# GFEM modeling bending of Functionally Graded Material (FGM) plates

## Palavras-chave:

Functionally graded material, Generalized finite element method, Reissner-Mindlin’s model## Resumo

This paper presents a Generalized Finite Element Method (GFEM) formulation for mechani-

cal analysis of Functionally Graded Material (FGM) plates acting both under mechanical loads and under

the effect of high gradient thermal fields. It describes the development, implementation and validation of

said formulation, based on a composite plate model ruled by Reissner-Mindlin’s first-order shear theory.

The calculation of temperature field along the structure’s thickness is made by solving the stead-state

heat conduction problem through Finite Difference Method, considering given the boundary conditions

on both faces of the plate and thermal conductivities of the base materials. Elasticity moduli and thermal

conductivities’ temperature-dependence is considered. Thickness-wise numerical integration procedures

are used to compute both the stiffness matrices of the plate and the thermal portions of nodal force

vectors. A C

k

continuous GFEM model with three-noded triangular shaped elements is considered and

a linear strain-displacement relationship is adopted. Shepard Partitions of unit with smooth approxima-

tion functions are used and enriched by linearly independent polynomials. Solutions are obtained through

Newton-Raphson method.