Solution for cross- and angle-ply laminated Kirchhoff nano plates in bending using strain gradient theory

Abstract

The static analysis of Kirchhoff nano plates subjected to uniformly (UDL) and sinusoidally (SSL) distributed load is computed. The strain gradient nonlocal theory has been employed in order to involve the size effects of nanostructures in classical continuum theory. The governing equation of motion of Kirchhoff in weak form are applied to nano plates, involving second-order strain gradient nonlocal theory. Thus, the obtained partial differential equations have an increased order of derivation respect to the classical theory, from the fourth to the sixth. The displacements are carried out following the Navier procedure for simply supported boundary conditions. Isotropic and antisymmetric orthotropic laminates, both cross- and angle-ply are studied, for different layouts involving different material properties. Dimensionless outcomes in terms of transverse displacements, and normal and shear stresses, are given to changing aspect ratio and non local ratio, also making a comparison with the classical theory.