Thermal buckling of functionally graded rectangular plates subjected to partial heating

Morimoto, Takuya; Tanigawa, Yoshinobu; Kawamura, Ryuusuke

doi:10.1016/j.ijmecsci.2006.03.015

Cited by 93 publications

(28 citation statements)

References 26 publications

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“…Thus, the boundary conditions (33) are all expressed in terms of N r and w. Finally, the Föppl-von Kármán equations of bimodular FGM thin plates in the axisymmetric case, Equations (31) and (32), may be solved under the boundary conditions (33), (36), and (37).…”

Section: Axisymmetric Casementioning

confidence: 99%

“…It seems to be unclear. Morimoto et al [36] and Abrate [37] noticed that there will be no stretching-bending coupling effect in constitutive equations if the reference surface is properly selected. Thereafter, based on physical neutral surface, Zhang and Zhou [38] and Zhang [39] carried out theoretical analyses to FGM plates and beams, respectively.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Non-Linear Bending of Functionally Graded Thin Plates with Different Moduli in Tension and Compression and Its General Perturbation Solution

Liu

et al. 2018

Applied Sciences

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Abstract:In this study, a set of Föppl-von Kármán equations for a bimodular functionally graded thin plate subjected to a uniformly distributed load is established, and its general perturbation solution in axisymmetric case is also obtained under different boundary conditions. First, the equation of equilibrium of the plate is established on the existence of the neutral layer when considering different properties in tension and compression. During the derivation of the consistency equation, the tensile effect in the thin plate with bimodular effect is fully taken into account. The perturbation method is used to solve the set of governing equations under different edge constraints, in which the central deflection and the load of the plate are taken as a perturbation parameter, respectively. The results indicate that the two selections for perturbation parameters are valid and consistent, and the two solutions are convenient for engineering application. This study also shows that the bimodular effect will modify the relation of load versus central deflection of the plate to some extent, and under the same edge constraint, the capacities resisting deformation in different cases of moduli depend on the relative magnitudes among the tensile modulus, the neutral layer modulus, and the compressive modulus.

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Section: Axisymmetric Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Non-Linear Bending of Functionally Graded Thin Plates with Different Moduli in Tension and Compression and Its General Perturbation Solution

Liu

et al. 2018

Applied Sciences

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“…[14][15][16][17][23][24][25][26][27]32]). The equilibrium equations of a rectangular plate can be obtained using principle of minimum total potential energy as [33] δ…”

Section: Equilibrium Equationsmentioning

confidence: 99%

“…Therefore, the stretching and bending equations of such plate are coupled. Morimoto et al [25], Abrate [26], Zhang and Zhou [27], Prakash et al [28] and Saidi and Jomehzadeh [29] showed that there is no stretching-bending coupling in constitutive equations if the reference surface is properly selected.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of functionally graded rectangular plates under nonlinearly varying in-plane loading resting on elastic foundation

Bodaghi

Saidi

2010

Arch Appl Mech

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In this research work, an exact analytical solution for buckling of functionally graded rectangular plates subjected to non-uniformly distributed in-plane loading acting on two opposite simply supported edges is developed. It is assumed that the plate rests on two-parameter elastic foundation and its material properties vary through the thickness of the plate as a power function. The neutral surface position for such plate is determined, and the classical plate theory based on exact neutral surface position is employed to derive the governing stability equations. Considering Levy-type solution, the buckling equation reduces to an ordinary differential equation with variable coefficients. An exact analytical solution is obtained for this equation in the form of power series using the method of Frobenius. By considering sufficient terms in power series, the critical buckling load of functionally graded plate with different boundary conditions is determined. The accuracy of presented results is verified by appropriate convergence study, and the results are checked with those available in related literature. Furthermore, the effects of power of functionally graded material, aspect ratio, foundation stiffness coefficients and in-plane loading configuration together with different combinations of boundary conditions on the critical buckling load of functionally graded rectangular thin plate are studied.

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“…Thus, stretching and bending deformations of FG beam are coupled. Some works (Ould Larbi et al 2013;Bousahla et al 2014;Yahoobi and Feraidoon 2010;Morimoto et al 2006;Bourada et al 2015) have shown that there is no stretching-bending coupling in constitutive equations if the reference surface is properly selected. In addition, in FGM fabrication, micro voids or porosities can occur within the materials during the process of sintering.…”

Section: Introductionmentioning

confidence: 99%

Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations

Atmane

Tounsi

Bernard

2015

Int J Mech Mater Des

161

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The novelty of this paper is the use of an efficient beam theory for bending, free vibration and buckling analysis of functionally graded material (FGM) beams on two-parameter elastic foundation. The present theory accounts for both shear deformation and thickness stretching effects by a parabolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the beam without requiring any shear correction factor. Due to porosities, possibly occurring inside FGMs during fabrication, it is therefore necessary to consider the vibration, bending and buckling behaviors of beams having porosities in this work. The equation of motion for FGM beams is obtained through Hamilton's principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. The validity of the present theory is investigated by comparing some of the present in literature. It can be concluded that the proposed theory is accurate and simple in solving the bending, free vibration and buckling behaviors of FGM sandwich beams.

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Thermal buckling of functionally graded rectangular plates subjected to partial heating

Cited by 93 publications

References 26 publications

Non-Linear Bending of Functionally Graded Thin Plates with Different Moduli in Tension and Compression and Its General Perturbation Solution

Non-Linear Bending of Functionally Graded Thin Plates with Different Moduli in Tension and Compression and Its General Perturbation Solution

Stability analysis of functionally graded rectangular plates under nonlinearly varying in-plane loading resting on elastic foundation

Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations

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