Longitudinal modeling and properties tailoring of functionally graded carbon nanotube reinforced composite beams: A novel approach

Highlights

• A novel finite element modeling for axially FG-CNTRC beams was developed.

• An Advanced numerical solution was proposed based on the ladder-pattern concept to overcome properties discontinuity.

• Numerical analysis was performed, including convergence test, static, and dynamic analysis with parametric studies.

• A longitudinal tailoring approach was introduced for AFG-CNTRC beams based on CNT orientation and gradation index.

Abstract

Carbon Nanotubes (CNTs) are considered a promising reinforcement for engineering advanced structures, such as aerospace applications. It became inevitable to tailor structures not only by conventional geometric but also by mechanical properties tailoring, to acquire the maximum load-carrying capacity. Therefore, this research presented a novel Finite Element (FE) modeling of Axially Functionally Graded CNT Reinforced Composite (AFG-CNTRC) beams, based on Timoshenko beam theory. However, an obstacle is raised due to properties discontinuity produced between consecutive elements in axial gradation. A solution is proposed based on the ladder-pattern concept. It defined a locally specific value at each element, satisfying the overall required distribution. It followed by a convergence test, static, and dynamic analysis with comprehensive parametric studies. The obtained results showed that the model is convergent, accurate, free of shear-locking, and suitable for axial gradation. Moreover, this study introduced an advanced technique for axial properties tailoring, utilizing privileges of CNT and aggregation. The longitudinal tailoring depends on both the CNT orientation angle and gradation index, which played a crucial role in response control and adjusting beam stiffness together with strength. This approach could solve enormous engineering problems, especially at critical cross-sections design and constraint response, without affecting the total weight.

Introduction

Recently, CNT Reinforced Composite (CNTRC) structures are considered one of the most influential research fields. Its usage spread widely in many applications. One of the most relevant candidates is aerospace structures. Although, this extensive usage existence, CNT still suffered from issues that represent a processing challenge in nanocomposites such as poor load transfer, dispersion, and interracial engineering [1]. Many types of researches discussed CNT after Iijima [2] in 1991, who is the first one observed it. Volder et al. [3] reviewed the different applications for CNT and the perspective of future ones. Thostenson et al. [4] and Kinloch et al. [1] both made an outlook on CNT composites advances and technologies. Griebel et al. [5] and Han et al. [6] performed Molecular Dynamic (MD) simulations to obtain the elastic properties of polymer/CNT composites. Lei et al. [7] introduced a multi-scale MD finite element method for modeling and analyzing the mechanical response of CNT.

Numerous investigations have been done on CNTs, concluding significant physical and mechanical properties of the new carbon form. It has unique electronic properties and thermal conductivity. Also, stiffness and strength are higher than any current materials. For example, theoretical and experimental results show that modulus of elasticity is greater than 1 TPa, which can not be compared with any other material except diamond 1.2 TPa and specific strength higher than the strongest steel ten to hundred times [4]. Moreover, low specific weight introduces it to be reinforcement for composite materials and nominates it in aerospace applications. At the same time, FG material structures can withstand the different types of loads by properties tailoring according to applied forces and moments. This ability allows it to have an equal interest in research fields. Especially at aircraft structures, the loading cases are varied along with the vehicle lateral direction or the local longitudinal direction of the specific structural part. For example, aerodynamic and inertia loads changed along the airplane wing. It assumed to be carried out by spars or stringers and by longerons for the fuselage case. Tailored AFG-CNTRC could be an excellent solution for adjusting beam stiffness and strength according to applied loads and utilizing CNT superior performance as structural reinforcement. All these privileges proposed without changing in the structural weight, wherein it is a governing factor in the aerospace engineering field.

The combination of advantages from CNT and FG to form Functionally Graded Carbon Nanotube Reinforced Composite (FG-CNTRC) appeared in many kinds of researches. Nguyen et al. [8] introduced a new method to analyze the non-linear vibration of defected FG-CNTRC curve shell subjected to blast and thermal loads. Also, Nguyen et al. [9] studied non-linear post-buckling of FG-CNTRC shell using NonUniform Rational B-Spline. Zghal et al. [10] statically analyzed FG-CNTRC shell and plate based on discrete double directors shell FE. They also used the same theory to investigate the free vibration of FG-CNTRC shell in Ref. [11]. Furthermore, the study of the non-linear bending of nanocomposites shell using discrete double directors shell FE and membrane enhancement had been introduced in Ref. [12]. Moreover, the mechanical buckling of FG-CNTRC plates and curved panels governed by power-law using the same double directors FE shell model was investigated in Ref. [13]. Frikha et al. [14] analyzed FG-CNTRC shell using three and four-node elements. After that, the same authors, [15] studied the dynamic behavior of FG-CNTRC plate and shell using double directors shell FE. Karami et al. [16] studied FG-CNTRC plates analytically. Ansari et al. [17] analyzed forced-vibration of FG-CNTRC plates using a numerical strategy. Also, Ansari et al. [18] studied the vibration of FG-CNTRC elliptic plate numerically. Lei et al. [19] analyzed large deformation of FG-CNTRC plates using element free kp-Ritz method. Moreover, Mellouli et al. [20] used the mesh-free radial interpolation point method in free vibration analysis of FG-CNTRC shell. Also, Mallek et al. [21] analyzed FG-CNTRC shell with piezoelectric layers bonded to the surface.

In the same context, Yas et al. [22] performed a dynamic analysis of randomly oriented FG-CNTRC beams subjected to a moving load. Ke et al. [23] conducted a parametric study for free vibration of FG-CNTRC beams using the Timoshenko beam and Von Karman geometric non-linearity, then analyzed FG-CNTRC beams for dynamic stability [24]. Ansari et al. [25] performed non-linear forced vibration analysis of FG-CNTRC Timoshenko beams. Zeighampour et al. [26] investigated the free vibration of AFG nanobeams with a variable radius using strain gradient theory. Wu et al. [27] studied free vibration and buckling of FG-CNTRC face sheet on a sandwich beam. And then, the same authors [28] represented non-linear vibration analysis of imperfect shear deformable FG-CNTRC beams. Moreover, Wu et al. [29] studied the harmonic resonance of the non-linear FG-CNTRC beams. Ranjbar et al. [30] analyzed AFG-CNTRC cantilever beam subjected to low-velocity impact. Vo-Duy et al. [31] applied a FE method to analyze the free vibration of FG-CNTRC beams. Heidari et al. [32] analyzed the free vibration of rotating FG-CNTRC Timoshenko beams. For tailoring approach, Tatting et al. [33], [34] performed FE analysis for elastic tailored plate design and manufacture.

Minimal kinds of researches dealt from far with modeling and analysis of AFG-CNTRC structures such as Ref. [26], [30], [35]. None of these researches represented a complete FE modeling rather than specific cases of study such as buckling analysis at Ref. [35] or dynamic analysis at Ref. [26], [30]. Presented research introduced a novel complete beam element for AFG-CNTRC as a potential alternative with broad analysis capabilities. Furthermore, the analysis method obtained advantages over the existed in literature. Such as the differential quadrature method, that is suffered from a shortage of systematic analysis conclusions as Ref. [36], [37], [38]. As well, analytical methods, which are incompatible with axial grading modeling as Ref. [16], [39]. Moreover, the proposed model is the first one that planned a solution to overcome the AFG-CNTRC beams convergence problem, using the FE method and ladder-pattern concept. Besides, all reviewed literature did not take into consideration the effect of CNT orientation angle and power-law index change on AFG-CNTRC beams response. This model took into account these parameters and introduced it to the longitudinal tailoring process.

Nowadays, traditional geometric tailoring becomes insufficient for the required progress in the design of the structures. This study aimed to present a novel approach for modeling and properties tailoring of FG-CNTRC beams in the longitudinal direction. It selected the beam as it is one of the most essential and most straightforward structural parts. Investigations started with theoretical and FE modeling of AFG-CNTRC beams. Then, a longitudinal FE problem is explained, and solutions are introduced. Convergence checks are performed to be sure from model efficiency and overcome difficulties of the axial gradation in FE modeling. After that, comprehensive parametric studies are done, including all essential affecting factors in response control and overall beam stiffness. Moreover, enhancement of strength and total mechanical properties due to using CNT as reinforcement, the proposed gradation of properties technique offered the ability of structure tailoring according to applied loads, required response, and specific weight limitations.