3-D bending analysis of thick functionally graded plate in different boundary conditions using Element-Free Galerkin (EFG) method

In this paper, the Element-Free Galerkin (EFG) method is employed to obtain three dimensional static behavior of thick functionally graded plates. The Poisson’s ratio is taken to be constant and the Young’s modulus is considered to be graded through the thickness of plate by an exponential function. The shape function is calculated using the 3D moving least squares (MLS) approximation. Because the MLS approximation lacks the Kronecker delta function property, therefore the constrained Galerkin weak-form is used. The Lagrange multiplier method is employed to enforce the essential boundary condition. Effects of weight functions, nodal density and the dimensionless size of the support domain are investigated and favorable value for the dimensionless size of the support domain is calculated. Also a new trigonometric weight function is introduced. Effects of functionally grading index, dimensionless thickness and boundary conditions on the stress and deformation of the plate are investigated. Several examples are presented for thick functionally graded plates under static load. Also in order to verify the obtained results, they are compared with the results of other data reported in the literature. Numerical results indicate that the rate of convergence of the proposed method is higher than that of finite element method especially for stress calculation.