The paper presents an efficient numerical optimization approach to deal with the optimization problem for maximizing the fundamental frequency of laminated functionally graded carbon nanotube-reinforced composite quadrilateral plates. The proposed approach is a combination of the cell-based smoothed discrete shear gap method (CS-DSG3) for analyzing the first natural frequency of the functionally graded carbon nanotube reinforced composite plates and a global optimization algorithm, namely adaptive elitist differential evolution algorithm (aeDE), for solving the optimization problem. The design variables are the carbon nanotube orientation in the layers and constrained in the range of integer numbers belonging to [−900 900]. Several numerical examples are presented to investigate optimum design of quadrilateral laminated functionally graded carbon nanotube reinforced composite plates with various parameters such as carbon nanotube distribution, carbon nanotube volume fraction, boundary condition and number of layers.

This study presents an extension of the cell-based smoothed discrete shear gap method (CS-DSG3) using three-node triangular elements for the static and free vibration analyses of carbon nanotube reinforced composite (CNTRC) plates. The single-walled carbon nanotubes (SWCNTs) are assumed to be uniformly distributed (UD) and functionally graded (FG) distributed along the thickness direction. The material properties of carbon nanotube-reinforced composite plates are estimated according to the rule of mixture. The governing equations are developed based on the first-order shear deformation plate theory (FSDT). In the CS-DSG3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the stabilized discrete shear gap method is used to compute the strains and to avoid the transverse shear locking. Then the strain smoothing technique on the whole triangular element is used to smooth the strains on these three sub-triangles. Effects of several parameters, such as the different distribution of carbon nanotubes (CNTs), nanotube volume fraction, boundary condition and width-to-thickness ratio of plates are investigated. In addition, the effect of various orientation angles of CNTs is also examined in detail. The accuracy and reliability of the proposed method are verified by comparing its numerical solutions with those of other available results in the literature.