A new higher-order shear deformation theory for static, buckling and free vibration analysis of functionally graded sandwich beams

Nguyen, Thanh Thuy; Nguyen, Ba-Duy

doi:10.1177/1099636215589237

Cited by 82 publications

(26 citation statements)

References 26 publications

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“…The power-law index of the facesheets is 0. The transverse deflection (w) at mid-span, normal stresses (σ xx ) at the top surface of the mid-span, transverse shear stress (σ xz ) at mid-plane at the left end, and natural frequencies of the sandwich beam are calculated and compared with the results from [59] in the following dimensionless form: Table 2 tabulates the dimensionless results, which show excellent consistency between the present results and the published results based on a high-order shear deformation theory. Meanwhile, 6 is a reasonable number of Chebyshev polynomial terms, which is sufficiently large to obtain accurate results.…”

Section: Convergence and Validation Studiesmentioning

confidence: 99%

Bending and Elastic Vibration of a Novel Functionally Graded Polymer Nanocomposite Beam Reinforced by Graphene Nanoplatelets

Wang

Xie

et al. 2019

Nanomaterials

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A novel functionally graded (FG) polymer-based nanocomposite reinforced by graphene nanoplatelets is proposed based on a new distribution law, which is constructed by the error function and contains a gradient index. The variation of the gradient index can result in a continuous variation of the weight fraction of graphene nanoplatelets (GPLs), which forms a sandwich structure with graded mechanical properties. The modified Halpin–Tsai micromechanics model is used to evaluate the effective Young’s modulus of the novel functionally graded graphene nanoplatelets reinforced composites (FG-GPLRCs). The bending and elastic vibration behaviors of the novel nanocomposite beams are investigated. An improved third order shear deformation theory (TSDT), which is proven to have a higher accuracy, is implemented to derive the governing equations related to the bending and vibrations. The Chebyshev–Ritz method is applied to describe various boundary conditions of the beams. The bending displacement, stress state, and vibration frequency of the proposed FG polymer-based nanocomposite beams under uniformly distributed loads are provided in detail. The numerical results show that the proposed distributions of GPL nanofillers can lead to a more effective pattern of improving the mechanical properties of GPL-reinforced composites than the common ones.

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Section: Convergence and Validation Studiesmentioning

confidence: 99%

Bending and Elastic Vibration of a Novel Functionally Graded Polymer Nanocomposite Beam Reinforced by Graphene Nanoplatelets

Wang

Xie

et al. 2019

Nanomaterials

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“…The free vibration and buckling behavior of the two directional FGBs can be investigated by using Eqs. 18and (19).…”

Section: Solution Proceduresmentioning

confidence: 99%

“…The simplest model is the FSBT which does not satisfy the zero traction boundary conditions at the top and the bottom surfaces of the beam; however a shear correction factor is required [1][2][3][4][5][6]. This leads to the proposition of the HSBT theories which refined the distribution of the transverse shear stress; ultimately no shear correction factor is needed [7][8][9][10][11][12][13][14][15][16][17][18][19]. On the other hand, HSBT theories do not consider the normal strain effect which becomes very important and should be considered for thick conventional FGBs.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a Four-Unknown Shear and Normal Deformable Beam Theory

Karamanlı¹

2018

ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY a - Applied Sciences and Engineering

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This study presents the free vibration and buckling behavior of two directional (2D) functionally graded beams (FGBs) under arbitrary boundary conditions (BCs) for the first time. A four-known shear and normal deformation (Quasi-3D) theory where the axial and transverse displacements are assumed to be cubic and parabolic variation through the beam depth is employed based on the framework of the Ritz formulation. The equations of motion are derived from Lagrange's equations. The developed formulation is validated by solving a homogeneous beam problem and considering different aspect ratios and boundary conditions. The obtained numerical results in terms of dimensionless fundamental frequencies and dimensionless first critical buckling loads are compared with the results from previous studies for convergence studies. The material properties of the studied problems are assumed to vary along both longitudinal and thickness directions according to the power-law distribution. The axial, bending, shear and normal displacements are expressed in polynomial forms with the auxiliary functions which are necessary to satisfy the boundary conditions. The effects of shear deformation, thickness stretching, material distribution, aspect ratios and boundary conditions on the free vibration frequencies and critical buckling loads of the 2D-FGBs are investigated.

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“…Free vibration analysis of FGM Sandwich beams was carried out by Amirani et al [23] and Yang et al [24] using the element-free Galerkin and mesh-free radial point interpolation methods. Vo et al [25][26][27] and Nguyen et al [28][29][30] presented various higher-order shear deformation theories for buckling, free vibration, and bending analyses of FGSW beams. e transverse displacement in the theories is split into bending and shear parts, and the effect of the thickness stretching is taken into account.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Behavior of a Bidirectional Functionally Graded Sandwich Beam under Nonuniform Motion of a Moving Load

Nguyen¹,

Le³

et al. 2020

Shock and Vibration

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A bidirectional functionally graded Sandwich (BFGSW) beam model made from three distinct materials is proposed and its dynamic behavior due to nonuniform motion of a moving point load is investigated for the first time. The beam consists of three layers, a homogeneous core, and two functionally graded face sheets with material properties varying in both the thickness and longitudinal directions by power gradation laws. Based on the first-order shear deformation beam theory, a finite beam element is derived and employed in computing dynamic response of the beam. The element which used the shear correction factor is simple with the stiffness and mass matrices evaluated analytically. The numerical result reveals that the material distribution plays an important role in the dynamic response of the beam, and the beam can be designed to meet the desired dynamic magnification factor by appropriately choosing the material grading indexes. A parametric study is carried out to highlight the effects of the material distribution, the beam layer thickness and aspect ratios, and the moving load speed on the dynamic characteristics. The influence of acceleration and deceleration of the moving load on the dynamic behavior of the beam is also examined and highlighted.

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A new higher-order shear deformation theory for static, buckling and free vibration analysis of functionally graded sandwich beams

Cited by 82 publications

References 26 publications

Bending and Elastic Vibration of a Novel Functionally Graded Polymer Nanocomposite Beam Reinforced by Graphene Nanoplatelets

Bending and Elastic Vibration of a Novel Functionally Graded Polymer Nanocomposite Beam Reinforced by Graphene Nanoplatelets

Free Vibration and Buckling Analysis of Two Directional Functionally Graded Beams Using a Four-Unknown Shear and Normal Deformable Beam Theory

Dynamic Behavior of a Bidirectional Functionally Graded Sandwich Beam under Nonuniform Motion of a Moving Load

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