Buckling of Functionally Graded Nanobeams Based on the Nonlocal New First-Order Shear Deformation Beam Theory

Houari, Mohammed Sid Ahmed; Bousahla, Abdelmoumen Anis; Bessaim, Aicha; Bedia, E.A. Adda; Tounsi, Abdelouahed

doi:10.1051/matecconf/20141101024

Cited by 4 publications

(2 citation statements)

References 10 publications

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“…where 0 u , 0 v , and 0 w are three unknown displacement functions of midplane of the plate and β is a parameter of the present displacement model. ) (z f is a shape function representing the distribution of the transverse shear strains and shear stresses through the thickness of the plate and is given as [65]:…”

Section: Kinematics Of the Present Plate Modelmentioning

confidence: 99%

Buckling Analysis of Orthotropic Nanoscale Plates Resting on Elastic Foundations

Kadari

Bessaim

Tounsi

et al. 2018

JNanoR

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This work presents the buckling investigation of embedded orthotropic nanoplates by using a new hyperbolic plate theory and nonlocal small-scale effects. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modeled with only three unknowns and three governing equation as the case of the classical plate theory (CPT) and which is even less than the first order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Nonlocal differential constitutive relations of Eringen is employed to investigate effects of small scale on buckling of the rectangular nanoplate. The elastic foundation is modeled as two-parameter Pasternak foundation. The equations of motion of the nonlocal theories are derived and solved via Navier's procedure for all edges simply supported boundary conditions. The proposed theory is compared with other plate theories. Analytical solutions for buckling loads are obtained for single-layered graphene sheets with isotropic and orthotropic properties. The results presented in this study may provide useful guidance for design of orthotropic graphene based nanodevices that make use of the buckling properties of orthotropic nanoplates. Verification studies show that the proposed theory is not only accurate and simple in solving the buckling nanoplates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns. Keywords: Buckling; orthotropic nanoplates; a simple 3-unknown theory; nonlocal elasticity theory; Pasternak’s foundations. * Corresponding author; Email-tou_abdel@yahoo.com

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Section: Kinematics Of the Present Plate Modelmentioning

confidence: 99%

Buckling Analysis of Orthotropic Nanoscale Plates Resting on Elastic Foundations

Kadari

Bessaim

Tounsi

et al. 2018

JNanoR

View full text Add to dashboard Cite

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“…Rychlewska (2014) presented the critical buckling loads for axially functionally graded (FG) beams subjected to a distributed axial load and found that the critical buckling loads of a homogeneous beam calculated by the proposed approach were in good agreement with those available in literature. Houari et al (2013) investigated the size-dependent buckling behaviour of functionally graded (FG) nanobeams on the basis of the nonlocal continuum model. The effects of the nonlocal parameter, aspect ratio, various material compositions on the stability responses of the FG nanobeams were discussed.…”

Section: Introductionmentioning

confidence: 99%

Mechanical buckling of functionally graded polyethylene/clay nanocomposites columns based on the Engesser-Timoshenko beam theory

Yas

Khorramabadi

2018

jtam

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This paper deals with mechanical buckling of polyethylene/clay nanocomposite beams of functionally graded and uniformly distributed of nanoclay subjected to axial compressive load with simply supported conditions at both ends. The Young moduli of functionally graded and uniformly distributed nanocomposites are calculated using a genetic algorithm procedure and then compared with experimental results. The formulation is modified to include the effect of nanoparticles weight fractions in the calculation of the Young modulus for uniform distribution. Also, it is modified to take into account the Young modulus as a function of the thickness coordinate. The displacement field of the beam is assumed based on the Engesser-Timoshenko beam theory. Applying the Hamilton principle, governing equations are derived. The influence of nanoparticles on the buckling load of the beam is presented. To investigate the accuracy of the present analysis, a compression study with the experimental results is carried out.

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Buckling capacity of functionally graded beams: A comparative study of different shear deformation beam theories

Selmi

2019

Int. J. Comp. Mat. Sci. Eng.

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This paper investigates the postbuckling response of simply supported functionally graded beams under axial loading using several beam theories; classical beam theory, CBT, Timoshenko beam theory, TBT and parabolic shear deformation beam theory, PSDBT. Hamilton’s principle is used to derive the governing equations which are solved by closed-form method. It is assumed that the Young’s modulus is varying continuously in the thickness direction according to power-law form while all other material properties are taken to be constant. The effects of the reinforcement distribution, the beam edge-to-thickness ratio and the phase contrast (ratio of the reinforcement Young’s modulus to the matrix Young’s modulus) on the postbuckling behavior and critical buckling load of functionally graded beam are studied. Results demonstrate the important contribution of the shear effect to both the buckling and postbuckling behaviors. Finally, the combinations of reinforcement distribution, beam edge-to-thickness ratio and phase contrast that correspond to the highest and the lowest buckling capacities are identified.

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Buckling of Functionally Graded Nanobeams Based on the Nonlocal New First-Order Shear Deformation Beam Theory

Cited by 4 publications

References 10 publications

Buckling Analysis of Orthotropic Nanoscale Plates Resting on Elastic Foundations

Buckling Analysis of Orthotropic Nanoscale Plates Resting on Elastic Foundations

Mechanical buckling of functionally graded polyethylene/clay nanocomposites columns based on the Engesser-Timoshenko beam theory

Buckling capacity of functionally graded beams: A comparative study of different shear deformation beam theories

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