Finite element modeling of beams with functionally graded materials

Gürol, Tolga
In this thesis a new beam element that is based on force formulation is proposed for modeling elastic and inelastic analysis of beams with functionally graded materials. The attempt of producing functionally graded materials (FGM) arose from mixing two materials in such a way that both of them preserve their physical, mechanical and thermal properties most effectively. FGM shows a gradation through the depth from typically a metallic material such as steel or aluminum at one face of the beam’s section depth to another material such as ceramic at the other face. The change of materials properties is taken according to a power law or an exponential law. The proposed beam element is based on the use of force interpolation functions instead of the approximation of displacement field. Since derivation of displacement interpolation functions is rather a tedious task for a beam with FGM, the proposed approach provides an easy alternative in this regard. The response of the proposed element is calculated through aggregation of responses of several monitoring sections. Section response is calculated by subdividing the depth of a monitoring section into several layers and by aggregating the material response on the layers. Since the formulation of the element is based on force interpolation functions that are accurate under both elastic and inelastic material response, the proposed element provides robust and accurate linear and nonlinear analyses of FGM beams with respect to the displacement-based approach. For the inelastic analysis, the von Mises plasticity model with isotropic and kinematic hardening parameters is assigned for both materials for simplicity. The consistent mass matrix for the proposed force-based element is also implemented for the validation of the vibration modes and shapes obtained from this element. For this effort, benchmark problems are both analyzed with the proposed beam element and with 3d solid elements in ANSYS. The results indicate that the proposed element provides accurate results not only in lower modes but also in higher modes of vibration.


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Citation Formats
T. Gürol, “Finite element modeling of beams with functionally graded materials,” M.S. - Master of Science, Middle East Technical University, 2014.