A new higher order shear deformation model for functionally graded beams

Hadji, Lazreg; Khelifa, Zoubida; Abbes, A.

doi:10.1007/s12205-015-0252-0

Cited by 20 publications

(9 citation statements)

References 36 publications

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“…The elasticity modulus of pure ferrite phases at bottom and top surface is E f = 178 GPa [36]; while that of martensite phases at core area is E m = 215 GPa [37]; The influence of Poisson's ratio on the deflection is much less than that of elasticity modulus [38]. Therefore, Poisson's ratio of the graded beams is assumed to be constant at 0.3.…”

Section: Methodsmentioning

confidence: 99%

Influence of Graded Surface Decarburization of Automobile Forging Front Axle on the Bending Behavior Based on a Third-Order Shear Deformation Beam Theory

Hua

et al. 2022

Machines

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During the forging process of automobile front axle, the steel near the surface is often decarburized for a certain depth. The mechanical properties at the decarburization layer are graded and different from the inner area, influencing the bending behavior of axles under heavy loads. In this paper, the decarburized forging of front axle is regarded as a rectangular thick sandwich beam, composed of a homogeneous core and the functionally graded layer coated on both bottom and top surface. A Third-order Shear Deformation Theory (TSDT) is employed to investigate the static bending behaviors under two point−loads. The properties of sandwich FG material are represented with a piecewise power−law function, and the displacement field governing equations are derived through the virtual work principle. The Navier analytical method and numerical DQM procedures are employed to obtain the bending responses under simply supported boundary conditions, and the results are validated through the comparison with an example in the literature. Then, the transverse deflection, rotation, axial stress, and shear stress are studied in terms of different power−law exponents, decarburization depth, unsymmetrical decarburization depth, unbalance loading, and beam sectional dimension. The study reveals the influence of surface decarburization on the bending behavior of forged automobile front axles, and contributes to the optimization of structure design.

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Section: Methodsmentioning

confidence: 99%

Influence of Graded Surface Decarburization of Automobile Forging Front Axle on the Bending Behavior Based on a Third-Order Shear Deformation Beam Theory

Hua

et al. 2022

Machines

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show abstract

“…This article assumes that material parameters change continuously along the width direction (y). The power-law (Hadji et al, 2015) is given by:where p(y) represents a typical material property such as elastic modulus E, mass density ρ, and Poisson’s ratio υ. pt and pb represent the material property values of the topmost and bottommost surfaces of the FG beam, respectively, and n is the non-negative power-law index.…”

Section: Physical Model and Methodsmentioning

confidence: 99%

Vibration band gap characteristics of two-dimensional functionally graded grids using the spectral element method

Yan

Shi

Zhang

et al. 2022

Journal of Vibration and Control

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In this article, the band gap characteristics of two-dimensional periodic grid structures composed of functionally graded materials are studied. According to the first-order shear deformation theory and the spectral element method, the motion equation of the functionally graded beam is established at first, and then the spectral stiffness matrix of the lattice structure is assembled through the coordinate transformation matrix. With the aid of the Bloch theorem, the in-plane wave dispersion relation of periodic grid structures composed of two functionally graded materials is analyzed. The availability and accuracy of the band gap calculation method are verified by structural vibration transmission results based on the finite element method. In addition, the influence of the material parameters of the structure on the dispersion relation of the in-plane wave is obtained. The results extend the range of research on two-dimensional grids which can be applied to the design of filters.

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“…Li formulated an analytical solution to analyze the static and dynamic behaviours of FGM Timoshenko and Euler-Bernoulli beams [25]. Higher order theories were investigated to introduce more complex characteristics such as shear deformation and warping, a sample of research papers [26][27][28][29][30][31][32][33][34][35][36][37][38] are quoted here which provide a good introduction on the subject.…”

Section: Literature Surveymentioning

confidence: 99%

Dynamic Finite Element (DFE) Formulation of Functionally Graded Beams

Gee¹

2021

Preprint

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The Dynamic Finite Element (DFE) theory is applied to calculate the natural frequencies of Functionally Graded Material (FGM) beams. The formulation derived is based on Euler-Bernoulli beam theory and material grading is assumed to follow a power law variation through the thickness of the beam. Results from DFE are numerically validated against methods such as Classical Finite Element Method (FEM) and the Dynamic Stiffness Method (DSM), as well as other data found in literature. Commercial software was used to further validate the proposed DFE formulation. The test cases showed that DFE results displayed excellent agreement to published results. When compared to the FEM method, DFE showed higher accuracy while requiring fewer elements to converge to the solution. Finally some general comments are made on possible future research paths for DFE method on FGM beams.

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A new higher order shear deformation model for functionally graded beams

Cited by 20 publications

References 36 publications

Influence of Graded Surface Decarburization of Automobile Forging Front Axle on the Bending Behavior Based on a Third-Order Shear Deformation Beam Theory

Influence of Graded Surface Decarburization of Automobile Forging Front Axle on the Bending Behavior Based on a Third-Order Shear Deformation Beam Theory

Vibration band gap characteristics of two-dimensional functionally graded grids using the spectral element method

Dynamic Finite Element (DFE) Formulation of Functionally Graded Beams

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