Islamic Azad University - Arak BranchJournal of Solid Mechanics2008-35057120150330Mixed-Mode Stress Intensity Factors for Surface Cracks in Functionally Graded Materials Using Enriched Finite Elements112514619ENJSheikhiCivil Engineering, Imam Hossein UniversityMPoorjamshidianDepartment of Mechanical Engineering, Imam Hossein UniversitySPeymanInstructor, Department of Mechanical Engineering, Imam Hossein UniversityJournal Article20141015Three-dimensional enriched finite elements are used to compute mixed-mode stress intensity factors (SIFs) for three-dimensional cracks in elastic functionally graded materials (FGMs) that are subject to general mixed-mode loading. The method, which advantageously does not require special mesh configuration/modifications and post-processing of finite element results, is an enhancement of previous developments applied so far on isotropic homogeneous and isotropic interface cracks. The spatial variation of FGM material properties is taken into account at the level of element integration points. To validate the developed method, two- and three-dimensional mixed-mode fracture problems are selected from the literature for comparison. Two-dimensional cases include: inclined central crack in a large FGM medium under uniform tensile strain loading and an edge crack in a finite-size plate under shear traction load. The three-dimensional example models a deflected surface crack in a finite-size FGM plate under uniform tensile stress loading. Comparisons between current results and those from analytical and other numerical methods yield good agreement. Thus, it is concluded that the developed three-dimensional enriched finite elements are capable of accurately computing mixed-mode fracture parameters for cracks in FGMs. http://jsm.iau-arak.ac.ir/article_514619_68ee0d5a046261d6336525b004279009.pdfIslamic Azad University - Arak BranchJournal of Solid Mechanics2008-35057120150330Frequency Analysis of Embedded Orthotropic Circular and Elliptical Micro/Nano-Plates Using Nonlocal Variational Principle1327514620ENAAnjomshoaDepartment of Mechanical Engineering, Isfahan University of TechnologyA.RShahidiDepartment of Mechanical Engineering, Isfahan University of TechnologyS.HShahidiDepartment of Mechanical Engineering, Isfahan University of TechnologyHNahviDepartment of Mechanical Engineering, Isfahan University of TechnologyJournal Article20141017In this paper, a continuum model based on the nonlocal elasticity theory is developed for vibration analysis of embedded orthotropic circular and elliptical micro/nano-plates. The nano-plate is bounded by a Pasternak foundation. Governing vibration equation of the nonlocal nano-plate is derived using Nonlocal Classical Plate Theory (NCPT). The weighted residual statement and the Galerkin method are applied to obtain a Quadratic Functional. The Ritz functions are used to form an assumed expression for transverse displacement which satisfies the kinematic boundary conditions. The Ritz functions eliminate the need for mesh generation and thus large degrees of freedom arising in discretization methods such as Finite Element Method (FEM). Effects of nonlocal parameter, lengths of nano-plate, aspect ratio, mode number, material properties and foundation parameters on the nano-plate natural frequencies are investigated. It is shown that the natural frequencies depend on the non-locality of the micro/nano-plate, especially at small dimensions. http://jsm.iau-arak.ac.ir/article_514620_befbe6d62ea92a01c7f829cb59675421.pdfIslamic Azad University - Arak BranchJournal of Solid Mechanics2008-35057120150330Exact 3-D Solution for Free Bending Vibration of Thick FG Plates and Homogeneous Plate Coated by a Single FG Layer on Elastic Foundations2840514621ENHSalehipourSchool of Mechanical Engineering, Isfahan University of TechnologyRHosseiniSchool of Mechanical Engineering, University of TehranKFiroozbakhshSchool of Mechanical Engineering, Sharif University of TechnologyJournal Article20141019This paper presents new exact 3-D (three-dimensional) elasticity closed-form solutions for out-of-plane free vibration of thick rectangular single layered FG (functionally graded) plates and thick rectangular homogeneous plate coated by a functionally graded layer with simply supported boundary conditions. It is assumed that the plate is on a Winkler-Pasternak elastic foundation and elasticity modulus and mass density of the FG layer vary exponentially through the thickness of the FG layer, whereas Poisson’s ratio is constant. In order to solve the equations of motion, a proposed displacement field is used for each layer. Influences of stiffness of the foundation, inhomogeneity of the FG layer and coating thickness-to-total thickness ratio on the natural frequencies of the plates are discussed. Numerical results presented in this paper can serve as benchmarks for future vibration analyses of single layered FG plates and coated plates on elastic foundations.http://jsm.iau-arak.ac.ir/article_514621_286d592f4f21209d7d48c0643b8ec0d0.pdfIslamic Azad University - Arak BranchJournal of Solid Mechanics2008-35057120150330Buckling Analysis of Rectangular Functionally Graded Plates with an Elliptic Hole Under Thermal Loads4157514622ENRRezaeFaculty of Mechanical Engineering, University of ShahroodA.RShaterzadehFaculty of Mechanical Engineering, University of Shahrood0000-0002-0516-9716SAbolghasemiFaculty of Mechanical Engineering, University of ShahroodJournal Article20141021This paper presents thermal buckling analysis of rectangular functionally graded plates (FG plates) with an eccentrically located elliptic cutout. The plate governing equations derived by the first order shear deformation theory (FSDT) and finite element formulation is developed to analyze the plate behavior subjected to a uniform temperature rise across plate thickness. It is assumed that the non-homogenous material properties vary through the plate thickness according to a power function. The developed finite element (FE) code with an extended mesh pattern is written in MATLAB software. The effects of aspect ratio of the plate, ellipse radii ratio, position and orientation of the cutout, boundary conditions (BCs) and volume fraction exponent are investigated in details. The results of present code are compared with those available in the literature and some useful design-orientated conclusions are achieved. http://jsm.iau-arak.ac.ir/article_514622_95f487656d0bc9cac760a1e330922fc8.pdfIslamic Azad University - Arak BranchJournal of Solid Mechanics2008-35057120150330Nonlinear Vibration Analysis of the Fluid-Filled Single Walled Carbon Nanotube with the Shell Model Based on the Nonlocal Elacticity Theory5870514623ENPSoltaniDepartment of Mechanical Engineering, Semnan branch, Islamic Azad universityRBahramianDepartment of Mechanical Engineering, Semnan branch, Islamic Azad universityJSaberianDepartment of Mechanical Engineering, Semnan branch, Islamic Azad universityJournal Article20141023Nonlinear vibration of a fluid-filled single walled carbon nanotube (SWCNT) with simply supported ends is investigated in this paper based on Von-Karman’s geometric nonlinearity and the simplified Donnell’s shell theory. The effects of the small scales are considered by using the nonlocal theory and the Galerkin's procedure is used to discretize partial differential equations of the governing into the ordinary differential equations of motion. To achieve an analytical solution, the method of averaging is successfully applied to the nonlinear governing equation of motion. The SWCNT is assumed to be filled by the fluid (water) and the fluid is presumed to be an ideal non compression, non rotation and in viscid type. The fluid-structure interaction is described by the linear potential flow theory. An analytical formula was obtained for the nonlinear model and the effects of an internal fluid on the coupling vibration of the SWCNT-fluid system with the different aspect ratios and the different nonlinear parameters are discussed in detail. Furthermore, the influence of the different nonlocal parameters on the nonlinear vibration frequencies is investigated according to the nonlocal Eringen’s elasticity theory.http://jsm.iau-arak.ac.ir/article_514623_1008591801b98964d0b19ef29c93957a.pdfIslamic Azad University - Arak BranchJournal of Solid Mechanics2008-35057120150330Modifying Stress-Strain Curves Using Optimization and Finite Elements Simulation Methods7182514624ENARezaei Pour AlmasiDepartment of Mechanical Engineering, Khoy Branch, Islamic Azad UniversityFFaribaDepartment of Mechanical Engineering ,Hamedan Branch ,Islamic Azad UniversitySRasoliYoung Researchers and Elite Club, Hamedan Branch, Islamic Azad universityJournal Article20141024Modifying stress-strain curves is one of the important topics in mechanical engineering and materials science. Real stress-strain curves should be modified after necking point as stress becomes three-dimensional after creation of throat, and consequently, equivalent stress should be used instead of axial one. Also, distribution of triple stresses across throat section is not uniform anymore, and it is not possible to calculate the stress through dividing force value by surface area. Methods presented to modify these curves mainly have some defects which enter the error resulting from simplifying assumptions into the results. Entrance of stress analysis softwares into mechanical engineering has caused use of finite elements methods in order to modify stress-strain curves. As you know, being as an input for stress analysis software, as one of the applications of these curves, has a direct effect on simulation results. Optimization methods have been developed and extended in engineering sciences. Modifying stress-strain curves may be an application of these methods. Considering the sample shape resulting from tension test as the basis in this research, we have changed the modified stress-strain curved in a way that the shape resulting from simulation coincides with the sample resulting from the test. Accordingly, the stress-strain curve has been modified, and the results have been verified, using results obtained from normal methods such as Bridgeman method.http://jsm.iau-arak.ac.ir/article_514624_1352055da2b91336688bcc09df6ac3e8.pdfIslamic Azad University - Arak BranchJournal of Solid Mechanics2008-35057120150330Free Vibration Analysis of Moderately Thick Functionally Graded Plates with Multiple Circular and Square Cutouts Using Finite Element Method8395514632ENJVimalDepartment of Mechanical Engineering, Motilal Nehru National Institute of Technology, Allahabad, IndiaR.KSrivastavaDepartment of Mechanical Engineering, Motilal Nehru National Institute of Technology, Allahabad, IndiaA.DBhattDepartment of Mechanical Engineering, Motilal Nehru National Institute of Technology, Allahabad, IndiaA.KSharmaDepartment of Mechanical Engineering, Madhav Institute of Technology & Science Gwalior, IndiaJournal Article20141028A simple formulation for studying the free vibration of shear-deformable functionally graded plates of different shapes with different cutouts using the finite element method is presented. The aim is to fill the void in the available literature with respect to the free vibration results of functionally graded plates of different shapes with different cutouts. The material properties of the plates are assumed to vary according to a power law distribution in terms of the volume fraction of the constituents. Validation of the formulation is done with the help of convergence studies with respect to the number of nodes and the results are compared with those from past investigations available only for simpler problems. In this paper rectangular, trapezoidal and circular plates with cutouts are studied and the effects of volume fraction index, thickness ratio and different external boundary conditions on the natural frequencies of plates are studied.http://jsm.iau-arak.ac.ir/article_514632_4638e68236ed925e62c3aeac8efc73b2.pdfIslamic Azad University - Arak BranchJournal of Solid Mechanics2008-35057120150330Nonlinear Instability of Coupled CNTs Conveying Viscous Fluid96120514633ENAGhorbanpour AraniFaculty of Mechanical Engineering, University of Kashan---
Institute of Nanoscience & Nanotechnology, University of KashanSAmirFaculty of Mechanical Engineering, University of KashanJournal Article20141028In the present study, nonlinear vibration of coupled carbon nanotubes (CNTs) in presence of surface effect is investigated based on nonlocal Euler-Bernoulli beam (EBB) theory. CNTs are embedded in a visco-elastic medium and placed in the uniform longitudinal magnetic field. Using von Kármán geometric nonlinearity and Hamilton’s principle, the nonlinear higher order governing equations are derived. The differential quadrature (DQ) method is applied to obtain the nonlocal frequency of coupled visco-CNTs system. The effects of various parameters such as the longitudinal magnetic field, visco-Pasternak foundation, Knudsen number, surface effect, aspect ratio and velocity of conveying viscous are specified. It is shown that the longitudinal magnetic field is responsible for an up shift in the frequency and an improvement of the instability of coupled system. Results also reveal that the surface effect and internal conveying fluid plays an important role in the instability of nano coupled system. Also, it is found that trend of figures have good agreement with previous researches. It is hoped that the nonlinear results of this work could be used in design and manufacturing of nano/micro mechanical system in advanced nanomechanics applications where in this study the magnetic field is a controller parameter.http://jsm.iau-arak.ac.ir/article_514633_947dac30710ce37e18620dc4069366b1.pdf