The discovery of carbon nanotubes (CNTs) is recognized to be a massive breakthrough in science. When compared to other traditional materials, CNTs have superior properties in mechanical, electrical and thermal aspects. For example, they are 100 times stronger than steel whilst simultaneously being significantly lighter with only 1/6th specific gravity. Such a strong and light material is preferable as a reinforcement choice for composites. As a result, CNTs are used in many applications as well as reinforcement of polymer composites leading to improving their mechanical properties effectively. In the functionally graded material (FGM) concept, a spatial variation in material properties is employed as the material is composed of at least two different components with gradual changing of volume fraction along at least one direction. The purpose of this concept is to combine the best properties of two or more constituents. According to the distribution pattern of CNTs inside the polymer matrix, the concept of FGM can be achieved. Detailed investigations on the various mechanical behaviors of functionally graded carbon nanotube-reinforced composites (FG-CNTRC) are extremely important.

On the other hand, Reddy’s higher-order shear deformation theory (HSDT) is valid for all thickness categories of plates without needing any shear correction factors which gives this theory superiority over other plate theories such as classical plate theory (CPT) and first-order shear deformation theory (FSDT). The HSDT accounts for the shear effect which is totally neglected in CPT assumptions limiting it only to study the thin plates. In addition, the HSDT does not require any shear correction factor as needed in the FSDT. Though the HSDT is more complex in terms of the computational aspect when compared to the CPT or FSDT, it is more accurate in the representation of actual shear deformation and more efficient in addressing the behaviors of thick, moderately thick and thin plates.

As a well-established numerical tool, the Finite Element Method (FEM) has achieved great success in both academic research and industrial applications; however, it still has some drawbacks. The FEM inherits the drawbacks of mesh-based techniques such as mesh-distortion in large deformation and discontinuities/moving discontinuities problems. As a result, meshless/mesh-free/element-free-based techniques arose to be an efficient alternative to deal with such problems. The usage of moving least-square (MLS) approximation is considered to represent a turning point resulting in substantial improvements in the element-free method. But on the other hand, MLS approximation still has some limitations such as the fact that the resulting system of algebraic equations may be ill-conditioned. In such cases, there are no mathematical techniques to investigate whether the system of algebraic equations is ill-conditioned before it is solved. Consequently an accurate solution for the system of algebraic equations may not be found/correctly found. The improved moving least-square (IMLS) approximation was proposed to overcome these drawbacks of MLS in the construction of shape function by utilizing a weighted orthogonal function.

Through scanning the open literature, it is remarkable that available studies investigating the mechanical behaviors of FG-CNTRC plates using the HSDT are limited compared to those with other plate theories. Moreover, there is a research gap in the investigation of these mechanical behaviors utilizing the HSDT in association with any of the element-free methods. This study presents a novel approach using both the HSDT and element-free IMLS-Ritz method to investigate some essential mechanical behaviors of carbon nanotube-reinforced composite (CNTRC) plates with uniform distribution (UD) as well as three different functionally graded (FG) distributions: FG-V, FG-O and FG-X with changing properties along the thickness direction. To estimate the effective material properties of the composites, two methods are employed: the extended rule of mixture method and two cases of Mori-Tanaka method for composites reinforced with randomly oriented or aligned straight CNTs inside an isotropic and elastic matrix. The obtained numerical results are compared with those found in the literature to validate the reliability and accuracy of the present approach showing evident agreement. In addition, new and novel results are presented for the first time as well. Furthermore, parametric studies were carried out to investigate the effects of some parameters such as CNT volume fractions, geometric configurations and boundary conditions on the results.

In this study, the static, vibration and buckling characteristics of the FG-CNTRC plates were investigated for various configurations. Furthermore, the vibration behavior of FG-CNTRC plates integrated with piezoelectric layers considering seven mechanical degrees of freedom (DOF) and one additional electrical DOF for each node of the discretized domain was investigated using a novel parametric study on the electromechanical coupling. Using the same novel approach, the active vibration control of FG-CNTRC plates integrated with piezoelectric layers was studied utilizing a constant velocity feedback controller. The system was solved as a state-space model. For the first time, the effectiveness of two different proposed positions of the piezoelectric sensor and actuator layers to control the vibration of FG-CNTRC plates is presented. Additionally, a detailed study on the impact behavior of FG-CNTRC plates was carried out employing the modified non-linear Hertz contact law to define the contact force between the FG-CNTRC target plates and the spherical impactor during the impact duration. The Newmark time integration method was utilized to identify the dynamic response of the FG-CNTRC plates and the impactor displacement. Eventually, the impact analysis of FG-CNTRC plates integrated with piezoelectric layers and controlling their dynamic response due to a moving spherical impactor are presented for the first time in the open literature.