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CONTENTS
Volume 7, Number 5, September 2019
 

Abstract
In this paper, thermal- buckling behavior of the functionally graded (FG) nanocomposite plates reinforced with graphene oxide powder (GOP) is studied under three types of thermal loading once the plate is supposed to be rested on a two-parameter elastic foundation. The effective material properties of the nanocomposite plate are considered to be graded continuously through the thickness according to the Halpin-Tsai micromechanical scheme. Four types of GOPs\' distribution namely uniform (U), X, V and O, are considered in a comparative way in order to find out the most efficient model of GOPs\' distribution for the purpose of improving the stability limit of the structure. The governing equations of the plate have been derived based on a refined higher-order shear deformation plate theory incorporated with Hamilton\'s principle and solved analytically via Navier\'s solution for a simply supported GOP reinforced (GOPR) nanocomposite plate. Some new results are obtained by applying different thermal loadings to the plate according to the GOPs\' negative coefficient of thermal expansion and considering both Winkler-type and Pasternak-type foundation models. Besides, detailed parametric studies have been carried out to reveal the influences of the different types of thermal loading, weight fraction of GOP, aspect and length-to-thickness ratios, distribution type, elastic foundation constants and so on, on the critical buckling load of nanocomposite plates. Moreover, the effects of thermal loadings with various types of temperature rise are investigated comparatively according to the graphical results. It is explicitly shown that the buckling behavior of an FG nanocomposite plate is significantly influenced by these effects.

Key Words
thermal buckling; graphene oxide powder; refined higher-order plate theory; elastic foundations

Address
(1) Farzad Ebrahimi, Mostafa Nouraei:
Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran;
(2) Ali Dabbagh:
School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran;
(3) Timon Rabczuk:
Institute of Structural Mechanics (ISM), Bauhaus-University Weimar, Weimar 1599423, Germany.

Abstract
The present study aims to evaluate the nonlinear and post-buckling behaviors of orthotropic graphene sheets exposed to end-shortening strain by implementing a semi-Galerkin technique, as a new approach. The nano-sheets are regarded to be on elastic foundations and different out-of-plane boundary conditions are considered for graphene sheets. In addition, nonlocal elasticity theory is employed to achieve the post-buckling behavior related to the nano-sheets. In the present study, first, out-of-plane deflection function is considered as the only displacement field in the proposed technique, which is hypothesized by an appropriate deflected form. Then, the exact nonlocal stress function is calculated through a complete solution of the von-Karman compatibility equation. In the next step, Galerkin's method is used to solve the unknown parameters considered in the proposed technique. In addition, three different scenarios, which are significantly different with respect to concept, are used to satisfy the natural in-plane boundary conditions and completely attain the stress function. Finally, the post-buckling behavior of thin graphene sheets are evaluated for all three different scenarios, and the impacts of boundary conditions, polymer substrate, and nonlocal parameter are examined in each scenario.

Key Words
nonlocal elasticity; nonlinear behavior; semi-Galerkin technique; nano-graphene sheets; polymer foundation

Address
New Technologies and Engineering Department, Shahid Beheshti University, G.C, Tehran, Iran.


Abstract
In the present study, nonlocal strain gradient theory (NSGT) is developed for wave propagation of functionally graded (FG) nanoscale plate in the thermal environment by considering the porosity effect. Si3N4 as ceramic phase and SUS304 as metal phase are regarded to be constitutive material of FG nanoplate. The porosity effect is taken into account on the basis of the newly extended method which considers coupling influence between Young's modulus and mass density. The motion relation is derived by applying Hamilton's principle. NSGT is implemented in order to account for small size effect. Wave frequency and phase velocity are obtained by solving the problem via an analytical method. The effects of different parameters such as porosity coefficient, gradient index, wave number, scale factor and temperature change on phase velocity and wave frequency of FG porous nanoplate have been examined and been presented in a group of illustrations.

Key Words
wave propagation; nonlocal strain gradient theory; thermal environment; porosity-dependent homogenization

Address
(1) Farzad Ebrahimi, Ali Seyfi:
Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran;
(2) Ali Dabbagh:
School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran.

Abstract
The size-dependent vibration analysis of a cross-/angle-ply laminated composite plate when embedded on the Pasternak elastic foundation and exposed to an in-plane magnetic field are investigated by adopting an analytical eigenvalue approach. The formulation, which is based on refined-hyperbolic-shear-deformation-plate theory in conjunction with the Eringen Nonlocal Differential Model (ENDM), is tested against considering problems for which numerical/analytical solutions available in the literature. The findings of this study demonstrated the role of magnetic field, size effect, elastic foundation coefficients, geometry, moduli ratio, lay-up numbers and ?ber orientations on the nonlocal frequency of cross-/angle-ply laminated composite plates.

Key Words
free vibration; Laminated composite plates; Pasternak foundation; Eringen nonlocal theory

Address
Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran.


Abstract
In this work, dynamic behavior of functionally graded (FG) porous nano-beams is studied based on nonlocal nth-order shear deformation theory which takes into the effect of shear deformation without considering shear correction factors. It has been observed that during the manufacture of "functionally graded materials" (FGMs), micro-voids and porosities can occur inside the material. Thus, in this work, the investigation of the dynamic analysis of FG beams taking into account the influence of these imperfections is established. Material characteristics of the FG beam are supposed to be vary continuously within thickness direction according to a "power-law scheme" which is modified to approximate material characteristics for considering the influence of porosities. A comparative study with the known results in the literature confirms the accuracy and efficiency of the current nonlocal nth-order shear deformation theory

Key Words
porosity; nonlocal elasticity theory; FG nanobeam; free vibration; nth-order shear deformation theory

Address
(1) Hana Berghouti, Amina Benkhedda:
Aeronautical sciences laboratory, Institute of Aeronautics and Space studies, University of Saad Dahlab Blida-1, Algeria;
(2) E.A. Adda Bedia:
Centre of Excellence for Advanced Materials Research, King Abdulaziz University, Jeddah, 21589, Saudi Arabia;
(3) Abdelouahed Tounsi:
Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria;
(4) Abdelouahed Tounsi:
Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia.

Abstract
This paper investigates the effectiveness of Single Walled Carbon Nanotubes, SWNT, in improving the dynamic behavior of cracked Aluminium alloy, Al-alloy, beams by using a method based on changes in modal strain energy. Mechanical properties of composite materials are estimated by the Eshelby-Mori-Tanaka method. The influence of SWNT volume fraction, SWNT aspect ratio, crack depth and crack location on the natural frequencies of the damaged 3D randomly oriented SWNT reinforced Al-alloy beams are examined. Results demonstrate the significant advantages of SWNT in reducing the effect of cracks on the natural frequencies of Al-alloy beams.

Key Words
aluminium alloy; crack; SWNT; vibration

Address
(1) Department of Civil Engineering, College of Engineeriwng in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia;
(2) Ecole Nationale d'Ingénieurs de Tunis (ENIT), Civil Engineering Laboratory, B.P. 37, Le belvédère 1002, Tunis, Tunisia.


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