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.


Hybrid finite element for analysis of functionally graded beams
Sarıtaş, Afşin; Soydas, Ozan (2017-01-01)
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...
Nonlinear vibrations of curved single and doublewalled carbon nanotubes /
Samandari, Hamed; Ciğeroğlu, Ender; Department of Mechanical Engineering (2014)
In this thesis, effects of Geometric, initial curvature, and van der Waals (vdW) interlayer force nonlinearities on the variation of nonlinear natural frequency of Carbon Nanotubes (CNTs) are investigated in detail throughout several case studies. Galerkin method with a single trial function, which is the eigenfunction of the linear system, is widely used in literature in studying nonlinear vibrations of CNTs. However, eigenfunctions of the nonlinear systems can be significantly different than the eigenfunc...
Nonlinear fiber modeling of steel-concrete partially composite beams with channel shear connectors
Öztürk, Alper; Baran, Eray; Department of Civil Engineering (2017)
The purpose of this study is to develop a nonlinear fiber-based finite element model of steel-concrete composite beams. The model was developed in OpenSees utilizing the available finite element formulations and the readily available uniaxial material constitutive relations. The model employed beam elements for the steel beam and the concrete slab, while zero-length connector elements were used for the steel-concrete interface. The channel shear connector response used in numerical models was based on the p...
Modeling of the nonlinear behavior of steel framed structures with semi rigid connections
Sarıtaş, Afşin; Özel, Halil Fırat (null; 2015-07-21)
A mixed formulation frame finite element with internal semi-rigid connections is presented for the nonlinear analysis of steel structures. Proposed element provides accurate responses for spread of inelasticity along element length by monitoring the nonlinear responses of several crosssections, where spread of inelasticity over each section is captured with fiber discretization. Each material point on the section considers inelastic coupling between normal stress and shear stress. The formulation of the ele...
Thermal fracture analysis of orthotropic functionally graded materials using an equivalent domain integral approach
Dağ, Serkan (2006-12-01)
A new computational method based on the equivalent domain integral (EDI) is developed for mode I fracture analysis of orthotropic functionally graded materials (FGMs) subjected to thermal stresses. By using the constitutive relations of plane orthotropic thermoelasticity, generalized definition of the J-integral is converted to an equivalent domain integral to calculate the thermal stress intensity factor. In the formulation of the EDI approach, all the required thermomechanical properties are assumed to ha...
Citation Formats
T. Gürol, “Finite element modeling of beams with functionally graded materials,” M.S. - Master of Science, Middle East Technical University, 2014.