The application of carbon nanotubes (CNTs) in innumerable areas of industry is increasing day-to-day. One of their most important applications is in composite materials as the reinforcing phase. Many researchers studied the behavior of composite materials reinforced with short fibers. This paper examines the effect of the position of short fibers on the total stiffness of a composite material reinforced with carbon nanotubes for various volume fractions. Three different situations have been suggested for the position of a CNT fiber with respect to the other fibers in the composite: completely separated fibers, fibers with overlap, and fibers connected through a shared node (long fibers). Three different cases including a case when just overlaps are allowed, a case when just long fibers are allowed and a case when both overlaps and long fibers are allowed have been investigated. It has been shown that the effect of these cases on the Young’s modulus of the composite is significant and that they should be considered for a better understanding of the reinforced composites behavior. In addition, it is shown that the effect of the investigated cases is more remarkable at higher numbers of randomness values
