Eringen's small length scale coefficient for buckling of nonlocal Timoshenko beam based on microstructured beam model

Abstract

This paper presents the determination of Eringen's small length scale coefficient e0 for buckling of nonlocal Timoshenko beam from a microstructured beam model. The microstructured beam model is composed of discrete rigid elements (of equal length), which are connected by rotational and shear springs that model the bending and shearing behaviors in a beam. The exact solution of e0 is given for nonlocal Timoshenko beam with small length scale term appearing in the normal stress-strain relation only. It is shown that e0 approaches 1/12≈0.289 which coincides with the one calibrated for nonlocal Euler beams. © 2013 AIP Publishing LLC.