Buckling analysis of axially functionally graded carbon nanotubes-reinforced columns using the meshless method

The spread of different material processing technologies has led to the novel methods developed for reinforcing structural members. One of these approaches is to add the carbon nanotubes (CNTs) with different distributions through the matrix phase of composite materials to improve its properties. Due to superior properties such as lightweight and high values of elastic modulus, elastic strain, and failure strain, CNTs can be used to reinforce structures and elements. The present paper aims to investigate the effect of adding CNTs as reinforcement of matrix on the buckling capacity of columns. The meshless local Petrov-Galerkin (MLPG) method is applied for buckling analysis of CNT-reinforced columns. Since the MLPG method uses some scattered nodes through the domain and boundaries for discretization (rather than the meshing), the functionally graded (FG) variation of material properties can be conveniently modeled under the influence of reinforcing elements (CNTs). Four types of volume fraction exponent functions are considered for modeling the FG variation of the CNT volume fraction to examine the effect of CNTs distribution on the buckling capacity of the column and determine the most optimal distribution of CNTs. Effective mechanical properties of the CNT-reinforced column are estimated based on the extended rule of mixture. Results show that reinforcing the polymer matrix with a low volume fraction of CNTs with appropriate distribution can significantly increase its buckling capacity. Using the obtained results, one can determine the best distribution pattern of CNTs in the longitudinal direction of the column at various boundary conditions.