Surface Effects on Large Deflection of a Curved Elastic Nanobeam Under Static Bending

Abstract

Curved structures are common shapes used in practical engineering. In this paper, the large deflection behavior of a curved elastic nanobeam with rectangular cross-section under static bending is investigated. Surface stresses in the curved nanobeam are considered as an external load and derived on the basis of the general Young-Laplace equation. The governing equations for the large deflection of the curved nanobeam with surface effect are established. By using the shooting method, the boundary value problem is solved numerically. Some numerical examples are given for cantilever, simply supported, and fixed–fixed nanobeams with positive and negative residual surface stresses. It is found that nanobeams in the presence of surface effect may be stiffer or more flexible, which is related to the residual surface stress, initial curvature of the nanobeam, the externally applied load, and boundary conditions. For nanobeams with smaller cross-sectional sizes, the height of the nanobeam can affect the deflection of the nanobeam considerably and the influence of the width of the nanobeam is negligible. The findings in the present investigation are helpful in understanding the mechanical behavior of curved nanobeams with surface effects.