An elasticity solution for functionally graded beams

Sankar, Bhavani V.

doi:10.1016/s0266-3538(01)00007-0

Cited by 584 publications

(228 citation statements)

References 3 publications

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“…The material properties of FGMs are inhomogeneous microscopically and change with changing temperature, therefore the material properties of FGMs depend on position and temperature. One of the mathematical models of material properties was used in a lot of research in order to study fracture mechanics, crack propagation, vibration, and bending, is exponential function [7,11,[19][20][21][22][23][24][25][26].…”

Section: Fgms Materials Propertiesmentioning

confidence: 99%

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Mechanical and Thermal Analysis of Classical Functionally Graded Coated Beam

2018

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Abstract. The governing equation of a classical rectangular coated beam made of two layers subjected to thermal and uniformly distributed mechanical loads are derived by using the principle of virtual displacements and based on Euler-Bernoulli deformation beam theory (EBT). The aim of this paper was to analyze the static behavior of clamped-clamped thin coated beam under thermo-mechanical load using MATLAB. Two models were considered for composite coated. The first model was consisting of ceramic layer as a coated and substrate which was metal (HC model). The second model was consisting of Functionally Graded Material (FGM) as a coated layer and metal substrate (FGC model). From the result it was apparent that the superiority of the FGC composite against conventional coated composite has been demonstrated. From the analysis, the stress level throughout the thickness at the interface of the coated beam for the FGC was reduced. Yet, the deflection in return was observed to increase. Therefore, this could cater to various new engineering applications where warrant the utilization of material that has properties that are well-beyond the capabilities of the conventional or yesteryears materials.

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Section: Fgms Materials Propertiesmentioning

confidence: 99%

“…Coating structures with FGMs are called FGC. FGC beams under mechanical, thermal and thermos-mechanical loads are studied by several of researches [11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Mechanical and Thermal Analysis of Classical Functionally Graded Coated Beam

2018

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“…The well-known elasticity solution for simply supported functionally gradient beams subjected to sinusoidal loading was developed by Sankar (2001). Material properties are assumed to vary according to an exponential law.…”

Section: Latin American Journal Of Solids and Structures 14 (2017) 18mentioning

confidence: 99%

A New Fifth-Order Shear and Normal Deformation Theory for Static Bending and Elastic Buckling of P-FGM Beams

Ghumare

Sayyad

2017

Lat. Am. j. solids struct.

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A new fifth-order shear and normal deformation theory (FOSNDT) is developed for the static bending and elastic buckling analysis of functionally graded beams. The properties of functionally graded material are assumed to vary through the thickness direction according to power-law distribution (P-FGM). The most important feature of the present theory is that it includes the effects of transverse shear and normal deformations. Axial and transverse displacements involve polynomial shape functions to include the effects of transverse shear and normal deformations. A polynomial shape function expanded up to fifth-order in terms of the thickness coordinate is used to account for the effects of transverse shear and normal deformations. The kinematics of the present theory is based on six independent field variables. The theory satisfies the traction free boundary conditions at top and bottom surfaces of the beam without using problem dependent shear correction factor. The closed-form solutions of simply supported FG beams are obtained using Navier's solution procedure and non-dimensional results are compared with those obtained by using classical beam theory, first order shear deformation theory and other higher order shear deformation theories. It is concluded that the present theory is accurate and efficient in predicting the bending and buckling responses of functionally graded beams.

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“…Due to the advantages and increasing use of FGMs and importance of the beam structures in the engineering field, many studies have been performed on the vibration problems of FG beams [14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Free Vibration of Functionally Graded Rayleigh Beam

Avcar¹,

Alwan²

2017

International Journal of Engineering &Amp; Applied Sciences

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In the present study, free vibration of Rayleigh beam composed of functionally graded materials (FGMs) is investigated. For this purpose, the equation of the motion of functionally graded (FG) beam derived according to Rayleigh beam theory. The material properties are assumed to vary continuously through the thickness of the beam according to the power-law form. Resulting equations are solved for simply supported boundary conditions. In order to validate the results, a comparison is carried out with available results for homogeneous beam. The effects of varying material properties on the dimensionless free vibration frequency parameters are examined. It is seen that varying material properties have significant effects on dimensionless free vibration frequency parameters of FG Rayleigh beam

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An elasticity solution for functionally graded beams

Cited by 584 publications

References 3 publications

Mechanical and Thermal Analysis of Classical Functionally Graded Coated Beam

Mechanical and Thermal Analysis of Classical Functionally Graded Coated Beam

A New Fifth-Order Shear and Normal Deformation Theory for Static Bending and Elastic Buckling of P-FGM Beams

Free Vibration of Functionally Graded Rayleigh Beam

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