Static and free vibration analysis of FGM beam based on unified and integrated of Timoshenko’s theory

Katili, Irwan; Syahril, Tito; Katili, Andi Makarim

doi:10.1016/j.compstruct.2020.112130

Cited by 37 publications

(16 citation statements)

References 27 publications

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“…For simplicity, Poisson's ratio of the beam is assumed to be constant in this study for that the effect of Poisson's ratio on deformation is much less than that of Young's modulus. 60 Type A: Single-layered FG beams. The beam is graded from a mixture of metal and ceramic, in which the composition is varied from the bottom to the top surface (see Figure 1(b)).…”

Section: Materials Proprietiesmentioning

confidence: 99%

Finite element bending analysis of symmetric and non-symmetric functionally graded sandwich beams using a novel parabolic shear deformation theory

Belarbi

Khechai

Bessaim

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part L:

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In this paper, the bending behavior of functionally graded single-layered, symmetric and non-symmetric sandwich beams is investigated according to a new higher order shear deformation theory. Based on this theory, a novel parabolic shear deformation function is developed and applied to investigate the bending response of sandwich beams with homogeneous hardcore and softcore. The present theory provides an accurate parabolic distribution of transverse shear stress across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the functionally graded sandwich beam without using any shear correction factors. The governing equations derived herein are solved by employing the finite element method using a two-node beam element, developed for this purpose. The material properties of functionally graded sandwich beams are graded through the thickness according to the power-law distribution. The predictive capability of the proposed finite element model is demonstrated through illustrative examples. Four types of beam support, i.e. simply-simply, clamped-free, clamped–clamped, and clamped-simply, are used to study how the beam deflection and both axial and transverse shear stresses are affected by the variation of volume fraction index and beam length-to-height ratio. Results of the numerical analysis have been reported and compared with those available in the open literature to evaluate the accuracy and robustness of the proposed finite element model. The comparisons with other higher order shear deformation theories verify that the proposed beam element is accurate, presents fast rate of convergence to the reference results and it is also valid for both thin and thick functionally graded sandwich beams. Further, some new results are reported in the current study, which will serve as a benchmark for future research.

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Section: Materials Proprietiesmentioning

confidence: 99%

Finite element bending analysis of symmetric and non-symmetric functionally graded sandwich beams using a novel parabolic shear deformation theory

Belarbi

Khechai

Bessaim

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part L:

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show abstract

“…For FG beams with a medium slenderness ratio, this theory considers the deformation to be less than the actual value and ignores the transverse shear deformation effects and estimates the natural frequencies to be larger than the actual value. Timoshenko's theory overcomes this classical theory limitation in research by researchers, for example, Li [5], Wu et al [6], and Katili et al [7]. A correction parameter is required in this theory because of the zero shear stress violation at the top and bottom of the beam.…”

Section: Introductionmentioning

confidence: 99%

Vibrations Evaluation of Functionally Graded Porous Beams in Thermal Surroundings by Generalized Differential Quadrature Method

Khakpour

Bazargan-Lari

Zahedinejad

et al. 2022

Shock and Vibration

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This study investigates how to obtain the natural frequency of functionally graded porous beams simply supported on an elastic substrate in thermal surroundings by the theory of third-order shear deformation. Temperature constantly changes in the beam thickness direction and step with the distribution of volume fraction power law of the ingredient has been affected on the material attributes. The distribution of uniform porosity at the pass phase is examined. To achieve the equations of governing, Hamilton's principle was carried out. To discretize these equations, the generalized differential quadrature method has been used. First, the approach's convergence is shown. Comparison with the results of other articles was performed for validation. Here, the impacts of numerous factors like index of power law, heat field type, temperature difference, slenderness ratio, and porosity coefficient and elastic substrate factors of a functionally graded porous beam on the natural frequencies were studied for simple boundary conditions. In addition to displaying these parameters’ impact on the beam’s thermomechanical evaluation, the conclusions also confirm the accuracy of the numerical technique used.

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“…Among three kinds of structure like beam, plate and shell, beam has always considered the interests of researchers because of its applications. There are many different beam theories used to analyze beam structures like simple beam theory [14][15], classical beam theory [16][17], first-order shear deformation theory [18][19] or higher-order shear deformation theory [20][21][22]. However, using a simple model helps us to reduce the computational cost with the resulting error within the allowable range.…”

Section: Introductionmentioning

confidence: 99%

Effect of porosity on free vibration of functionally graded porous beam based on simple beam theory

To¹

2022

TJDU

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In this paper, the natural frequencies of functionally graded porous (FGP) beam are determined associated with two kinds of porosity. The simple beam theory is applied in this study with various boundary conditions. The results obtained in this paper are presented and compared with other results in the references to verify the correctness in implementing the formula and writing the Matlab code. Last but not least, this article can help researchers to have an overview of the free vibration characteristics of the functionally graded porous beams.

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Static and free vibration analysis of FGM beam based on unified and integrated of Timoshenko’s theory

Cited by 37 publications

References 27 publications

Finite element bending analysis of symmetric and non-symmetric functionally graded sandwich beams using a novel parabolic shear deformation theory

Finite element bending analysis of symmetric and non-symmetric functionally graded sandwich beams using a novel parabolic shear deformation theory

Vibrations Evaluation of Functionally Graded Porous Beams in Thermal Surroundings by Generalized Differential Quadrature Method

Effect of porosity on free vibration of functionally graded porous beam based on simple beam theory

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