Coupled buckling behavior of two-directional coated functionally graded nanobeams resting on Winkler-Pasternak-Kerr foundations

Ahmed Amine Daikh , Aicha Remil , Aicha Bessaim , Meriem Sahla , Mohammed Sid Ahmed Houari , Mohamed Oujedi Belarbi , Ahmed Drai , Mohamed Guerroudj , Mohamed A. Eltaher

Abstract

A novel refined shear deformation theory with three variables is proposed to investigate the buckling behavior of two-directional coated functionally graded nanobeams. The displacement field is formulated based on the principles of Euler-Bernoulli beam theory. This study examines two distinct categories of coated functionally graded nanobeams: Hardcore and Softcore nanobeams. Three material distribution patterns are considered: a bidirectional configuration, a unidirectional transverse distribution, and a unidirectional axial arrangement. The strain gradient nonlocal elasticity theory is implemented to account for small-scale effects. The equilibrium equations governing nanobeams are derived using the total potential energy principle. A refined solution approach, leveraging Galerkin's method, addresses various boundary conditions efficiently. The functionally graded beam is modelled on an elastic foundation described by the Winkler, Pasternak, and Kerr models. The obtained results show that the buckling behavior of the coated nanobeams is significantly influenced by the coating layer's thickness, material properties, boundary conditions, and gradient distribution. We find that the two-directional coating configuration can improve buckling resistance and reduce sensitivity to loading direction compared to traditional one-directional coatings. The findings of this study have important implications for the design and optimisation of nanoscale structures and devices, particularly in applications where mechanical stability and reliability are critical, such as in nanoelectromechanical systems (NEMS) and nanoscale sensors.

Key Words

buckling; complex elastic foundation; small scale effect; two-directional FGM

Address

Ahmed Amine Daikh — Artificial Intelligence Laboratory for Mechanical and Civil Structures, and Soil, University of Naama, P.O. Box 66, 45000 Naama, 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, 29000 Mascara, 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, 29000 Mascara, Algeria
Aicha Bessaim — 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, 29000 Mascara, Algeria; Faculty of Architecture and Civil Engineering, USTO, BP 155, Oran El Mnaoer, Oran, Algeria
Meriem Sahla — 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, 29000 Mascara, Algeria
Mohammed Sid Ahmed Houari — 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, 29000 Mascara, Algeria
Mohamed Oujedi Belarbi — Laboratoire de Recherche en Génie Civil, LRGC, Université de Biskra, B.P. 145, 07000 Biskra, Algeria
Ahmed Drai — Laboratory of Applied Biomechanics and Biomaterials, EN Oran, BP1513 El Mnaour, 31000 Oran, Algeria; Department of Mechanical Engineering, University of Mustapha Stambouli, Mascara, Algeria
Mohamed Guerroudj — Laboratory of Applied Biomechanics and Biomaterials, EN Oran, BP1513 El Mnaour, 31000 Oran, Algeria
Mohamed A. Eltaher — Mechanical Design and Production Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt; Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabi

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