Static finite element analysis of thin laminated strain gradient nanoplates in hygro-thermal environment

The manuscript aims to investigate the static behavior of laminated nanoplates in hygro-thermal environment. The theoretical framework is based on the Kirchhoff hypothesis for thin structures including the effect of material length scales, which is described by a nonlocal model. For this purpose, the plane stress constitutive laws for laminates are enriched by a size-dependent parameter according to the principles of strain gradient theory. The variational form of such a peculiar theoretical formulation is developed to obtain the corresponding finite element (FE) model, due to the lack of similar numerical approaches in the literature. The difficulties arisen by the presence of higher-order derivatives of the displacements are overcome by using Hermite interpolating polynomials. Conforming and nonconforming FE formulations are presented to this aim. A broad validation procedure is carried out in terms of displacement and stress analysis to verify the accuracy of the approach. The comparison is accomplished taking into account the analytical solution given by the Navier methodology for cross-ply and angle-ply simply supported plates in hygro-thermal environment. The general model allows to extend the analysis to various boundary conditions and lamination schemes.