LAUSR

This paper presents exact elasticity solutions for nano-plane structures subjected to any distribution of inplane body forces. In deriving the plane stress solutions, three different models are used. They are a lattice elasticity model called the Hencky bar-grid model (eHBM), the continualised nonlocal plane model (CNM) and Eringen’s nonlocal plane model (ENM). eHBM is a physical structural model comprising a system of rigid bar grids with bars connected by axial and torsional springs. CNM is a nonlocal model derived by continualising the governing discrete equations of the eHBM. ENM is a stress gradient nonlocal model. The use of three models allows independent confirmation of the solutions as well as providing a better understanding of the phenomenological similarities between them. Based on the exact solutions for a nano-plane structure under a partial uniformly inplane body force, it is found that by setting the bar grid length of eHBM to be equal to the characterisitc length $$\ell $$ of CNM and ENM, the maximum inplane displacements predicted by eHBM and CNM are in exact agreement when CNM small length scale coefficient $$c_{{0}}=1/\sqrt{12} $$ . However, the ENM maximum inplane displacements are in agreement with eHBM solutions only when ENM’s small length scale coefficient $$e_{{0}}$$ lies between $$1/\sqrt{50} $$ and $$1/\sqrt{10} .$$ These results confirm some phenomenological similarities among eHBM, CNM and ENM; with CNM being closely related to the eHBM physical structure model.