Theoretical buckling analysis of inhomogeneous plates under various thermal gradients and boundary conditions

Laid Lekouara, Belgacem Mamen, Abdelhakim Bouhadra, Abderahmane Menasria, Kouider Halim Benrahou, Abdelouahed Tounsi and Mohammed A. Al-Osta

Abstract

This study investigates the theoretical thermal buckling analyses of thick porous rectangular functionally graded (FG) plates with different geometrical boundary conditions resting on a Winkler-Pasternak elastic foundation using a new higherorder shear deformation theory (HSDT). This new theory has only four unknowns and involves indeterminate integral variables in which no shear correction factor is required. The variation of material properties across the plate's thickness is considered continuous and varied following a simple power law as a function of volume fractions of the constituents. The effect of porosity with two different types of distribution is also included. The current formulation considers the Von Karman nonlinearity, and the stability equations are developed using the virtual works principle. The thermal gradients are involved and assumed to change across the FG plate's thickness according to nonlinear, linear, and uniform distributions. The accuracy of the newly proposed theory has been validated by comparing the present results with the results obtained from the previously published theories. The effects of porosity, boundary conditions, foundation parameters, power index, plate aspect ratio, and side-to-thickness ratio on the critical buckling temperature are studied and discussed in detail.

Key Words

FG plates; porosity; thermal buckling; Von Karman nonlinearity

Address

Laid Lekouara: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Department of Civil Engineering, Faculty of Science and Technology, University of Abbès Laghrour Khenchela, Algeria Belgacem Mamen: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Department of Civil Engineering, Faculty of Science and Technology, University of Abbès Laghrour Khenchela, Algeria Abdelhakim Bouhadra: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Department of Civil Engineering, Faculty of Science and Technology, University of Abbès Laghrour Khenchela, Algeria Abderahmane Menasria: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Department of Civil Engineering, Faculty of Science and Technology, University of Abbès Laghrour Khenchela, Algeria Kouider Halim Benrahou: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Princess Nourah bint Abdulrahman University, Saudi Arabia Abdelouahed Tounsi: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia Mohammed A. Al-Osta: Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia; Interdisciplinary Research Center for Construction and Building Materials, KFUPM, Dhahran, Saudi Arabia

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