Curvature sensitive model of isogeometric collocation for multiple nonlinear equilibria of reinforced porous curved microbeams

Abstract

This research examination aims to demonstrate for the first time the multiple nonlinear equilibria attributed to the curvature sensitivity in thermomechanical stability characteristics of clamped porous curved microbeams. The modeled microstructures are reinforced by graphene nanoplatelet including the roles of couple and nonlocal stress tensors. In this regard, curved microbeams possessing different magnitudes of curvature are taken into account which classified as microbeams with small, medium, and large curvatures. Based upon a power law, the porosity is graded in thickness direction, along which the graphene nanoplatelet reinforcements are dispersed uniformly. Through implementation of the size dependencies within the formulations of the third-order shear flexibility, an efficient curvature sensitive model of isogeometric collocation is established. The employed numerical approach embodies the Greville abscissae associated with the employed spline space and knot vector. It comes to the conclusion that for a higher value of the porosity index, the prominence attributed to the both effects of the couple and nonlocal stress tensors diminishes on the lateral loads at the upper limit points for the reinforced porous microbeam with small curvature, while it intensifies on the lateral loads at the upper limit points for the reinforced porous microbeams with medium and large curvatures. This venture becomes opposite on the lateral loads at the lower limit points.