Static and vibrational analysis of fullerene using a newly designed spherical super element

Accurate prediction of static and dynamic response of nano structures under external excitations has been one of the interests of scientists in the last decade. Several applications of nano machines make it necessary to analyze their components, such as nano bearing, precisely. In this paper, the static and vibrational behavior of a fullerene as a sensitive part of nano bearing under external forces is simulated by a newly designed spherical super element.This super element is designed in such a way that the user can select as many numbers of nodes as desired, so that it can be implemented in different desired precisions. In this study, a 228-node super element, which is similar to a hollow sphere (114 nodes on each inner and outer surface), is used, and the formulation of shape functions are introduced. Also, the mechanical properties of fullerene and the boundary conditions of nano ball bearings are presented. Two strategies are utilized to validate the results; the super element and conventional elements. Findings indicate that applying one super element for simulation of the fullerene leads to the same results as implementing 154764 conventional elements. Infinitesimal relative errors show the accuracy of calculations and shape functions of the super element