A unified size-dependent plate model based on nonlocal strain gradient theory including surface effects

Based on the nonlocal strain gradient theory and surface elasticity theory, a unified size-dependent plate model is developed for buckling analysis of rectangular nanoplates. The developed model is capable of capturing nonlocal effect, strain gradient effect as well as surface energy effects simultaneously. Moreover, by selecting appropriate shape function, the present model can be reduced to not only Kirchhoff and Mindlin plate models but also various higher-order shear deformation plate models. The non-classical governing equations and associated boundary conditions are established by using the principle of minimum potential energy. Analytical solutions for critical buckling load of rectangular nanoplates under various boundary conditions are obtained. Verification of the proposed model is carried out by comparing the degenerated results with those reported in open literature. The effects of nonlocal parameter, material length scale parameter, geometric parameters, shear deformation and surface energy on the buckling behavior of rectangular nanoplates under different boundary conditions are discussed in detail. The numerical results show that the critical buckling load evaluated by nonlocal strain gradient theory is lower than that predicted by classical continuum theory when the nonlocal parameter is larger than the material length scale parameter, and is higher than that evaluated by classical continuum theory when the nonlocal parameter is smaller than the material length scale parameter. However, when taking surface effects into account, the critical buckling load is mainly affected by surface effects at large length-to-thickness ratio, and depends on the combined effects of nonlocality, strain gradient and surface energy at small lengthto-thickness ratio. (C) 2018 Elsevier Inc. All rights reserved.