Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation

Abdelillah Benahmed , Bouazza Fahsi , Abdelnour Benzair , Mohamed Zidour , Fouad Bourada , Abdelouahed Tounsi

Abstract

This paper presents an efficient higher-order nonlocal beam theory for the Critical buckling, of functionally graded (FG) nanobeams with porosities that may possibly occur inside the functionally graded materials (FG) during their fabrication, the nonlocal elastic behavior is described by the differential constitutive model of Eringen. The material properties of (FG) nanobeams with porosities are assumed to vary through the thickness according to a power law. The governing equations of the functionally graded nanobeams with porosities are derived by employing Hamilton\'s principle. Analytical solutions are presented for a simply supported FG nanobeam with porosities. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature, Illustrative examples are given also to show the effects of porosity volume fraction, and thickness to length ratios on the critical buckling of the FG beams.

Key Words

nanobeam; nonlocal; higher-order; buckling; functionally graded; porosity

Address

Abdelillah Benahmed, Bouazza Fahsi and Abdelnour Benzair — Laboratory de Modelisation et Simulation Multi-echaelle, Département de Physique, Faculte des Science Exactes Universite de Sidi Bel Abbes, Algeria
Mohamed Zidour — Civil Engineering Department, Universite Ibn Khaldoun, BP 78 Zaaroura, 14000 Tiaret, Algeria
Fouad Bourada — Civil Engineering Department, Laboratory of Materials et Hydrology, University of Sidi Bel Abbes, BP 89 Cite Ben M\'hidi, 22000 Sidi Bel Abbes, Faculty of Technology, Algeria
Abdelouahed Tounsi — 1) Civil Engineering Department, Laboratory of Materials et Hydrology, University of Sidi Bel Abbes, BP 89 Cite Ben M\'hidi, 22000 Sidi Bel Abbes, Faculty of Technology, Algeria 2) Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

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