Free vibration analysis of uniform or tapered beams with transversely functionally graded materials

Koçkaya, Okan
There are several analysis techniques in the literature for structural members with functionally graded material (FGM). Solutions based on theory of elasticity are the most common. Finite element approach with plate, shell or solid elements is an alternative popular solution technique. Beam elements are being recently used in the finite element approach for this purpose. Displacement (DB) and force based (FB) elements are the two main choices in this regard: while the FB method is a more recent approach, DB counterpart is the more commonly used technique. In this thesis, the proposed FB methodology for analyzing beams wi th FGM is verified using linear elastic free vibration analyses with comparison to the numerical results in the literature. The benchmark examples are selected solutions from the literature as well as the solution of the problem using the well-known and verified DB general purpose finite element code ANSYS. First five modal frequencies obtained using the proposed methodology are compared to the benchmark results for different cases. For the validation, uniform and tapered geometries are considered separately with homogeneous material and transversely distributed FGM. The effects of different boundary conditions and aspect ratios are taken into account.


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Dağ, Serkan (ASME International, 2008-09-01)
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Hybrid finite element for analysis of functionally graded beams
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A hybrid finite element model is presented, where stiffness and mass distributions over a beam with functionally graded material (FGM) are accurately modeled for both elastic and inelastic material responses. Von Mises and Drucker-Prager plasticity models are implemented for metallic and ceramic parts of FGM, respectively. Three-dimensional stress-strain relations are solved by a general closest point projection algorithm, and then condensed to the dimensions of the beam element. Numerical examples and veri...
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Three Dimensional Modeling of Inclined Surface Cracks in FGM Coatings
Kosker, S.; Dağ, Serkan; YILDIRIM, BORA (2008-09-25)
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Finite element modeling of beams with functionally graded materials
Gürol, Tolga; Sarıtaş, Afşin; Department of Civil Engineering (2014)
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...
Citation Formats
O. Koçkaya, “Free vibration analysis of uniform or tapered beams with transversely functionally graded materials,” M.S. - Master of Science, Middle East Technical University, 2018.