Buckling analysis of nanoplates incorporating surface stress effects

Nano-electromechanical systems (NEMS) are miniaturized structures with nanometer length scaled features. In such structures, due to the fewer neighbouring surface atoms, the top and bottom layers of a nanoplate possess excess energies over atoms in the bulk. The existence of surface stresses in nanoplates may greatly influence the mechanical behaviours of such structures. In this study, the buckling behaviours of nanoplates with surface stress effects are investigated. The material model is derived in which the bulk core of the plates is assumed to be single crystalline materials and have certain crystallographic directions. The top and bottom layers of the plates are covered by atomic layers with the same crystallographic directions. Surface stresses are considered to be induced by mismatching of the material properties between the surface layer and the underlying bulk materials which can be evaluated via molecular dynamics simulations. The first order shear deformable plate theory is employed to derive the total energy functional of the plate. The p-Ritz method is then applied to derive the eigenvalue equation which can be solved to obtain the buckling load of the nanoplates subject to the influence of surface stresses. It was found that as the nanoplates become thinner or subject to weaker boundary conditions, the surface stresses can significantly increase the buckling load. While the percentage increase of the buckling load factor depends on the type of material and its crystallographic surfaces and directions.