Beam element with spatial variation of material properties for multiphysics analysis of functionally graded materials

In this paper, two different methods for modelling of functionally graded material (FGM) beam with continuous spatially varying material properties will be presented and compared, namely the multilayering method and the direct integration method. Both the methods are related to homogenization of spatially varying material properties of real FGM beam and to calculation of the secondary variables of the FGM beams. The multilayering method is based on the laminate theory, which is very often used by modelling of the multilayer composite beams. The direct integration method transform spatial continuous varying material properties to the effective ones by direct integration of derived homogenization rules. In next part of the paper, new multiphysical beam finite element will be presented, which in conjunction with the proposed homogenization methods can be used for very effective analysis of the FGM beam structures. The numerical experiment will be presented concerning the multiphysical (electro–thermal–structural) analysis of the chosen FGM beams with spatial continuous variation of material properties.