Modelling and mechanical analysis of carbon nanotube structures using finite element methodology

In this study, carbon nanotube structures are modeled, and vibrational characteristics of carbon nanotubes are studied. In the introduction part, brief information about carbon nanotube structures has been given. Mechanical characteristics, production methods, and deficiency types have been discussed. Carbon nanotubes have been formulated analytically according to the Euler-Bernoulli beam theory. Equation of motions according to local elasticity theory and nonlocal elasticity theory has been obtained. The analytical solution is found for simple-simple boundary conditions. Numerical models have been established. Two approaches have been used. Firstly, the finite element method-based Ansys Mechanical APDL software has been used to model carbon nanotubes as mass and beam elements using the local elasticity theorem. The gap between nanotube modeling software and APDL language is bridged by using self-developed Python scripts. Solutions obtained with Ansys Mechanical APDL are compared to similar works from the literature. After obtaining the model verification, elastic foundation effects are implemented as an application model. The effects of elastic foundation on mode shapes and natural frequencies are investigated. Secondly, a finite element code has been developed using the Python programming language. In the Python program, the carbon nanotube is modeled using the local Euler-Bernoulli beam theory, and element formulations are defined according to this theory. Global stiffness and mass matrices are assembled, and solutions are obtained. Obtained results are compared with the literature and the approaches obtained in this work