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.


Sliding frictional contact between a rigid punch and a laterally graded elastic medium
Dağ, Serkan; Yidirim, Bora; Ozatag, A. Cihan (2009-11-01)
Analytical and computational methods are developed for contact mechanics analysis of functionally graded materials (FGMs) that possess elastic gradation in the lateral direction. In the analytical formulation, the problem of a laterally graded half-plane in sliding frictional contact with a rigid punch of an arbitrary profile is considered. The governing partial differential equations and the boundary conditions of the problem are satisfied through the use of Fourier transformation. The problem is then redu...
Mixed-mode fracture analysis of orthotropic functionally graded material coatings using analytical and computational methods
Dağ, Serkan (ASME International, 2008-09-01)
This article presents analytical and computational methods for mixed-mode fracture analysis of an orthotropic functionally graded material (FGM) coating-bond coat-substrate structure. The analytical solution is developed by considering an embedded crack in the orthotropic FGM coating. The embedded crack is assumed to be loaded through arbitrary self-equilibrating mixed-mode tractions that are applied to its surfaces. Governing partial differential equations for each of the layers in the trilayer structure a...
Formulation and implementation of a fractional order viscoelastic material model into finite element software and material model parameter identification using in-vivo indenter experiments for soft biological tissues
Demirci, Nagehan; Tönük, Ergin; Department of Mechanical Engineering (2012)
Soft biological tissue material models in the literature are frequently limited to integer order constitutive relations where the order of differentiation of stress and/or strain is integer-valued. However, it has been demonstrated that fractional calculus theory applied in soft tissue material model formulation yields more accurate and reliable soft tissue material models. In this study, firstly a fractional order (where the order of differentation of stress in the constitutive relation is non-integer-valu...
Fatigue crack growth analysis models for functionally graded materials
Dağ, Serkan; YILDIRIM, BORA (2006-10-18)
The objective of this study is to develop crack growth analysis methods for functionally graded materials (FGMs) subjected to mode I cyclic loading. The study presents finite elements based computational procedures for both two and three dimensional problems to examine fatigue crack growth in functionally graded materials. Developed methods allow the computation of crack length and generation of crack front profile for a graded medium subjected to fluctuating stresses. The results presented for an elliptica...
Three Dimensional Modeling of Inclined Surface Cracks in FGM Coatings
Kosker, S.; Dağ, Serkan; YILDIRIM, BORA (2008-09-25)
This study presents a three dimensional finite element method for mixed-mode fracture analysis of an FGM coating-bond coat-substrate structure. The FGM coating is assumed to contain an inclined semi-elliptical crack at the free surface. The trilayer structure is examined under the effect of transient thermal stresses. Strain singularity around the crack front is simulated by utilizing collapsed wedge-shaped singular elements. The modes I, II and III stress intensity factors are computed by applying the disp...
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.