Size-dependent geometrically nonlinear bending and postbuckling of nanocrystalline silicon rectangular plates based on mindlin’s strain gradient theory

Abstract

Using a numerical variational approach, the nonlinear bending and postbuckling problems of rectangular plates made of nanocrystalline materials (NCMs) are addressed in this paper. The most general form of strain gradient theory is utilized in order to consider small-scale influences. Employing a micromechanical model, the effective properties of NCMs are calculated. Moreover, the plates are modeled based on the first-order shear deformation theory (FSDT) and the von Kármán hypothesis. The variational differential quadrature (VDQ) technique is applied to obtain and discretize the weak-form governing differential equations. In order to obtain the nonlinear bending and postbuckling responses, the pseudo-arc-length continuation algorithm is employed to solve the resulting discretized nonlinear equations. The effects of thickness-to-length scale ratio, average inclusion radius, the volume fraction of the inclusion phase, length-to-thickness ratio, and density ratio on the nonlinear bending, and postbuckling responses of plates under various boundary conditions are investigated. © 2019 by Begell House, Inc.