Analytical Solution of Bending, Buckling, and Vibration of Functionally Graded Nanobeams based on Nonlocal Elasticity

• Published in: Tekirdag Namik Kemal University Institute of Natural and Applied Sciences
• Main Author: UYMAZ, Bahar
• Format: Journal Article
• Language: English
• Published: 30.04.2023
• ISSN: 2822-4566; 2822-4566
• DOI: 10.55848/jbst.2023.29

Navier solution presented for bending, buckling, and free vibration of simply supported functionally graded nanobeams based on generalized shear deformation theory. The results are obtained for parabolic shear deformation theory corresponding to Reddy beam theory using nonlocal differential constitutive equations which were formulated by Eringen [1,2,3]. The material properties of the functionally graded nanobeam vary through the thickness direction according to a simple power law. Effects of the nonlocal parameter, different material composition and length-to-thickness ratio on the maximum deflection, critical buckling load, and natural frequencies of the nanobeam are investigated. The results show that the scale effects, material composition, and dimensional changes are affected by considered parameters. Nonlocal elasticity theory predicts softening material behavior compared to classical elasticity theory because it takes into account the effects of long-range interactions between material particles. As a result of this, the maximum deflections, critical buckling loads, and natural frequencies obtained by the classical theory are higher than obtained by the nonlocal theory in all considered conditions.