Buckling investigation of cylindrical shell using size-dependent new super element

In this paper, using modified couple stress theory, a new cylindrical shell element is introduced. Since classical continuum theory is unable to correctly compute stiffness and account for size effects in micro/nanostructures, higher order continuum theories such as modified couple stress theory have taken on great appeal. In this paper, using modified couple stress theory and using shell model in place of beam model, buckling of nanotubes is investigated via the finite element method. The new cylindrical shell element based on super element’s shape function defined and the mass-stiffness matrix has been developed. In addition to modified couple stress cylindrical shell element, the classical cylindrical shell super element can also be defined by setting size effects parameter to zero in the equations. In special cases, in order to investigate the application of the equations developed, the cylindrical nanoshell buckling is studied using modified couple stress cylindrical shell element and the results are validated using the analytical method. In addition, the effects of parameters such as size effects parameter, length, and thickness on cylindrical shell buckling are investigated.