Static bending and free vibration of FGM beam using an exponential shear deformation theory

Hadji, Lazreg; Khelifa, Zoubida; Daouadji, Tahar Hassaine; Bedia, E.A. Adda

doi:10.12989/csm.2015.4.1.099

Cited by 12 publications

(6 citation statements)

References 38 publications

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“…They also examined the effects of the material gradient index on the bending behavior of the considered structures. A refined exponential shear deformation theory was suggested by [9] to study the bending behavior of FG beams. [10] developed an analytical relationship between the static response of Euler Bernoulli and Timoshenko FG beams.…”

Section: Introductionmentioning

confidence: 99%

Static Analysis of FG Beams via Complementary Functions Method

Noori

Aslan

Temel

2020

European Mechanical Science

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The bending response of Functionally Graded (FG) beams is carried out by the Complementary Functions Method (CFM). The mechanical properties of the material, Young's modulus, of the straight beams are considered to be graded only in the thickness direction. Poisson's ratio is supposed to be constant. Governing equations of the considered problem are obtained with the aid of minimum total potential energy principle based on Timoshenko's beam theory (FSDT). The main purpose of this paper is the infusion of the CFM to the bending analysis of FG straight beams. The effectiveness and accuracy of the proposed scheme are confirmed by comparing its numerical results with those of the available literature. The application of this efficient method provides accurate results of static response for FGM beams with different variations of material properties.

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Section: Introductionmentioning

confidence: 99%

Static Analysis of FG Beams via Complementary Functions Method

Noori

Aslan

Temel

2020

European Mechanical Science

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“…The elastic buckling and bending of a functionally graded, Timoshenko theory-based porous beam, with transversal cosine-dependent material parameters is studied by Chen [11]. Hadji [12] analyzes the static bending and free vibrations of a shear-deformable FGM beam where the strains are assumed to be exponentially distributed in the transverse direction and the material parameters are powerlaw distributed. A similar analysis of a shear-deformable FGM beam is found in Guenfod [13].…”

Section: Introductionmentioning

confidence: 99%

Extension of Boley’s method to functionally graded beams

Gahleitner

Schoeftner

2020

Acta Mech

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The objective of this contribution is the computation of the Airy stress function for functionally graded beam-type structures subjected to transverse and shear loads. For simplification, the material parameters are kept constant in the axial direction and vary only in the thickness direction. The proposed method can be easily extended to material varying in the axial and thickness direction. In the first part an iterative procedure is applied for the determination of the stress function by means of Boley’s method. This method was successfully applied by Boley for two-dimensional (2D) isotropic plates under plane stress conditions in order to compute the stress distribution and the displacement field. In the second part, a shear loaded cantilever made of isotropic, functionally graded material is studied in order to verify our theory with finite element results. It is assumed that the Young’s modulus varies exponentially in the transverse direction and the Poisson ratio is constant. Stresses and displacements are analytically determined by applying our derived theory. Results are compared to a 2D finite element analysis performed with the commercial software ABAQUS. It is found that the analytical and numerical results are in perfect agreement.

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“…Li et al [23] have presented a free vibration analysis of laminated composite beams of various boundary conditions using various higher-order shear deformation beam theories and spectral finite element method. Hadji et al [24] have developed a refined exponential shear deformation theory for the static and free vibration analysis of functionally graded beams. Vo et al [25,26] have developed a new quasi-3D theory for the static, free vibration and buckling analysis of functionally graded sandwich beams using a finite element method.…”

Section: Introductionmentioning

confidence: 99%

On the static deformation of FG sandwich beams curved in elevation using a new higher order beam theory

Avhad

Sayyad

2020

Sādhanā

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This article presents the static analysis of FG sandwich beams curved in elevation. Navier-type semi-analytical solutions are obtained based on polynomial type fifth order shear and normal deformation theory. The beam has FG skins and isotropic core. Material properties of FG skins are graded in z-direction according to the power-law distribution. The present theory accounts for a fifth-order distribution of axial displacement and fourth-order distribution of transverse displacement. The present theory considers the effect of thickness stretching and gives a realistic variation of transverse shear stress through the thickness of the beam. The governing equations are obtained within the framework of the principle of virtual work. Semi-analytical static solutions for the simply supported FG sandwich beams curved in elevation are obtained using Navier's technique. The beam is subjected to uniformly distributed load. The non-dimensional numerical values for displacements and stresses are obtained for various power-law index and thickness of the core. The present results are found in good agreement with previously published results.

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Static bending and free vibration of FGM beam using an exponential shear deformation theory

Cited by 12 publications

References 38 publications

Static Analysis of FG Beams via Complementary Functions Method

Static Analysis of FG Beams via Complementary Functions Method

Extension of Boley’s method to functionally graded beams

On the static deformation of FG sandwich beams curved in elevation using a new higher order beam theory

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