Numerical modelling of a Timoshenko FGM beam using the finite element method

Ziou, Hassina; Guenfoud, Hamza; Guenfoud, Mohamed

doi:10.1504/ijstructe.2016.077719

Cited by 11 publications

(5 citation statements)

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“…The properties of functionally graded materials (FGMs) beams vary continuously through the thickness according to the volume fraction of the constituent materials (metal and ceramic). The power-law (P-FGM) most commonly describes differences in the properties of materials [34][35][36][37].…”

Section: Functionally Graded Materials (Fgms)mentioning

confidence: 99%

Analysis of FGM Cantilever Beams under Bending-torsional Behavior Using a Refined 1D Beam Theory

Guendouz

Khebizi

Guenfoud

et al. 2022

Period. Polytech. Civil Eng.

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The static bending-torsion problem of functionally graded cantilever beams is studied using a refined 1D/3D beam theory (Refined beam theory RBT and Refined beam theory with distortion modes RBT*) built on the 3D Saint-Venant (SV) solution. In these theories, the displacement models include Poisson's effects, out-of-plane deformations and distortions. For a given section, the sectional displacement modes are derived from the computation of the particular 3D Saint-Venant’s solution. These modes, which reflect the mechanical behavior of the cross-section, lead to a beam theory that actually corresponds to the cross-section type in terms of shape and material. In addition, the models take into account edge effects to predict a 3D solution in a larger internal region to better describe the overall behavior of FGM beams. The models examined are implemented on the CSB (Cross-Section and Beam Analysis) tool. It is based on the RBT/SV (Refined Beam Theory based on the 3D SV’s solution) theory of FGM beams. The mechanical and physical characteristics of the FGM beams vary continuously, according to a power-law distribution, through the thickness of the beams. The numerical and 3D results obtained with homogeneous and FGM beams are systematically compared with other models in the literature and those provided by the full Saint-Venant beam theory (SVBT) calculations.

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Section: Functionally Graded Materials (Fgms)mentioning

confidence: 99%

Analysis of FGM Cantilever Beams under Bending-torsional Behavior Using a Refined 1D Beam Theory

Guendouz

Khebizi

Guenfoud

et al. 2022

Period. Polytech. Civil Eng.

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“…The Young's modulus variation in the S-FGM can be calculated using a similar expression as P-FGM but uses volume fraction for each part separately as shown in Equations ( 5) and (6).…”

Section: Sigmoid Materials Function (S-fgm)mentioning

confidence: 99%

“…A combined Fourier series and Galerkin method for solving the two-dimensional elasticity equations for a functionally graded beam subjected to transverse loads using a polynomial function to account for the variation of Young's modulus through the beam thickness was reported in [4]. Finite element method for characterizing the dynamic free vibration of a functionally graded beam with material graduation axially or transversely through the thickness based on the power-law function and a finite element method to study the static behavior of Timoshenko FGM cantilever beam subjected to a concentrated load at the free end and using power law for varying material properties through-beam thickness was investigated and proposed in [5,6]. The static behavior of functionally graded metal-ceramic beams under transverse loading using higher-order shear deformation theory, assuming power-law function to account for material variation through-beam thickness was studied in [7].…”

Section: Introductionmentioning

confidence: 99%

A Simplified Stress Analysis of Functionally Graded Beams and Influence of Material Function on Deflection

Althoey

Ali

2021

Applied Sciences

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This paper aims at providing a simplified analytical solution for functionally graded beam stress analysis and optimized material gradation on the beam deflection. The power-law (P-FGM) and exponential (E-FGM) material functions were considered for an exact solution of the normal and shear stress distributions across the beam thickness. Optimization of material function on the FGM beam deflection, which is new of its kind, was also investigated considering both simply supported and cantilever beams. It was observed that the non-dimensional normal stress and shear stress are independent of the elastic moduli values of the constituent materials but rather depends on both the ratio of the elastic moduli and the location across the beam thickness in the E-FGM material function model. This observation was first validated from available kinds of literature and through numerical simulation using ABAQUS and extended to the P-FGM stress analysis. The maximum deflection on the FGM beam occurred for a homogenous steel beam while the minimum deflection was observed on the beam with a P-FGM material function. The results of this work demonstrate that if properly designed and optimized, FGMs can provide an alternative material solution in structural applications.

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“…The distance between middle plane and neutral plane is given as [35]: The normal strain and stress of functionally graded Rayleigh beam are given as [29] x…”

Section: Theorymentioning

confidence: 99%

Transverse Vibration of Cracked Graded Rayleigh Beam with Axial Motion

Bachaya¹,

Elaikh²

2021

UTJES

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The paper presents the transverse vibration of an open edge crack graded Rayleigh beam with axial motion. The vibration equation was obtained relying on Hamilton's precept and resolved by the approach of Galerkin's. The power-law is adopted to represent the gradient of properties of the material composing the beam along the direction of the thickness. Cracks were modeled as rotational massless spring. The effects of axial velocity, material property change index, location, and depth of cracking on the vibration characteristics are observed. Also, the corresponding mode shapes are found for cracked moving graded Rayleigh beam with simply supported, and fixed-fixed end supports. The results clear up that the natural frequencies drop due to the rise in the axial velocity, the crack depth, and the material property index

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Numerical modelling of a Timoshenko FGM beam using the finite element method

Cited by 11 publications

References 0 publications

Analysis of FGM Cantilever Beams under Bending-torsional Behavior Using a Refined 1D Beam Theory

Analysis of FGM Cantilever Beams under Bending-torsional Behavior Using a Refined 1D Beam Theory

A Simplified Stress Analysis of Functionally Graded Beams and Influence of Material Function on Deflection

Transverse Vibration of Cracked Graded Rayleigh Beam with Axial Motion

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