Eringen'S Small Length Scale Coefficient for Buckling of Nonlocal Timoshenko Beam Based on Microstructured Beam Model

This paper presents the determination of Eringen's small length scale coefficient e(0) 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 e(0) is given for nonlocal Timoshenko beam with small length scale term appearing in the normal stress-strain relation only. It is shown that e(0) approaches 1/root 12 approximate to 0.289 which coincides with the one calibrated for nonlocal Euler beams. (C) 2013 AIP Publishing LLC.