Static bending response of axially randomly oriented functionally graded carbon nanotubes reinforced composite nanobeams

Ahmed Amine Daikh,Ahmed Drai,Mohamed Ouejdi Belarbi,Mohammed Sid Ahmed Houari,Benoumer Aour,Mohamed A. Eltaher,Norhan A. Mohamed Techno-Press 2024 Advances in nano research Vol.16 No.3

In this work, an analytical model employing a new higher-order shear deformation beam theory is utilized to investigate the bending behavior of axially randomly oriented functionally graded carbon nanotubes reinforced composite nanobeams. A modified continuum nonlocal strain gradient theory is employed to incorporate both microstructural effects and geometric nano-scale length scales. The extended rule of mixture, along with molecular dynamics simulations, is used to assess the equivalent mechanical properties of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) beams. Carbon nanotube reinforcements are randomly distributed axially along the length of the beam. The equilibrium equations, accompanied by nonclassical boundary conditions, are formulated, and Navier's procedure is used to solve the resulting differential equation, yielding the response of the nanobeam under various mechanical loadings, including uniform, linear, and sinusoidal loads. Numerical analysis is conducted to examine the influence of inhomogeneity parameters, geometric parameters, types of loading, as well as nonlocal and length scale parameters on the deflections and stresses of axially functionally graded carbon nanotubes reinforced composite (AFG CNTRC) nanobeams. The results indicate that, in contrast to the nonlocal parameter, the beam stiffness is increased by both the CNTs volume fraction and the length-scale parameter. The presented model is applicable for designing and analyzing microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS) constructed from carbon nanotubes reinforced composite nanobeams.

Bending of axially functionally graded carbon nanotubes reinforced composite nanobeams

Ahmed Drai,Ahmed Amine Daikh,Mohamed Oujedi Belarbi,Mohammed Sid Ahmed Houari,Benoumer Aour,Amin Hamdi,Mohamed A. Eltaher Techno-Press 2023 Advances in nano research Vol.14 No.3

This work presents a modified analytical model for the bending behavior of axially functionally graded (AFG) carbon nanotubes reinforced composite (CNTRC) nanobeams. New higher order shear deformation beam theory is exploited to satisfy parabolic variation of shear through thickness direction and zero shears at the bottom and top surfaces.A Modified continuum nonlocal strain gradient theoryis employed to include the microstructure and the geometrical nano-size length scales. The extended rule of the mixture and the molecular dynamics simulations are exploited to evaluate the equivalent mechanical properties of FG-CNTRC beams. Carbon nanotubes reinforcements are distributed axially through the beam length direction with a new power graded function with two parameters. The equilibrium equations are derived with associated nonclassical boundary conditions, and Navier's procedure are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear, or sinusoidal mechanical loadings. Numerical results are carried out to investigate the impact of inhomogeneity parameters, geometrical parameters, loadings type, nonlocal and length scale parameters on deflections and stresses of the AFG CNTRC nanobeams. The proposed model can be used in the design and analysis of MEMS and NEMS systems fabricated from carbon nanotubes reinforced composite nanobeam.

Static analysis of multilayer nonlocal strain gradient nanobeam reinforced by carbon nanotubes

Ahmed Amine Daikh,Ahmed Drai,Mohamed Sid Ahmed Houari,Mohamed A. Eltaher 국제구조공학회 2020 Steel and Composite Structures, An International J Vol.36 No.6

This article presents a comprehensive static analysis of simply supported cross-ply carbon nanotubes reinforced composite (CNTRC) laminated nanobeams under various loading profiles. The nonlocal strain gradient constitutive relation is exploited to present the size-dependence of nano-scale. New higher shear deformation beam theory with hyperbolic function is proposed to satisfy the zero-shear effect at boundaries and parabolic variation through the thickness. Carbon nanotubes (CNTs), as the reinforced elements, are distributed through the beam thickness with different distribution functions, which are, uniform distribution (UD-CNTRC), V- distribution (FG-V CNTRC), O- distribution (FG-O CNTRC) and X- distribution (FG-X CNTRC). The equilibrium equations are derived, and Fourier series function are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear or sinusoidal mechanical loadings. Numerical results are obtained to present influences of CNTs reinforcement patterns, composite laminate structure, nonlocal parameter, length scale parameter, geometric parameters on center deflection ad stresses of CNTRC laminated nanobeams. The proposed model is effective in analysis and design of composite structure ranging from macro-scale to nano-scale.

Shear correction factors of a new exponential functionally graded porous beams

Mohammed Sid Ahmed Houari,Aicha Bessaim,Tarek Merzouki,Ahmed Amine Daikh,Aman Garg,Abdelouahed Tounsi,Mohamed A. Eltaher,Mohamed-Ouejdi Belarbi 국제구조공학회 2024 Structural Engineering and Mechanics, An Int'l Jou Vol.89 No.1

This article introduces a novel analytical model for examining the impact of porosity on shear correction factors (SCFs) in functionally graded porous beams (FGPB). The study employs uneven and logarithmic-uneven modified porositydependent power-law functions, which are distributed throughout the thickness of the FGP beams. Additionally, a modified exponential-power law function is used to estimate the effective mechanical properties of functionally graded porous beams. The correction factor plays a crucial role in this analysis as it appears as a coefficient in the expression for the transverse shear stress resultant. It compensates for the assumption that the shear strain is uniform across the depth of the cross-section. By applying the energy equivalence principle, a general expression for static SCFs in FGPBs is derived. The resulting expression aligns with the findings obtained from Reissner’s analysis, particularly when transitioning from the two-dimensional case (plate) to the onedimensional case (beam). The article presents a convenient algebraic form of the solution and provides new case studies to demonstrate the practicality of the proposed formulation. Numerical results are also presented to illustrate the influence of porosity distribution on SCFs for different types of FGPBs. Furthermore, the article validates the numerical consistency of the mechanical property changes in FG beams without porosity and the SCF by comparing them with available results.

A new simple shear and normal deformations theory for functionally graded beams

Mohamed Bourada,Abdelouahed Tounsi,Abdelhakim Kaci,Mohammed Sid Ahmed Houari 국제구조공학회 2015 Steel and Composite Structures, An International J Vol.18 No.2

In the present work, a simple and refined trigonometric higher-order beam theory is developed for bending and vibration of functionally graded beams. The beauty of this theory is that, in addition to modeling the displacement field with only 3 unknowns as in Timoshenko beam theory, the thickness stretching effect (εz= 0) is also included in the present theory. Thus, the present refined beam theory has fewer number of unknowns and equations of motion than the other shear and normal deformations theories, and it considers also the transverse shear deformation effects without requiring shear correction factors. The neutral surface position for such beams in which the material properties vary in the thickness direction is determined. Based on the present refined trigonometric higher-order beam theory and the neutral surface concept, the equations of motion are derived from Hamilton's principle. Numerical results of the present theory are compared with other theories to show the effect of the inclusion of transverse normal strain on the deflections and stresses.

A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams

Mohamed Zidi,Mohammed Sid Ahmed Houari,Abdelouahed Tounsi,Aicha Bessaim,S. R. Mahmoud 국제구조공학회 2017 Structural Engineering and Mechanics, An Int'l Jou Vol.64 No.2

In this article, a novel simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded (FG) beams is proposed. The beauty of this theory relies on its 2-unknowns displacement field as the Euler- Bernoulli beam theory, which is even less than the Timoshenko beam theory. A shear correction factor is, therefore, not needed. Equations of motion are obtained via Hamilton‟s principle. Analytical solutions for the bending and free vibration analysis are given for simply supported beams. Efficacy of the proposed model is shown through illustrative examples for bending and dynamic of FG beams. The numerical results obtained are compared with those of other higher-order shear deformation beam theory results. The results obtained are found to be accurate.

On static bending of multilayered carbon nanotube-reinforced composite plates

Ahmed Amine Daikh,Ismail Bensaid,Attia Bachiri,Mohamed Sid Ahmed Houari,Abdelouahed Tounsi,Tarek Merzouki 사단법인 한국계산역학회 2020 Computers and Concrete, An International Journal Vol.26 No.2

In this paper, the bending behavior of single-walled carbon nanotube-reinforced composite (CNTRC) laminated plates is studied using various shear deformation plate theories. Several types of reinforcement material distributions, a uniform distribution (UD) and three functionally graded distributions (FG), are inspected. A generalized higher-order deformation plate theory is utilized to derive the field equations of the CNTRC laminated plates where an analytical technique based on Navier’s series is utilized to solve the static problem for simply-supported boundary conditions. A detailed numerical analysis is carried out to examine the influence of carbon nanotube volume fraction, laminated composite structure, side-to-thickness, and aspect ratios on stresses and deflection of the CNTRC laminated plates.

A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates

Ahmed Hamidi,Abdelouahed Tounsi,Mohammed Sid Ahmed Houari,S. R. Mahmoud 국제구조공학회 2015 Steel and Composite Structures, An International J Vol.18 No.1

In this research, a simple but accurate sinusoidal plate theory for the thermomechanical bending analysis of functionally graded sandwich plates is presented. The main advantage of this approach is that, in addition to incorporating the thickness stretching effect, it deals with only 5 unknowns as the first order shear deformation theory (FSDT), instead of 6 as in the well-known conventional sinusoidal plate theory (SPT). The material properties of the sandwich plate faces are assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The core layer is made of an isotropic ceramic material. Comparison studies are performed to check the validity of the present results from which it can be concluded that the proposed theory is accurate and efficient in predicting the thermomechanical behavior of functionally graded sandwich plates. The effect of side-to-thickness ratio, aspect ratio, the volume fraction exponent, and the loading conditions on the thermomechanical response of functionally graded sandwich plates is also investigated and discussed.

A novel first-order shear deformation theory for laminated composite plates

Mohamed Sadoune,Abdelouahed Tounsi,Mohammed Sid Ahmed Houari,El Abbes Adda Bedia 국제구조공학회 2014 Steel and Composite Structures, An International J Vol.17 No.3

In the present study, a new simple first-order shear deformation theory is presented for laminated composite plates. Moreover, the number of unknowns of this theory is the least one comparing with the traditional first-order and the other higher-order shear deformation theories. Equations of motion and boundary conditions are derived from Hamilton's principle. Analytical solutions of simply supported antisymmetric cross-ply and angle-ply laminates are obtained and the results are compared with the exact three-dimensional (3D) solutions and those predicted by existing theories. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of laminated composite plates.

Finite element bending and buckling analysis of functionally graded carbon nanotubes-reinforced composite beam under arbitrary boundary conditions

Mohamed-Ouejdi Belarbi,Sattar Jedari Salami,Aman Garg,Hicham Hirane,Daikh Ahmed Amine,Mohammed Sid Ahmed Houari 국제구조공학회 2022 Steel and Composite Structures, An International J Vol.44 No.4

In the present paper, the static bending and buckling responses of functionally graded carbon nanotubes-reinforced composite (FG-CNTRC) beam under various boundary conditions are investigated within the framework of higher shear deformation theory. The significant feature of the proposed theory is that it provides an accurate parabolic distribution of transverse shear stress through the thickness satisfying the traction-free boundary conditions needless of any shear correction factor. Uniform (UD) and four graded distributions of CNTs which are FG-O, FG-X, FG- and FG-V are selected here for the analysis. The effective material properties of FG-CNTRC beams are estimated according to the rule of mixture. To model the FG-CNTRC beam realistically, an efficient Hermite–Lagrangian finite element formulation is successfully developed. The accuracy and efficiency of the present model are demonstrated by comparison with published benchmark results. Moreover, comprehensive numerical results are presented and discussed in detail to investigate the effects of CNTs volume fraction, distribution patterns of CNTs, boundary conditions, and length-to-thickness ratio on the bending and buckling responses of FGCNTRC beam. Several new referential results are also reported for the first time which will serve as a benchmark for future studies in a similar direction. It is concluded that the FG-X-CNTRC beam is the strongest beam that carries the lowest central deflection and is followed by the UD, V, Λ, and FG-O-CNTRC beam. Besides, the critical buckling load belonging to the FG-XCNTRC beam is the highest, followed by UD and FG-O.