Shahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45364320180701Transient Natural Convection in an Enclosure with Variable Thermal Expansion Coefficient and Nanofluid Properties1331391309910.22055/jacm.2017.22206.1128ENEsmaeilGhahremaniDepartment of Energy Engineering and Physics, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Islamic Republic of IranJournal Article20170527Transient natural convection is numerically investigated in an enclosure using variable thermal conductivity, viscosity, and the thermal expansion coefficient of Al2O3-water nanofluid. The study has been conducted for a wide range of Rayleigh numbers (10<sup>3</sup>≤ Ra ≤ 10<sup>6</sup>), concentrations of nanoparticles (0% ≤ ϕ ≤ 7%), the enclosure aspect ratio (AR =1), and temperature differences between the cold and hot walls (∆T= 30). Transient parameters such as development time and time-average Nusselt number along the cold wall are also presented as a non-dimensional form. Increasing the Rayleigh number shortens the non-dimensional time of the initializing stage. By increasing the volume fraction of nanoparticles, the flow development time shows different behaviors for various Rayleigh numbers. The non-dimensional development time decreases by enhancing the concentration of nanoparticles.Shahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45364320180701Buckling Analysis of Embedded Nanosize FG Beams Based on a Refined Hyperbolic Shear Deformation Theory1401461315210.22055/jacm.2017.22996.1146ENAichaBessaimDépartement de génie civil, Faculté des Sciences et Technologie, Université Mustapha Stambouli de Mascara, 29000, AlgérieLaboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, 22000, AlgérieLaboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, AlgérieMohammed SidAhmed HouariDépartement de génie civil, Faculté des Sciences et Technologie, Université Mustapha Stambouli de Mascara, 29000, AlgérieLaboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, 22000, AlgérieLaboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, Algérie0000-0001-9006-5390BousahlaAbdelmoumen AnisLaboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, AlgérieLaboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, AlgeriaCentre Universitaire de Relizane, AlgérieAbdelhakimKaciLaboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, AlgérieAbdelouahedTounsiLaboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, 22000, AlgérieLaboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, AlgérieEl AbbesAdda BediaLaboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, AlgeriaJournal Article20170811In this study, the mechanical buckling response of refined hyperbolic shear deformable (FG) functionally graded nanobeams embedded in an elastic foundation is investigated based on the refined hyperbolic shear deformation theory. Material properties of the FG nanobeam change continuously in the thickness direction based on the power-law model. To capture small size effects, Eringen’s nonlocal elasticity theory is adopted. Employing Hamilton’s principle, the nonlocal governing equations of FG nanobeams embedded in the elastic foundation are obtained. To predict the buckling behavior of embedded FG nanobeams, the Navier-type analytical solution is applied to solve the governing equations. Numerical results demonstrate the influences of various parameters such as elastic foundation, power-law index, nonlocal parameter, and slenderness ratio on the critical buckling loads of size dependent FG nanobeams.Shahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45364320180701Differential Quadrature Method for Dynamic Buckling of Graphene Sheet Coupled by a Viscoelastic Medium Using Neperian Frequency Based on Nonlocal Elasticity Theory1471601323510.22055/jacm.2017.22661.1138ENMohammadMalikanDepartment of Mechanical engineering, faculty of engineering, Islamic Azad University, Mashhad branch, Iran0000-0001-7356-2168Mohammad NaserSadraee FarDepartment of mechanical engineering, Islamic Azad university, MashhadJournal Article20170704In the present study, the dynamic buckling of the graphene sheet coupled by a viscoelastic matrix was studied. In light of the simplicity of Eringen's non-local continuum theory to considering the nanoscale influences, this theory was employed. Equations of motion and boundary conditions were obtained using Mindlin plate theory by taking nonlinear strains of von Kármán and Hamilton's principle into account. On the other hand, a viscoelastic matrix was modeled as a three-parameter foundation. Furthermore, the differential quadrature method was applied by which the critical load was obtained. Finally, since there was no research available for the dynamic buckling of a nanoplate, the static buckling was taken into consideration to compare the results and explain some significant and novel findings. One of these results showed that for greater values of the nanoscale parameter, the small scale had further influences on the dynamic buckling.Shahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45364320180701Moving Mesh Non-standard Finite Difference Method for Non-linear Heat Transfer in a Thin Finite Rod1611661320210.22055/jacm.2017.22854.1141ENMortezaBisheh-NiasarDepartment of Applied Mathematics, Faculty of Mathematical Science, University of
Kashan, Kashan, Iran.MaryamArab AmeriDepartment of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.Journal Article20170722In this paper, a moving mesh technique and a non-standard finite difference method are combined, and a moving mesh non-standard finite difference (MMNSFD) method is developed to solve an initial boundary value problem involving a quartic nonlinearity that arises in heat transfer with thermal radiation. In this method, the moving spatial grid is obtained by a simple geometric adaptive algorithm to preserve stability. Moreover, it uses variable time steps to protect the positivity condition of the solution. The results of this computational technique are compared with the corresponding uniform mesh non-standard finite difference scheme. The simulations show that the presented method is efficient and applicable, and approximates the solutions well, while because of producing unreal solution, the corresponding uniform mesh non-standard finite difference fails.Shahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45364320180701Inherent Irreversibility of Exothermic Chemical Reactive Third-Grade Poiseuille Flow of a Variable Viscosity with Convective Cooling1671741319410.22055/jacm.2017.22933.1144ENS.O.SalawuDepartment of Mathematics, Landmark University, Omu-aran, NigeriaS.I.OkeDepartment of Mathematical Sciences, University of Zululand, Zululand, South AfricaJournal Article20170803In this study, the analysis of inherent irreversibility of chemical reactive third-grade poiseuille flow of a variable viscosity with convective cooling is investigated. The dissipative heat in a reactive exothermic chemical moves over liquid in an irreversible way and the entropy is produced unceasingly in the system within the fixed walls. The heat convective exchange with the surrounding temperature at the plate surface follows Newton’s law of cooling. The solutions of the dimensionless nonlinear equations are obtained using weighted residual method (WRM). The solutions are used to obtain the Bejan number and the entropy generation rate for the system. The influence of some pertinent parameters on the entropy generation and the Bejan number are illustrated graphically and discussed with respect to the parameters.Shahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45364320180701Exact Radial Free Vibration Frequencies of Power-Law Graded Spheres1751861324310.22055/jacm.2017.22987.1145ENVebilYıldırımCukurova University, Department of Mechanical Engineering, Turkey0000-0001-9955-8423Journal Article20170810This study concentrates on the free pure radial vibrations of hollow spheres made of hypothetically functionally simple power rule graded materials having identical inhomogeneity indexes for both Young’s modulus and the density in an analytical manner. After offering the exact elements of the free vibration coefficient matrices for free-free, free-fixed, and fixed-fixed restraints, a parametric study is fulfilled to study the effects of both the aspect ratio and the inhomogeneity parameters on the natural frequencies. The outcomes are presented in both graphical and tabular forms. It was seen that the fundamental frequency is mostly affected by the inhomogeneity parameters rather than the higher ones. However, the natural frequencies except the fundamental ones are dramatically affected by the thickness of the sphere. It is also revealed that there is a linear relationship between the fundamental frequency and others in higher modes of the same sphere under all boundary conditions.Shahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45364320180701Bending of Shear Deformable Plates Resting on Winkler Foundations According to Trigonometric Plate Theory1872011323410.22055/jacm.2017.23057.1148ENAtteshamuddinSayyadSRES College of Engineering, Kopargaon, Maharashtra, India.0000-0002-3702-4167Yuwaraj M.GhugalHead of Department of Applied Mechanics, Govt. College of EngineeringKarad, Shivaji University, Maharashtra-415124, IndiaJournal Article20170820A trigonometric plate theory is assessed for the static bending analysis of plates resting on Winkler elastic foundation. The theory considers the effects of transverse shear and normal strains. The theory accounts for realistic variation of the transverse shear stress through the thickness and satisfies the traction free conditions at the top and bottom surfaces of the plate without using shear correction factors. The governing equations of equilibrium and the associated boundary conditions of the theory are obtained using the principle of virtual work. A closed-form solution is obtained using double trigonometric series. The numerical results are obtained for flexure of simply supported plates subjected to various static loadings. The displacements and stresses are obtained for three different values of foundation modulus. The numerical results are also generated using higher order shear deformation theory of Reddy, first order shear deformation theory of Mindlin, and classical plate theory for the comparison of the present results.Shahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45364320180701Semi-Analytical Solution for Vibration of Nonlocal Piezoelectric Kirchhoff Plates Resting on Viscoelastic Foundation2022151320310.22055/jacm.2017.23096.1149END.P.ZhangCollege of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, ChinaYongjunLeiCollege of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, ChinaZ.B.ShenCollege of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, ChinaJournal Article20170822Semi-analytical solutions for vibration analysis of nonlocal piezoelectric Kirchhoff plates resting on viscoelastic foundation with arbitrary boundary conditions are derived by developing Galerkin strip distributed transfer function method. Based on the nonlocal elasticity theory for piezoelectric materials and Hamilton's principle, the governing equations of motion and boundary conditions are first obtained, where external electric voltage, viscoelastic foundation, piezoelectric effect, and nonlocal effect are considered simultaneously. Subsequently, Galerkin strip distributed transfer function method is developed to solve the governing equations for the semi-analytical solutions of natural frequencies. Numerical results from the model are also presented to show the effects of nonlocal parameter, external electric voltages, boundary conditions, viscoelastic foundation, and geometric dimensions on vibration responses of the plate. The results demonstrate the efficiency of the proposed methods for vibration analysis of nonlocal piezoelectric Kirchhoff plates resting on viscoelastic foundation.Shahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45364320180701The Complementary Functions Method (CFM) Solution to the Elastic Analysis of Polar Orthotropic Rotating Discs2162301329310.22055/jacm.2017.23188.1150ENVebilYıldırımDepartment of Mechanical Engineering, Çukurova University, Adana, 01330, Turkey0000-0001-9955-8423Journal Article20170830This study primarily deals with introducing an efficient numerical technique called the Complementary Functions Method (CFM) for the solutions of the initial value problem for the linear elastic analysis of anisotropic rotating uniform discs. To bring the performance of the method to light, first, closed form formulas are derived for such discs. The governing equation of the problem at stake is solved analytically with the help of the Euler-Cauchy technique under three types of boundary conditions namely free-free, fixed-free, and fixed-guided constraints. Secondly, the CFM is applied to the same problem. It was found that both numerical and analytical results coincide with each other up to a desired numerical accuracy. Third, after verifying the results with the literature, a parametric study with CFM on the elastic behavior of discs made up of five different materials which physically exist is performed. And finally, by using hypothetically chosen anisotropy degrees from 0.3 through 5, the effects of the anisotropy on the elastic response of such structures are investigated analytically. Useful graphs are provided for readers.Shahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45364320180701Verification and Validation of Common Derivative Terms Approximation in Meshfree Numerical Scheme2312441329210.22055/jacm.2017.23557.1163ENZhiboMaInstitute of Applied Physics and Computational Mathematics, ChinaYazhouZhaoDivision of Water Resources and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, ChinaJournal Article20171002In order to improve the approximation of spatial derivatives without meshes, a set of meshfree numerical schemes for derivative terms is developed, which is compatible with the coordinates of Cartesian, cylindrical, and spherical. Based on the comparisons between numerical and theoretical solutions, errors and convergences are assessed by a posteriori method, which shows that the approximations for functions and derivatives are of the second accuracy order, and the scale of the support domain has some influences on numerical errors but not on accuracy orders. With a discrete scale h=0.01, the relative errors of the numerical simulation for the selected functions and their derivatives are within 0.65%.