A Material Model-based Finite Element Free Vibration Analysis of One-, Two- and Three-dimensional Axially FGM Beams

Abaqus user-defined material model subroutines (UMAT) have been developed in a unified way to provide a numerical implementation of functionally graded material (FGM) properties of one-, two-and three-dimensional beams in the framework of finite element free vibration analysis. A series of UMAT routines are programmed in the FORTRAN environment. They assign material inhomogeneity at the level of integration points of the appropriate conventional one-, two-and three-dimensional finite elements, discarding the need for custom-designed elements. Free vibration analyses of one-, two-and three-dimensional axially FGM beams have been carried out with Abaqus' solver. The user material subroutine-based modeling technique supplies a valuable service to scientists and engineers facing the structural analysis of FGM structural components.