A review of mechanical analyses of rectangular nanobeams and single-, double-, and multi-walled carbon nanotubes using Eringen’s nonlocal elasticity theory

Abstract

This article is intended to present an overview of various mechanical analyses of rectangular nanobeams and single-, double-, and multi-walled (SW-, DW-, and MW-) carbon nanotubes (CNTs) with combinations of simply supported, free, and clamped edge conditions embedded or non-embedded in an elastic medium, including bending, free vibration, buckling, coupled thermo-elastic and hygro-thermo-elastic, dynamic instability, wave propagation, geometric nonlinear bending, and large amplitude vibration analyses. This review introduces the development of various nonlocal beam and shell theories incorporating Eringen’s nonlocal elasticity theory and the application of strong- and weak-form-based formulations to the current issue. Based on the principle of virtual displacements and Reissner’s mixed variational theorem, the corresponding strong- and weak-form formulations of the local Timoshenko beam theory are reformulated for the free vibration analysis of rectangular nanobeams and SW-, DW-, and MW-CNTs, and presented for illustrative purposes. A comparative study of the results obtained using assorted nonlocal beam and shell theories in combination with the analytical and numerical methods is carried out.