Mechanical and thermal buckling analysis of P-FG plate using an innovative HSDT and Airy stress function

Ahmed Bakoura , Aicha Remil , Aicha Bessaim , Mohammed Sid Ahmed Houari , Sahla Meriem , Ibka Mohamed Soufiane , Abdelouahed Tounsi

Abstract

In this article, the mechanical and thermal buckling analysis of simply-supported functionally graded plates resting on an elastic foundation is conducted using an innovative higher shear deformation theory (HSDT) in conjunction with the Airy stress function method. The key novelty of this work lies in the exact resolution of the equilibrium equations through the Airy stress function, eliminating the need for shear correction factors, and in the introduction of a new transverse shear function that ensures a parabolic variation of transverse shear stresses across the thickness while naturally satisfying the stress-free boundary conditions at the surfaces. Three types of thermal loads are considered: uniform, linear, and nonlinear distributions through the thickness. The material properties of the plate vary according to a power-law distribution based on the volume fraction of its constituents. Numerical results are presented to assess the effects of the power-law index the foundation stiffness and geometric ratios on the critical buckling load and the critical buckling temperature, highlighting the accuracy and efficiency of the proposed methodology.

Key Words

airy stress function; analytical modeling; buckling; computational modeling; functionally graded plate; refined plate theory

Address

Ahmed Bakoura — Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes, Algeria; Département de Génie Civil, Faculté d'Architecture et de Génie Civil, Université des Sciences et de la Technologie d'Oran, BP 1505 El M'naouer, USTO, Oran, Algeria
Aicha Remil — Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli, B.P. 305, R.P. 29000 Mascara, Algeria
Aicha Bessaim — Département de Génie Civil, Faculté d'Architecture et de Génie Civil, Université des Sciences et de la Technologie d'Oran, BP 1505 El M'naouer, USTO, Oran, Algeria; Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli, B.P. 305, R.P. 29000 Mascara, Algeria
Mohammed Sid Ahmed Houari — Laboratoire Signaux et Images (LSI), University of Science and Technology of Oran, Mohammed Boudiaf, Bir El Djir 31000, Algeria
Sahla Meriem — Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli, B.P. 305, R.P. 29000 Mascara, Algeria
Ibka Mohamed Soufiane — Laboratoire Signaux et Images (LSI), University of Science and Technology of Oran, Mohammed Boudiaf, Bir El Djir 31000, Algeria
Abdelouahed Tounsi — Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes, Algeria

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