Complete solution of elastica for a clamped-hinged beam, and its applications to a carbon nanotube

This paper treats an exact elastica solution for a clamped-hinged beam, and its applications to a carbon nanotube. Although the elastica has a long history, and the exact post-buckling solution for the Euler buckling problem has been known for at least 150 years, it seems that the elastica solution for a post-buckled clamped-hinged beam has never been obtained. Therefore, the exact solution obtained in this paper constitutes an addition to the existing family of elastica solutions. As an application of the results, a post-buckling analysis of a single wall carbon nanotube is studied. Also, a potential use of the post-buckling analysis of the carbon nanotube for the determination of its Young's modulus has been indicated.