Generalized power-law exponent based shear deformation theory for free vibration of functionally graded beams

Pradhan, Karan Kumar; Chakraverty, Snehashish

doi:10.1016/j.amc.2015.07.032

Cited by 28 publications

(7 citation statements)

References 42 publications

(76 reference statements)

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“…Tables 2-5. It can be seen that the current solutions are in excellent agreement with previous studies for both vibration ( [2], [4], [10], [14]) and buckling problems ( [10], [33] (Fig. 4), the first, second, third and fourth buckling occurs at � = 103.732, 161.925, 237.383 and 274.285, respectively.…”

Section: Buckling Analysissupporting

confidence: 79%

“…Due to the excellent properties in mechanical and thermal behaviours, a wide range of application for functionally graded (FG) structures can be found in different fields, leading to the intensive study in many types of FG structures in the last three decades. Chebyshev collocation method, finite element method and differential quadrature method [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. For analytical approaches, a Navier solution has been widely used to study various mechanical behaviours of simply supported beams [16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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An analytical method for the vibration and buckling of functionally graded beams under mechanical and thermal loads

Trinh

Vo²,

Thai

et al. 2016

Composites Part B: Engineering

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An analytical method for vibration and buckling behaviours of Functionally Graded (FG) beams with various boundary conditions under mechanical and thermal loads is presented. Based on linear straindisplacement relations, equations of motion and essential boundary conditions are derived from Hamilton's principle. In order to account for thermal effects, three cases of the temperature rise through the thickness, which are uniform, linear and nonlinear, are considered. The exact solutions are derived using the state space approach. Numerical results are presented to investigate the effects of boundary conditions, temperature distributions, material parameters and slenderness ratios on the critical temperatures, critical buckling loads, and natural frequencies as well as load-frequencies curves, temperature-frequencies curves of FG beams under thermal/mechanical loads. The accuracy and effectiveness of proposed model are verified by comparison with previous research.

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Section: Buckling Analysissupporting

confidence: 79%

Section: Introductionmentioning

confidence: 99%

An analytical method for the vibration and buckling of functionally graded beams under mechanical and thermal loads

Trinh

Vo²,

Thai

et al. 2016

Composites Part B: Engineering

View full text Add to dashboard Cite

show abstract

“…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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“…22 proposed a hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded sandwich and composite plates. In addition, Pradhan and Chakraverty 23 developed a generalized power-law exponent-based shear deformation theory for dynamic analysis of FGM beams subjected to different sets of boundary conditions. In terms of the inverse trigonometric shear deformation theory, Kulkarni et al.…”

Section: Introductionmentioning

confidence: 99%

A refined sinusoidal model for functionally graded plates subjected to thermomechanical loading

Ren

2018

Journal of Composite Materials

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A refined sinusoidal model considering transverse normal strain has been developed for thermoelastic analysis of functionally graded material plate. Although transverse normal strain has been considered, the additional displacement parameters are not increased as transverse normal strain only includes the thermal expansion coefficient and thermal loading. Moreover, the merit of the previous sinusoidal model satisfying tangential stress-free boundary conditions on the surfaces can be maintained. It is important that the effects of transverse normal thermal deformation are incorporated in the in-plane displacement field, which can actively influence the accuracy of in-plane stresses. To assess the performance of the proposed model, the thermoelastic behaviors of functionally graded material plates with various configurations have been analyzed. Without increase of displacement variables, accuracy of the proposed model can be significantly improved by comparing to the previous sinusoidal model. Agreement between the present results and quasi-dimensional solutions are very good, and the proposed model only includes the five displacement variables which can illustrate the accuracy and effectiveness of the present model. In addition, new results using several models considered in this paper have been presented, which can serve as a reference for future investigations.

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Generalized power-law exponent based shear deformation theory for free vibration of functionally graded beams

Cited by 28 publications

References 42 publications

An analytical method for the vibration and buckling of functionally graded beams under mechanical and thermal loads

An analytical method for the vibration and buckling of functionally graded beams under mechanical and thermal loads

Dynamic Finite Element (DFE) Formulation of Functionally Graded Beams

A refined sinusoidal model for functionally graded plates subjected to thermomechanical loading

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