Using a homogeneous beam element to analyse functionally graded beams

Abstract

When an appropriate reference plane is used, the coupling between axial and bending deformations in the stiffness matrix of a functionally graded beam (FGB) element vanishes. Then the stiffness matrix of the FGB element reduces to the same form as that of the homogeneous beam element. However, the coupling in the mass matrix of the FGB element cannot be eliminated at the same time. Consequently, in an analysis that does not involve mass, it is possible to use a homogeneous beam element to obtain the same results as would be achieved with an FGB element. This paper focuses on explaining a procedure to use ANSYS's BEAM3 element to analyse FGBs. The BEAM3 element has the ability to deal with a linear temperature gradient that is sufficient to analyse any arbitrary temperature distribution shape through thickness.