Linear eigenvalue analysis of laminated thin plates including the strain gradient effect by means of conforming and nonconforming rectangular finite elements. (December 2021) - Bacciocchi, Michele; Fantuzzi, Nicholas; Luciano, Raimondo; Tarantino, Angelo Marcello
Highlights: Laminated Kirchho nanoplates are analyzed considering the strain gradient theory. A finite element method is developed to evaluate frequencies and buckling loads. Higher-order requirements in terms of element continuity are enforced. Membrane and bending degrees of freedom are approximated through Hermite functions. A wide validation procedure based on analytical methods is presented. Abstract: 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.