials. The mathematical model includes the quadratic variation of transverse shear stresses within each layer of the plate. The principle of virtual displacement (PVD) is used to derive Euler-Lagrange differential equation of mechanical bending problem. In plane the weak form is discretized using nine node Lagrangian isoparametric finite element or 2D quadratic in-plane interpolation, while 1D Lagrangian interpolation is used for discretization through the thickness. The original MATLAB computer program is coded for the finite element (FEM) solution. The accuracy of the numerical model is verified by comparison with the available results from the literature. It is found that the effects of power low index affect the stress and displacement fields of FGM plates and should be taken into account when designing ...