Buckling of rectangular nanoplates - Advances in Engineering Materials, Structures and Systems: Innovations, Mechanics and Applications

Abstract

Size-dependent behaviour is a key characteristic of nanostructures such as nanotubes, nanoplates and nanobeams. The primary reason for size-dependent behavior is the high surface energy of nanomaterials and nanostructures. Atoms near the surfaces of a nanomaterial/nanostructure have different energy compared to atoms in the bulk. Nanoscale plates are used in various nanotechnology devices, such as nano-electromechanical systems (NEMS), resonators, sensors, etc. Mechanical stability of nanostructures is an important issue in both design and fabrication. In this study, buckling response of rectangular nanoplates under compressive in-plane loading is considered by using a modified continuum theory. In classical continuum mechanics, strain energy is stored in the bulk and surface energy is neglected. Size-dependency can be incorporated into modelling by using a modified continuum theory that accounts for surface energy. The governing equations for bucking of rectangular nanoplate are developed by employing the Gurtin-Murdoch continuum model that accounts for surface energy. Analytical techniques are used in the analysis and closed-form solutions are presented for simply-supported rectangular nanoplates under uniaxial and biaxial compression. Selected numerical results are presented for critical loads and buckled shapes, and the influence of surface residual stress and surface elastic properties are investigated.