Mathematical modelling and numerical study for buckling study in concrete beams containing carbon nanotubes

This paper deals with the mathematical modelling and numerical study for buckling analysis in concrete beams containing carbon nanotubes (CNTs). In order to modelling the concrete structure, Euler-Bernoulli beam is utilized. For assuming the influences of CNTs in the concrete beam and the agglomeration of CNTs, the Mori-Tanaka model is utilized. The principle of Hamilton is utilized for calculating the final equations and solved by two procedures of differential quadrature (DQ) and analytical method of Navier. The comparison of obtained results from DQ and Navier methods are shown the validation of this work. In addition, the outcomes are compared with other papers in the literature. The influences of boundary condition, CNT volume fraction, CNT agglomeration, length to thickness ratio and mode number are shown on the normalized buckling load. The outcome presents with enhancing the volume fraction of reinforcing the beam by nanoparticles, the buckling load of structure is improved. Indeed, the agglomeration of CNTs can reduces the buckling load and stability of beam.