Investigation of elastic and buckling properties of carbon nanocones using molecular mechanics approach Mir Masoud Seyyed Fakhrabadi a,⇑ , Navid Khani b , Rose Omidvar c , Abbas Rastgoo b a Karaj Branch, Islamic Azad University, Karaj, Iran b School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran c Science and Research Branch, Islamic Azad University, Tehran, Iran article info Article history: Received 11 February 2012 Received in revised form 28 March 2012 Accepted 6 April 2012 Available online 15 May 2012 Keywords: Carbon nanocones Elastic modulus Buckling Molecular mechanics abstract This paper presents the elastic and buckling behaviors of carbon nanocones with different dimensions including different apex angles and lengths. The well-known molecular mechanics based finite element method is used to study the mentioned properties of theses nanostructures. Next, the elastic moduli of carbon nanocones with various dimensions are reported. Furthermore, the critical compressive forces of the axial buckling phenomena of carbon nanocones with the various dimensions and boundary condi- tions are presented in detail. The results show that with increasing the lengths and apex angles of the carbon nanocones, the elastic moduli and critical compressive forces decrease. Finally, the critical torque and the corresponding mode shapes of torsional buckling of these nanostructures are reported. Ó 2012 Elsevier B.V. All rights reserved. 1. Introduction Nanotechnology in all of its related fields has been developed tremendously during the past decades. Nanoelectronics, nanoma- terial and nanomechanics are the different fields of nanotechnol- ogy engineering relating to modeling, analyzing and applying nanostrucstures such as carbon nanotubes (CNTs), carbon nano- cones (CNCs) and buckyballs. Nanomechanics engineering, in par- ticular, is one of the most interesting and important fields studying the mechanical behaviors of the mentioned nanostructures includ- ing their vibrational [1], elastic [2] and buckling [3] properties as well as their applications in nanofluids [4] and nano-heat transfer [5,6]. Moreover, the applications of the nanostructures in conjunc- tion with the other materials such as composite materials have been attended extensively [7–9]. The CNT has been investigated broadly in all points of views. Aydogdu investigated the vibrational behaviors of the multi- walled CNTs using generalized shear deformation theory [10]. In his paper, the free vibration of a multi-walled CNT with simple supports was analyzed in detail. Lee and Chang studied the vibra- tion of a single-walled CNT embedded in elastic medium and conveying viscous fluid [11]. In their article, some attached springs to the CNT were used to model the surrounding elastic medium and the results of variations in frequencies for various flow proper- ties such as different velocities, viscosities and aspect ratios were reported. In another work, Yun and Park obtained the resonant fre- quencies of the CNTs using finite element method (FEM) to apply in nanoscales mass sensing [12]. In the mentioned paper, the sur- face Cauchy–Born model was used to analyze the CNTs in one dimension. In addition, Zhong et al. applied the nonequilibrium molecular dynamics (MD) simulation to study the thermal conductivities of the deformed CNTs [13]. The results presented that, in case of the cross sectional deformations, this factor decreased for distor- tion ratios lower than one and increased for higher values. In another study, continuum modeling was applied by He et al. to investigate buckling of the multi-walled CNTs with considering vdW interactions [14]. In their paper, the elastic cylindrical shell theory and well-known Lennard-Jones potential for vdW effects were applied to study buckling phenomena of the mentioned nanostructures. Wang et al. applied the MD simulation of the CNTs to obtain their elastic moduli and buckling mode shapes [15]. In their paper, the variations of the elastic moduli vs. radii of the CNTs as well as the critical stresses leading to axial buckling were reported. The researches presented above were some exemplary samples of the broad studies related to investigation of the mechanical properties of the CNTs both in single and multi-walled structures. Some of the mentioned papers clarified the behaviors of zigzag and armchair CNTs in detail. On the other hand, unlike the CNTs, the CNCs have not been characterized completely. Although some researchers investigated some aspects of the mechanical behaviors of the CNCs; nonetheless, 0927-0256/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2012.04.029 ⇑ Corresponding author. Tel.: +98 935 5928477. E-mail address: msfakhrabadi@gmail.com (M.M.S. Fakhrabadi). Computational Materials Science 61 (2012) 248–256 Contents lists available at SciVerse ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci