In this article, the Carrera unified formulation (CUF) is developed for the buckling analysis of multilayered functionally graded carbon nanotube (MFG-CNT) reinforced cylinders. For this purpose, the CUF is obtained in the cylindrical coordinate system as a first step. Then, the displacement-based CUF is derived from the principle of virtual work in each individual layer in the framework of the element free Galerkin (EFG) method. The mechanical properties of each CNTs-reinforced layer are estimated using the modified Halpin–Tsai (H-T) micromechanical model and rule of mixture. In this model, the waviness, interphase, and agglomeration of CNTs are accounted using influencing factors in terms of CNTs geometric and processing characteristics. Four types of laminates, which are composed of several reinforced layers with different arrangements (distributions) along the radial direction, are taken into account to examine the effect of the layers’ arrangement on the buckling capacity of the cylinder. The proposed CUF-EFG formulations and solution method are validated by comparing the present buckling loads with those obtained by theoretical formula for the homogeneous slender cylinders. A parametric study is conducted to investigate the effects of CNTs weight fraction, waviness, agglomeration and interphase of CNT, distribution of layers, power-law index, radius-to-thickness ratio, length-to-radius ratio, and boundary conditions (BCs) on the critical buckling loads of MFG-CNT reinforced cylinder. The results show the high performance of the proposed CUF-EFG method for buckling analysis of MFG-CNT reinforced cylinders with a wide range of aspect ratios.

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