The elliptic phenomenon effect of cross section on the torsional buckling of a nanocomposite beam reinforced by a single-walled carbon nanotube

Abstract

In this article, the elliptic phenomenon effect of cross section on the torsional buckling of a nanocomposite beam reinforced by a single-walled carbon nanotube based on the continuum mechanics theory is presented. The Airy stress function method is applied to obtain the deformation of the matrix. In addition, the cross-sectional change in the single-walled carbon nanotube in torsion is considered. By using the Airy stress function, the radial and tangential displacements of the matrix and single-walled carbon nanotube, the strain energy for both the matrix and single-walled carbon nanotube is determined. Then, the stress distribution in terms of strain for different torsional curvatures, matrix thickness, single-walled carbon nanotube percentage and flatting ratio is studied. It is found from the results that with the increase in matrix thickness, the tangential and longitudinal strains in single-walled carbon nanotube decrease and vice versa for the interface stress and the dimensionless stress of the outer surface. It can be seen that in thicker matrix layers, the critical torsional buckling load of single-walled carbon nanotube decreases. Moreover, the stresses and strains of single-walled carbon nanotube and matrix will increase with an increase in the flattening ratios.