A non-polynomial four variable refined plate theory for free vibration of functionally graded thick rectangular plates on elastic foundation

Meftah, A.; Bakora, Ahmed; Zaoui, Fatima Zohra; Tounsi, Abdelouahed; Bedia, E.A. Adda

doi:10.12989/scs.2017.23.3.317

Cited by 11 publications

(8 citation statements)

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“…The span-to-thickness ratio of the plate is considered to be l/h = 100/15. The present solutions are compared with results from Akavci [84], Meftah et al [59], Hosseini et al [85], Mantari et al [86], and Zaoui et al [80]. It can be observed in this table that the present solutions produced with IHSDT, SDTSF, and ITSDT have excellent accuracy, thus confirming the current shear deformation models.…”

Section: Resultssupporting

confidence: 78%

“…The FG plate is a rectangular plate with an aspect ratio (l/b) of 1.5. The current solutions are compared with results from Akavci [84], Meftah et al [59], Hosseini et al [85], and Zaoui et al [80,87]. The excellent accuracy of IHSDT, SDTSF, and ITSDT is again verified in this example.…”

Section: Resultsmentioning

confidence: 59%

“…The current solutions are compared with results from Akavci [84], Meftah et al. [59], Hosseini et al. [85], and Zaoui et al.…”

Section: Resultsmentioning

confidence: 99%

“…Mechab et al [58] investigated the effects of porosities on the free vibration response of FGM nanoplates supported on elastic foundations. Meftah et al [59] studied the free vibration response of FGM plates supported by Winkler-Pasternak's foundation. Gupta and Talha [60] presented the finite element (FE) solutions for geometrically imperfect FGM plates supported on elastic foundations.…”

Section: Introductionmentioning

confidence: 99%

“…Meftah et al. [59] studied the free vibration response of FGM plates supported by Winkler‐Pasternak's foundation. Gupta and Talha [60] presented the finite element (FE) solutions for geometrically imperfect FGM plates supported on elastic foundations.…”

Section: Introductionmentioning

confidence: 99%

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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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