Vibrations and Buckling of nonlocal laminated nanoplates solved by Finite Element Method

This work presents a novel finite element (FE) based formulation for analysing the linear buckling and free vibration problems of plates governed by strain gradient theory. The present model is able to deal with general lamination schemes and arbitrary boundary conditions and its validity is tested against semi-analytical results as well as other solutions available in the existing literature. The constitutive relationship deals with stress components at each layer as a function of the nonlocal strains, according to the principles of the aforementioned strain gradient theory. The present FE formulation is based on the weak form of the governing motion equations derived via Hamilton’s Principle. Such principle allows the identification of primary variables which are constitute by classical thin plate displacements as well as their first and higher-order derivatives. Therefore, membrane and bending degrees of freedom must be all approximated by means of Hermite interpolating functions. In particular, Conforming (C) and nonconforming (NC) approaches are consequently developed and compared in the present study in order to test their performances in terms of numerical computations. Validation and novel applications are provided for further studies within the present research topic.