Bending and buckling analysis of FGM plates resting on elastic foundations in hygrothermal environment

Zenkour, Ashraf M.; Radwan, Ahmed F.

doi:10.1007/s43452-020-00116-z

Cited by 23 publications

(3 citation statements)

References 54 publications

(61 reference statements)

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“…In literature, various theories are available for the analysis of composite, sandwich, and FGM structures under different loading conditions [12][13][14][15][16][17][18][19][20][21][22][23]. However, for the analysis of nanoplates, these theories must be modified in order to include size-dependent effects [24], as considered by a nonlocal strain gradient theory (NSGT), Eringen's nonlocal theory, modified couple stress theory (MCST), and so on.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal vibration of functionally graded nanoplates using a layerwise theory

Belarbi

Houari

et al. 2022

Mathematics and Mechanics of Solids

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This work studies the size-dependent free vibration response of functionally graded (FG) nanoplates using a layerwise theory. The proposed model supposes not only a higher-order displacement field for the core but also the first-order displacement field for the two face sheets, thereby maintaining an interlaminar displacement continuity among layers. Unlike the conventional layerwise models, the number of variables is kept fixed and does not increase for an increased number of layers. This is a very important feature compared to conventional layerwise models and facilitates significantly the engineering analyses. The material properties of the FG nanoplate are graded continuously through the thickness direction in accordance with a power-law function. The Eringen’s nonlocal elasticity theory is here adopted to relax the continuum axiom required in classical continuum mechanics and hence hopeful to capture the small size effects of naturally discrete nanoplates. The equations of motion of the problem are obtained via a classical Hamilton’s principle. The present layerwise model is implemented with a computationally efficient C0- continuous isoparametric serendipity elements and applied to solve a large-scale discrete numerical problem. The robustness and reliability of the developed finite element model are demonstrated by a comparative evaluation of results against predictions from literature. The comparative studies show that the proposed finite element model is: (a) free of shear locking, (b) accurate with a fast rate convergence for both thin and thick FG nanoplates, and (c) excellent in terms of numerical stability. Moreover, a detailed parametric analysis checks for the sensitivity of the vibration response of FG nanoplates to the aspect ratio, length-to-thickness ratio, nonlocal parameter, boundary conditions, power-law index, and modes shapes. Referential results are also reported, for the first time, for natural frequencies of FGM nanoplates which will serve as benchmarks for further computational investigations.

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Section: Introductionmentioning

confidence: 99%

Nonlocal vibration of functionally graded nanoplates using a layerwise theory

Belarbi

Houari

et al. 2022

Mathematics and Mechanics of Solids

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“…Singh and Harsha [61] developed closed‐form analytical solutions for the bending and buckling analysis of sigmoid FGM plates resting on elastic foundations using a four‐variable non‐polynomial HSDT. Zenkour and Radwan [62] presented hygro‐thermal effects on the bending and buckling analysis of FGM plates supported on Pasternak's foundations. In the above‐mentioned works, it is observed that the elastic foundations have a significant impact on the stresses and natural frequencies of the FGM plates.…”

Section: Introductionmentioning

confidence: 99%

Assessment of non‐polynomial shear deformation theories for the free vibration and transient analysis of plates with functionally‐graded materials supported on an elastic foundation

et al. 2023

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In this article, various non‐polynomial higher‐order shear deformation theories are applied for the first time to analyze the free vibration and transient responses of plates with functionally graded material (FGM) supported on an elastic foundation. The shear deformation theories account for the non‐linear variation of the transverse shear strains with various warping functions, namely trigonometric, inverse hyperbolic, and inverse trigonometric ones. These models also inherently satisfy the traction‐free boundary conditions of transverse shear stresses at the top and bottom surfaces of the plates and do not require any shear correction factor. A two‐parameter model, namely Winkler‐Pasternak's elastic foundation model, is utilized to develop the interaction between the FGM plates and the elastic medium. The governing equations of motion are obtained using Hamilton's principle and solved analytically using Navier's solution scheme. Furthermore, the transient responses of the plates are obtained using Newmark's average acceleration method. The applicability of the present theories is established by solving several numerical problems and validating the results with the solutions available in the literature. The effects of various parameters like span‐thickness ratios, aspect ratios, gradation coefficients, mechanical loads, and foundation stiffness on the fundamental frequencies and the transient responses of the plates are thoroughly investigated. The comparison of the results reveals the efficiency of the non‐polynomial functions, and the capability of efficient prediction of the structural responses of the FGM plates at a similar computational cost compared to established models in the literature. Furthermore, the results show that the stiffness of the elastic foundation can tweak the stiffness characteristics of the FGM plate resulting in significant changes in the natural frequencies and more controlled displacement‐time responses.

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“…They derived nonlinear governing equations for temperature, moisture content, and displacement fields and solved them through the differential quadrature method. Zenkour also studied how the thermal and hygrometric fields affect the bending and the buckling of plates embedding FGMs [39]. In this case, also, the authors considered a material grading in the thickness direction of the structure.…”

Section: Introductionmentioning

confidence: 99%

3D Stress Analysis of Multilayered Functionally Graded Plates and Shells under Moisture Conditions

Brischetto

Torre

2022

Applied Sciences

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This paper presents the steady-state stress analysis of single-layered and multilayered plates and shells embedding Functionally Graded Material (FGM) layers under moisture conditions. This solution relies on an exact layer-wise approach; the formulation is unique despite the geometry. It studies spherical and cylindrical shells, cylinders, and plates in an orthogonal mixed curvilinear coordinate system (α, β, z). The moisture conditions are defined at the external surfaces and evaluated in the thickness direction under steady-state conditions following three procedures. This solution handles the 3D Fick diffusion equation, the 1D Fick diffusion equation, and the a priori assumed linear profile. The paper discusses their assumptions and the different results they deliver. Once defined, the moisture content acts as an external load; this leads to a system of three non-homogeneous second-order differential equilibrium equations. The 3D problem is reduced to a system of partial differential equations in the thickness coordinate, solved via the exponential matrix method. It returns the displacements and their z-derivatives as a direct result. The paper validates the model by comparing the results with 3D analytical models proposed in the literature and numerical models. Then, new results are presented for one-layered and multilayered FGM plates, cylinders, and cylindrical and spherical shells, considering different moisture contents, thickness ratios, and material laws.

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Bending and buckling analysis of FGM plates resting on elastic foundations in hygrothermal environment

Cited by 23 publications

References 54 publications

Nonlocal vibration of functionally graded nanoplates using a layerwise theory

Nonlocal vibration of functionally graded nanoplates using a layerwise theory

Assessment of non‐polynomial shear deformation theories for the free vibration and transient analysis of plates with functionally‐graded materials supported on an elastic foundation

3D Stress Analysis of Multilayered Functionally Graded Plates and Shells under Moisture Conditions

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