A Theoretical Analysis of Functionally Graded Beam under Thermal Loading

El-Megharbel, Abla

doi:10.4236/wjet.2016.43044

Cited by 9 publications

(8 citation statements)

References 16 publications

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“…Substituting the expressions for U , U , V and K from Equations (18), (20), (24) and (25) into Equation (17), the following equations of motion are obtained by integrations by parts taking into account the previous boundary conditions, and putting together the coe cients of 0 , , and .…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…ey used Hamilton's principle to derive the equations of motion taking into account the thermal effect. El-Megharbel [20] introduced a mathematical analysis to study the FG beam under a thermal loading by assuming two cases of heat distribution along the beam depth: Power and exponential distributions. Şimşek [21] investigated the buckling of the two-dimensional FG beams with different boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Buckling Temperature and Natural Frequencies of Thick Porous Functionally Graded Beams Resting on Elastic Foundation in a Thermal Environment

Ibnorachid

Boutahar

Bikri

et al. 2019

Advances in Acoustics and Vibration

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In this paper, free vibrations of Porous Functionally Graded Beams (P-FGBs), resting on two-parameter elastic foundations, and exposed to three forms of thermal field, uniform, linear, and sinusoidal, are studied using a Refined Higher-order shear Deformation Theory. The present theory accounts for shear deformation by considering a constant transverse displacement and a higher-order variation of the axial displacement through the thickness of the beam. The stress-free boundary conditions are satisfied on the upper and lower surfaces of the beam without using any shear correction factor. The material properties are temperature-dependent and vary continuously through the depth direction of the beam, based on a modified power-law rule, in which two kinds of porosity distributions, uniform, and nonuniform, through the cross-section area of the beam, are considered. Hamilton’s principle is applied to obtain governing equations of motion, which are solved using a Navier-type analytical solution for simply supported P-FGB. Numerical examples are proposed and discussed in detail, to prove the effect of the thermal environment, the porosity distribution, and the influence of several parameters such as the power-law index, porosity volume fraction, slenderness ratio, and elastic foundation parameters on the critical buckling temperatures and the natural frequencies of the P-FGB.

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Section: Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Buckling Temperature and Natural Frequencies of Thick Porous Functionally Graded Beams Resting on Elastic Foundation in a Thermal Environment

Ibnorachid

Boutahar

Bikri

et al. 2019

Advances in Acoustics and Vibration

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“…Functionally graded materials (FGMs) are novel materials having dimensions related properties gradually changeable with time [1]. It is the advanced development technique of formerly used composite materials [2]. FGMs are also a kind of composites, having two or more materials prepared by continues changing of material composition [3].…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis for mechanical behaviour of beams made by composite and functionally graded materials

Asiri

2022

murjet

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Functionally graded materials are important in laboratory and industry. These materials have opened a new area of research. These functionally graded materials can be produced as a result of composite material by the adding more materials to get desired properties to make it perfect for suitable applications. In this paper, the focus is on the modelling of functionally graded material that is developed to resist wear by any friction or erosion by any liquid. Cemented Carbide (WC) was selected as a composite material that is commonly used in industrial or lab. Before developing the model of functionally graded material (FGM), a detailed study has been carried out on the composite material using the finite element method to find a numerical solution and compared it to the exact one. The analytical solution was obtained by using MATLAB and numerical solution by ANSYS. Besides these software’s SolidWorks and SkyCIV programs were utilized for analysis and plotting purposes. At the end of the project, one layer titanium carbonitride (TiCN) was added to one face and the same layer was added to the four faces to make the comparison between the two cases to select the best model using the results of a total of deformation.

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“…The thermal post-buckling and free vibration analysis of Timoshenko beams was presented by Gunda (2014) using the Rayleigh–Ritz method. El-Megharbel (2016) gave an analytical solution for FG Timoshenko beams under two kinds of temperature fields. The thermal–mechanical vibration of 2D FG porous nanobeams was studied by Mirjavadi et al (2017).…”

Section: Introductionmentioning

confidence: 99%

Analysis of thick beams with temperature-dependent material properties under thermomechanical loads

Zhong

Zhou

et al. 2020

Advances in Structural Engineering

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This study focuses on the thermoelastic behavior of simply supported thick beams with temperature-dependent material properties under thermomechanical loads. The heat conduction analysis is based on the one-dimensional Fourier’s law, and the displacement and stress analysis is based on the two-dimensional thermoelasticity theory. The solution of temperature field across the thickness is obtained. By dividing the beam into a series of thin slices, the temperature and the material properties in each slice are considered to be uniform. The state space method is used to give the displacements and stresses for every slice. The transfer-matrix method is used to give the displacements and stresses for the beam. Finally, an example is conducted to analyze the temperature, displacement, and stress fields in a carbon steel beam. The example reveals that the temperature not only produces displacements and stresses itself but also affects the displacements and stresses induced by the mechanical load.

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A Theoretical Analysis of Functionally Graded Beam under Thermal Loading

Cited by 9 publications

References 16 publications

Buckling Temperature and Natural Frequencies of Thick Porous Functionally Graded Beams Resting on Elastic Foundation in a Thermal Environment

Buckling Temperature and Natural Frequencies of Thick Porous Functionally Graded Beams Resting on Elastic Foundation in a Thermal Environment

Numerical analysis for mechanical behaviour of beams made by composite and functionally graded materials

Analysis of thick beams with temperature-dependent material properties under thermomechanical loads

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