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CONTENTS
Volume 9, Number 3, June 2020
 

Abstract
This paper employs differential quadrature method (DQM) and nonlocal strain gradient theory (NSGT) for studying free vibrational characteristics of porous functionally graded (FG) nanoplates coupled by visco-elastic foundation. A secant function based refined plate theory is used for mathematical modeling of the nano-size plate. Two scale factors are included in the formulation for describing size influences based on NSGT. The material properties for FG plate are porosity-dependent and defined employing a modified power-law form. Visco-elastic foundation is presented based on three factors including a viscous layer and two elastic layers. The governing equations achieved by Hamilton\'s principle are solved implementing DQM. The nanoplate vibration is shown to be affected by porosity, temperature rise, scale factors and viscous damping.

Key Words
composite plate; FG material; nonlocal strain gradient theory; visco-elastic foundation; DQM

Address
Mohammed Abdulraoof Abdulrazzaq, Ahmed K. Muhammad, Zeyad D. Kadhim and Nadhim M. Faleh: Engineering Collage, Al-Mustansiriah University, P.O. Box 46049, Bab-Muadum, Baghdad 10001, Iraq

Abstract
Natural convection of nanofluid flow between two vertical flat plates has been analyzed in uncertain environment. A non-Newtonian fluid Sodium Alginate (SA) as base fluid and nanoparticles of Copper (Cu) are taken into consideration. In the present study, we have taken nanoparticle volume fraction as an uncertain parameter in terms of fuzzy number. Fuzzy uncertainties are controlled by r-cut and parametric concept. Homotopy Perturbation Method (HPM) has been used to solve the governing fuzzy coupled differential equations for the titled problem. For validation, present results are compared with existing results for some special cases viz. crisp case and they are found to be in good agreement.

Key Words
natural convection; nanofluid; coupled system; homotopy perturbation method; fuzzy number; uncertainty

Address
U. Biswal, S. Chakraverty and B.K. Ojha: Department of Mathematics, National Institute of Technology Rourkela, Rourkela-769008, Odisha, India

Abstract
This article investigates the static behaviour of functionally graded (FG) plates sometimes declared as advanced composite plates by using a simple and accurate quasi-3D and 2D hyperbolic higher-order shear deformation theories. The properties of functionally graded materials (FGMs) are assumed to vary continuously through the thickness direction according to exponential law distribution (E-FGM). The kinematics of the present theories is modeled with an undetermined integral component and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate; therefore, it does not require the shear correction factor. The fundamental governing differential equations and boundary conditions of exponentially graded plates are derived by employing the static version of principle of virtual work. Analytical solutions for bending of EG plates subjected to sinusoidal distributed load are obtained for simply supported boundary conditions using Navier\'is solution procedure developed in the double Fourier trigonometric series. The results for the displacements and stresses of geometrically different EG plates are presented and compared with 3D exact solution and with other quasi-3D and 2D higher-order shear deformation theories to verify the accuracy of the present theory.

Key Words
E-FGM; static behaviour; quasi-3D; shear deformation; bending

Address
Ali Youcef: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Laboratory of Mechanics of Structures and Solids (LMSS), Faculty of Technology, Department of Mechanical Engineering, University Sidi Bel Abbes University, Algeria
Mohamed Bourada: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
Kada Draiche: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Departement de Genie Civil, Universite Ibn Khaldoun Tiaret, BP 78 Zaaroura, 14000 Tiaret, Algerie
Belhadj Boucham: Laboratory of Mechanics of Structures and Solids (LMSS), Faculty of Technology, Department of Mechanical Engineering, University Sidi Bel Abbes University, Algria
Fouad Bourada: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Departement des Sciences et de la Technologie, Centre Universitaire de Tissemsilt, BP 38004 Ben Hamouda, Algerie
Farouk Yahia Addou: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria

Abstract
In this paper, a new refined hyperbolic shear deformation beam theory for the free vibration analysis of functionally graded beam is presented. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the functionally graded beam without using shear correction factors. In addition, the effect of different micromechanical models on the free vibration response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams whose properties vary continuously across the thickness according to a simple power law. Based on the present theory, the equations of motion are derived from the Hamilton\'s principle. Navier type solution method was used to obtain frequencies, and the numerical results are compared with those available in the literature. A detailed parametric study is presented to show the effect of different micromechanical models on the free vibration response of a simply supported FG beams.

Key Words
functionally graded beam; free vibration; micromechanical models; Hamilton

Address
Lazreg Hadji: Department of Mechanical Engineering, University of Tiaret, BP 78 Zaaroura, Tiaret, 14000, Algeria; Laboratory of Geomatics and Sustainable Development, Ibn Khaldoun University of Tiaret, Algeria

Abstract
Nanotechnology is an upcoming technology that can provide solution for combating pollution by controlling shape and size of materials at the nanoscale. This review provides comprehensive information regarding the role of nanotechnology in pollution control at concrete structures. Titanium dioxide (TiO2) nanoparticles are a good item for concrete structures for diminishing the air polluting affect by gasses of exhaust. In this article, the mixture rule is presented for the effect of nanoparticles in environmental pollution reduction in concrete structures. The compressive strength, elastic modulus and reduction of steel bars in the concrete structures are studied. The Results show that TiO2 nanoparticles have significant effect on the reduction of environmental pollution and increase of stiffness in the concrete structures. In addition, the nanoparticles can reduce the use of steel bars in the concrete structure.

Key Words
environmental pollution reduction; nanoparticles; concrete structures; mixture rule; steel bar

Address
Javad Tabatabaei: Department of Petroleum and Geology, Meymeh Branch, Islamic Azad University, Meymeh, Iran
Seyed Hesam Nourbakhsh: Department of Civil Engineering, Meymeh Branch, Islamic Azad University, Meymeh, Iran
Mahdi Siahkar: Department of Mining Engineering, Mahallat Branch, Islamic Azad University, Mahallat, Iran

Abstract
The paper studies the fluid flow profile contained between the orthotropic plate and rigid wall under the action of the moving load on the plate and main attention is focused on the fluid velocity profile in the load moving direction. It is assumed that the plate material is orthotropic one and the fluid is viscous and barotropic compressible. The plane-strain state in the plate and the plane flow of the fluid is considered. The motion of the plate is described by utilizing the exact equations of elastodynamics for anisotropic bodies, however, the flow of the fluid by utilizing the linearized Navier-Stokes equations. For the solution of the corresponding boundary value problem, the moving coordinate system associated with the moving load is introduced, after which the exponential Fourier transformation is employed with respect to the coordinate which indicates the distance of the material points from the moving load. The exact analytical expressions for the Fourier transforms of the sought values are obtained, the originals of which are determined numerically. Presented numerical results and their analyses are focused on the question of how the moving load acting on the face plane of the plate which is not in the contact with the fluid can cause the fluid flow and what type profile has this flow along the thickness direction of the strip filled by the fluid and, finally, how this profile changes ahead and behind with the distance of the moving load.

Key Words
fluid flow profile; orthotropic plate; compressible viscous fluid; moving load; hydro-elastic system; Fourier transform

Address
Surkay D. Akbarov: Department of Mechanical Engineering, Yildiz Technical University, 34349, Besiktas, Istanbul, Turkey; Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan, AZ1141, Baku, Azerbaijan
Tarana V. Huseynova: Ganja State University, Ganja, Azerbaijan


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