investigation of torsional buckling of carbon nanotubes using structural mechanics

Carbon nanotubes (cnts) are smart materials that have many applications in the fabrication of various precision engineering tools. due to the mechanical strength of these materials, their use in various sensors, composites, actuators, etc. has become very popular in recent years. due to the very high length-to-diameter ratio of cnts, the possibility of buckling even under low loading for them is very high. torsional buckling occurs because of applying a torsional loadings or transverse forces on the surface of the cnts. in this case, the structure becomes unstable due to this moment and causes the loss of structural resistance against applied load. determining the critical torsional moment is one of the important parameters for designing tools based on cnts. the use of experimental methods to determine the critical moment has many limitations in the laboratory. in addition, experimental costs can also be high. to reduce initial design costs, numerical methods such as continuum mechanics and molecular mechanics are widely proposed. in continuum mechanics, which is a very fast method, the structure of cnt is considered as continuous, which causes ignoring important structures such as armchair and zigzag in design. in molecular mechanics method, considering the interactions of all atoms with each other, in large nanotubes, computational cost becomes very high. to overcome the problems of these two methods, structural mechanics method is proposed which has the advantages of both methods. in this method, by combining continuum mechanics and molecular mechanics, three-dimensional beam element equivalent is used to model covalent and van der waals bonds. after creating three-dimensional elements between atoms of structure, the whole cnt is modeled in finite element environment. to calculate critical torsional buckling, first one side of cnt is constrained and a torsional moment of 1 unit is applied to the other side. then, by obtaining stress distribution in whole system, using eigenvalue method, different buckling modes can be calculated along with critical torsional moment. then different structures of cnt such as zigzag and armchair are investigated. the results show that critical torsional moment of zigzag structure is larger than armchair structure which indicates higher torsional strength of zigzag than armchair. also, by increasing length, critical moment decreases which is consistent with theoretical results. this paper shows that structural mechanics method due to simultaneous use of continuum mechanics and molecular mechanics methods has very good accuracy along with high speed for calculating critical torsional moment of cnts.