Yanmei Yue

Abstract:

A new Kirchhoff microplate model with surface effect is developed by using simplified strain gradient elasticity theory and surface elasticity theory. This new model can be used to describe size-dependent behaviors and surface effects. Different from others plate models, our present model contains surface induced residual stresses which are induced by initial surface stress to balance the plate. Based on whether the plates having surface induced residual stress or not, their governing equations have a distinct difference. The new plate model is applied to analyze the size-dependent behaviors of simply supported Kirchhoff microplate. And how the initial surface stress affects the response of Kirchhoff microplate is also studied. As the surface induced residual stresses are generally neglected in the existing research, the influence of surface induced internal residual stresses is mainly explored. The numerical results reflect that when the simply supported microplates do not have surface induced residual stresses, internal length scale and surface stress have a significant influence on the deflection of the microplates. However, when the simply supported microplates have nonzero surface induced residual stresses, the effects of internal length scale and surface stress are very weak.