Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept

Mama Ahouel , Mohammed Sid Ahmed Houari , E.A. Adda Bedia , Abdelouahed Tounsi

Abstract

A nonlocal trigonometric shear deformation beam theory based on neutral surface position is developed for bending, buckling, and vibration of functionally graded (FG) nanobeams using the nonlocal differential constitutive relations of Eringen. The present model is capable of capturing both small scale effect and transverse shear deformation effects of FG nanobeams, and does not require shear correction factors. The material properties of the FG nanobeam are assumed to vary in the thickness direction. The equations of motion are derived by employing Hamilton\'s principle, and the physical neutral surface concept. Analytical solutions are presented for a simply supported FG nanobeam, and the obtained results compare well with those predicted by the nonlocal Timoshenko beam theory.

Key Words

nanobeam; nonlocal elasticity theory; bending; buckling; vibration; functionally graded materials; neutral surface position

Address

(1) Mama Ahouel, Mohammed Sid Ahmed Houari, E.A. Adda Bedia and Abdelouahed Tounsi — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
(2) Mohammed Sid Ahmed Houari — Département de génie civil, Université de Mascara, Algeria
(3) Abdelouahed Tounsi — Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, Faculté de Technologie, Département de génie civil, Algeria
(4) Abdelouahed Tounsi — Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria.

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