Comparison of nano-plate bending behaviour by Eringen nonlocal plate, Hencky bar-net and continualised nonlocal plate models

This paper is concerned with the bending behaviour of small-scale simply supported plates as predicted by using the Eringen nonlocal plate model (ENM), the Hencky bar-net model (HBM) and the continualised nonlocal plate model (CNM). HBM comprises rigid beam segments connected by rotational and torsional springs. CNM is a nonlocal model derived by using a continualisation approach that does away with the unknown scale coefficient e in ENM. The exact bending solutions for simply supported rectangular nano-plates are derived by using ENM, HBM and CNM. By making the segment length ℓ of HBM equal to the scale length of continualised and Eringen’s nonlocal plate model and noting the phenomenological similarities between ENM, HBM and CNM, the Eringen’s length scale value e is found to be dependent on the aspect ratio of the simply supported plate and independent of the applied transverse loading. For a very small scale length ℓ, e of ENM converges to values ranging from 1/8 to 1/6 for square plate to longish rectangular plate when calibrated by either HBM or CNM.