Modified Nonlocal Mindlin Plate Theory for Buckling Analysis of Nanoplates

Abstract

This article presents a modified nonlocal Mindlin plate theory for stability analysis of nanoplates subjected to both uniaxial and biaxial in-plane loadings. Closed-form solutions of buckling load are presented according to the nonlocal Kirchhoff, first-order and higher-order shear deformation plate theories for simply supported rectangular plates. It is shown that the nonlocal shear deformation plate theories cannot predict the critical buckling load correctly because the buckling load approaches zero as the mode numbers approach infinity. To find the critical buckling load by accounting for either the small scale or the shear deformation effects, a modified nonlocal first-order shear deformation plate theory is adapted. Finally, the critical buckling load and buckling mode numbers of nanoplates are obtained on the basis of the presented modified theory. The results show that variation of buckling load versus the mode number is physically acceptable.