A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates

Hafid Khetir , Mohamed Bachir Bouiadjra , Mohammed Sid Ahmed Houari , Abdelouahed Tounsi , S.R. Mahmoud

Abstract

In this paper, a new nonlocal trigonometric shear deformation theory is proposed for thermal buckling response of nanosize functionally graded (FG) nano-plates resting on two-parameter elastic foundation under various types of thermal environments. This theory uses for the first time, undetermined integral variables and it contains only four unknowns, that is even less than the first shear deformation theory (FSDT). It is considered that the FG nano-plate is exposed to uniform, linear and sinusoidal temperature rises. Mori-Tanaka model is utilized to define the gradually variation of material properties along the plate thickness. Nonlocal elasticity theory of Eringen is employed to capture the size influences. Through the stationary potential energy the governing equations are derived for a refined nonlocal four-variable shear deformation plate theory and then solved analytically. A variety of examples is proposed to demonstrate the importance of elastic foundation parameters, various temperature fields, nonlocality, material composition, aspect and side-to-thickness ratios on critical stability temperatures of FG nano-plate.

Key Words

nonlocal elasticity theory; FG nanoplate; thermal buckling refined theory; elastic foundation

Address

Hafid Khetir — Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Faculté de Technologie, Département de Génie Civil, Université de Sidi Bel Abbes, Algeria
Mohamed Bachir Bouiadjra — Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Faculté de Technologie, Département de Génie Civil, Université de Sidi Bel Abbes, Algeria; Algerian National Thematic Agency of Research in Science and Technology (ATRST), Algeria
Mohammed Sid Ahmed Houari — Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Faculté de Technologie, Département de Génie Civil, Université de Sidi Bel Abbes, Algeria; Department of Civil Engineering, Université Mustapha Stambouli de Mascara, Mascara, Algeria
Abdelouahed Tounsi — Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals,31261 Dhahran, Eastern Province, Saudi Arabia; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Algerian National Thematic Agency of Research in Science and Technology (ATRST), Algeria
S.R. Mahmoud — Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

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