Thermal buckling analysis of shear deformable laminated orthotropic plates by differential quadrature

Moradi, Shapour; Mansouri, M.H.

doi:10.12989/scs.2012.12.2.129

Cited by 15 publications

(4 citation statements)

References 25 publications

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“…Numerical results given in the present paper render a benchmark for the analyses of FGM thick plates on elastic foundations in the future. We note that the present approach can be extended to study the thermal buckling of laminated orthotropic plates [Moradi and Mansouri (2012)] and the nonlinear analysis of FGM plates [Benatta et al (2013)]. …”

Section: Resultsmentioning

confidence: 99%

A New Simple Hyperbolic Shear Deformation Theory for Functionally Graded Plates Resting on Winkler–pasternak Elastic Foundations

Said¹,

Ameur

Bousahla³

et al. 2014

Int. J. Comput. Methods

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An improved simple hyperbolic shear deformation theory involving only four unknown functions, as against five functions in case of first or other higher-order shear deformation theories, is introduced for the analysis of functionally graded plates resting on a WinklerPasternak elastic foundation. The governing equations are derived by employing the principle of virtual work and the physical neutral surface concept. The accuracy of the present analysis is demonstrated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories.

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Section: Resultsmentioning

confidence: 99%

A New Simple Hyperbolic Shear Deformation Theory for Functionally Graded Plates Resting on Winkler–pasternak Elastic Foundations

Said¹,

Ameur

Bousahla³

et al. 2014

Int. J. Comput. Methods

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“…This theory does not satisfy the stress-free boundary conditions on the surfaces of the plate and requires an arbitrary shear correction factor. Many studies of the mechanical behavior of plates have been carried out using FSDT (see literature [7–10]). Yaghoobi and Yaghoobi [11] presented analytical solutions for the buckling of symmetric sandwich plates with FGM face sheets resting on an elastic foundation based on the first-order shear deformation plate theory and subjected to mechanical, thermal and also thermo-mechanical loads.…”

Section: Introductionmentioning

confidence: 99%

An analytical solution for bending, buckling and vibration responses of FGM sandwich plates

Meksi

Benyoucef

Mahmoudi

et al. 2017

Jnl of Sandwich Structures & Materials

103

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In this study, a new shear deformation plate theory is introduced to illustrate the bending, buckling and free vibration responses of functionally graded material sandwich plates. A new displacement field containing integrals is proposed which involves only four variables. Based on the suggested theory, the equations of motion are derived from Hamilton’s principle. This theory involves only four unknown functions and accounts for quasi-parabolic distribution of transverse shear stress. In addition, the transverse shear stresses are vanished at the top and bottom surfaces of the sandwich plate. The Navier solution technique is adopted to derive analytical solutions for simply supported rectangular sandwich plates. The accuracy and effectiveness of proposed model are verified by comparison with previous research. A detailed numerical study is carried out to examine the influence of the critical buckling loads, deflections, stresses, natural frequencies and sandwich plate type on the bending, buckling and free vibration responses of functionally graded sandwich plates.

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“…First-order shear deformation theory (Reissner 1945, Mindlin 1951 considers the transverse shear deformation effects, but needs a shear correction factor in order to satisfy the zero transverse shear stress boundary conditions at the top and bottom of the plate. Many studies of the mechanical behavior of plates have been carried out using FSDT (Moradi 2012, Menaa 2012, Yaghoubi 2013Gafour 2015, Baghdadi 2015, Rashidi 2012. To avoid the use of shear correction factors, several higher-order shear deformation plate theories have been proposed such as the theory propounded by Nelson and Lorch (1974) with nine unknowns, Lo et al (1977) with eleven unknowns, Bhi-maraddi and Stevens (1984) with five unknowns, Reddy (1984) with five unknowns.…”

Section: Introductionmentioning

confidence: 99%

Effects of thickness stretching in FGM plates using a quasi-3D higher order shear deformation theory

Adim¹,

Daouadji²

2016

Advances in materials Research

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In this paper, a higher order shear and normal deformation theory is presented for functionally graded material (FGM) plates. By dividing the transverse displacement into bending, shear and thickness stretching parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Indeed, the number of unknown functions involved in the present theory is only five, as opposed to six or even greater numbers in the case of other shear and normal deformation theories. The present theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of ail displacements across the thickness and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The obtained results are compared with three-dimensional and quasi-three-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates.

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Thermal buckling analysis of shear deformable laminated orthotropic plates by differential quadrature

Cited by 15 publications

References 25 publications

A New Simple Hyperbolic Shear Deformation Theory for Functionally Graded Plates Resting on Winkler–pasternak Elastic Foundations

A New Simple Hyperbolic Shear Deformation Theory for Functionally Graded Plates Resting on Winkler–pasternak Elastic Foundations

An analytical solution for bending, buckling and vibration responses of FGM sandwich plates

Effects of thickness stretching in FGM plates using a quasi-3D higher order shear deformation theory

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