Linear eigenvalue analysis of laminated thin plates including the strain gradient effect by means of conforming and nonconforming rectangular finite elements

The paper presents a finite element method to investigate the critical buckling loads and the natural frequencies of laminated Kirchhoff plates including the nonlocal strain gradient effect, which could have considerably consequences at the nanoscale. With respect to the existing literature, the proposed numerical methodology is developed to deal with general stacking sequences of orthotropic layers with arbitrary orientations and various boundary conditions. The resulting membrane-bending coupling is emphasized in the formulation, which requires to study the whole set of partial differential equations. The membrane and bending degrees of freedom are all approximated by means of Hermite interpolating functions with higher-order continuity requirements. To this aim, regular rectangular finite elements based on conforming (C) and nonconforming (NC) approaches are used. A wide validation procedure is carried out to prove the effectiveness of the proposed formulation. A set of new results is presented for general mechanical configurations with arbitrary restraints.