Eringen’s length scale coefficient for buckling of nonlocal rectangular plates from microstructured beam-grid model

Based on a microstructured beam-grid model, closed form solutions for Eringen’s length scale coefficient are derived for the buckling of nonlocal rectangular plates under compressive uniaxial load. The microstructured beam-grid model comprises rigid beam elements connected by rotational springs and torsional springs. Stiffness of the rotational springs and torsional springs are expressed in terms of the plate flexural and torsional rigidities, respectively. Exact buckling solutions are obtained for the microstructured beam-grid model. By interpreting the rigid element length as the internal characteristic length, the Eringen’s length scale coefficient e0e0 may be determined by comparing the buckling load from the microstructured beam-grid model and the nonlocal rectangular plate model. The small length scale coefficient is shown to be dependent on the buckling mode, the aspect ratio of plate and boundary conditions.