New concept of finite element method for FGM materials

The aim of this paper is new concept of nonhomogeneous finite elements due to FGM composite material. The main idea of functionally graded materials is a smooth variation of material properties, such as modulus of elasticity, coefficient of thermal conductivity or coefficient of thermal expansion, due to continuous change of microstructure. Composite material containing metal or metal alloy as a matrix and ceramic as fibres without FGM interface thin layer may lead to damage or failure due to delamination of the ceramic film from the substrate. This is the result of localized stress gradients at the interface. Classical finite element formulation contains constant material properties, which leads to numerical errors. A proper approach to solve this problem requires application of nonhomogeneous FE containing additional approximation functions in order to interpolate material properties at the level of each finite element. In practice, material shape functions can be represented by exponential or power functions describing individual character of inhomogeneity.