

مجله مكانيك جامدات
Journal of Solid Mechanics
ISSN 20083505
فصلنامه داراي رتبه علمي  پژوهشي (فني مهندسي) به زبان انگليسي
سال هشتم، شماره 4، Autumn 2016




 Vibration Analysis of Carotid Arteries Conveying NonNewtonian Blood Flow Surrounding by Tissues A.H Ghorbanpour Arani , A Rastgoo , A. Ghorbanpour Arani * , R Kolahchi Pages 693704 Abstract Full Text [PDF 658KB]   The high blood rate that often occurs in arteries may play a role in artery failure and tortuosity which leads to blackouts، transitory ischemic attacks and other diseases. However، vibration and instability analysis of carotid arteries are lacking. The objective of this study is to investigate the vibration and instability of the carotid arteries conveying blood under axial tension with surrounding tissue support. Arteries are modeled as elastic cylindrical vessels based on first order shear deformation theory (FSDT) within an elastic substrate. The elastic medium is simulated with viscoPasternak foundation. The blood flow in carotid artery is modeled with nonNewtonian fluid based on Carreau، power law and Casson models. Applying energy method، Hamilton principle and differential quadrature method (DQM)، the frequency، critical blood velocity and transverse displacement of the carotid arteries are obtained. It can be seen that increasing the tissue stiffness would delay critical blood velocity. The current model provides a powerful tool for further experimental investigation arteries tortuosity. In addition، the dimensionless transverse displacement predicted by Newtonian model is lower than that of nonNewtonian models.
Keywords: Carotid artery; Non, Newtonian fluid; Critical blood velocity; FSDT; Tissue matrix
  
 Mechanical Stresses in a Linear Plastic FGM Hollow Cylinder Due to NonAxisymmetric Loads M Shokouhfar * , M Jabbari Pages 705718 Abstract Full Text [PDF 1340KB]   In this paper، an analytical solution for computing the linear plastic stresses and critical pressure in a FGM hollow cylinder under the internal pressure due to nonAxisymmetric Loads is developed. It has been assumed that the modulus of elasticity was varying through thickness of the FGM material according to a power law relationship. The Poisson's ratio was considered constant throughout the thickness. The general form of mechanical boundary conditions is considered on the inside surfaces. In the analysis presented here the effect of nonhomogeneity in FGM cylinder was implemented by choosing a dimensionless parameter، named m، which could be assigned an arbitrary value affecting the stresses in the cylinder. Distribution of stresses in radial، circumferential and shear directions for FGM cylinders under the influence of internal pressure were obtained. Graphs of variations of stress versus radius of the cylinder were plotted. The direct method is used to solve the Navier equations.
Keywords: Hollow cylinder; Non, Homogenous; Non, Axisymmetri; FGM; Elastic, plastic analysis
  
 Finite Difference Method for Biaxial and Uniaxial Buckling of Rectangular Silver Nanoplates Resting on Elastic Foundations in Thermal Environments Based on Surface Stress and Nonlocal Elasticity Theories M karimi * , A.R Shahidi Pages 719733 Abstract Full Text [PDF 1376KB]   In this article، surface stress and nonlocal effects on the biaxial and uniaxial buckling of rectangular silver nanoplates embedded in elastic media are investigated using finite difference method (FDM). The uniform temperature change is utilized to study thermal effect. The surface energy effects are taken into account using the GurtinMurdoch’s theory. Using the principle of virtual work، the governing equations considering small scale for both nanoplate bulk and surface are derived. The influence of important parameters including، the Winkler and shear elastic moduli، boundary conditions، inplane biaxial and uniaxial loads، and widthtolength aspect ratio، on the surface stress effects are also studied. The finite difference method، uniaxial buckling، nonlocal effect for both nanoplate bulk and surface، silver material properties، and belowmentioned results are the novelty of this investigation. Results show that the effects of surface elastic modulus on the uniaxial buckling are more noticeable than that of biaxial buckling، but the influences of surface residual stress on the biaxial buckling are more pronounced than that of uniaxial buckling.
Keywords: Biaxial and uniaxial buckling; Surface stress theory; Finite difference method; Thermal environment; Nonlocal elasticity theory
  
 Finite Element Analysis of Reinforced RC Bracket Using CFRP Plates A Rafati , S.V Razavi * Pages 734743 Abstract Full Text [PDF 743KB]   CFRP composites have unique application qualities such as high resistance and durability to environmental conditions، having relatively low weight and easy to install in strengthening concrete structure elements. The brackets should be strengthen sufficiently if they are not calculated and implemented well. Application of the CFRP is one of the methods for such purposes. The study involves using five different configurations of CFRP sheets as a means of strengthening bracket، using finite element and nonlinear dynamic analysis method within the ABAQUS software. Comparative analysis results of nonstrengthened bracket model، show a 24.06% increase in the loadcarrying capacity of strengthened models using the CFRP compared with the initial model (without CFRP). Results further show an increase of 24.96% of energy absorption in the strengthened models compared with the nonstrengthened model.
Keywords: Bracket; Load carrying capacity; Energy absorption; CFRP; ABAQUS
  
 Ductile Failure and Safety Optimization of Gas Pipeline P Zamani , A Jaamialahmadi * , M Shariati Pages 744755 Abstract Full Text [PDF 996KB]   Safety and failure in gas pipelines are very important in gas and petroleum industry. For this reason، it is important to study the effect of different parameters in order to reach the maximum safety in design and application. In this paper، a three dimensional finite element analysis is carried out to study the effect of crack length، crack depth، crack position، internal pressure and pipe thickness on failure mode and safety of API X65 gas pipe. Four levels are considered for each parameter and finite element simulations are carried out by using design of experiments (DOE). Then، multiobjective Taguchi method is conducted in order to minimize x and y coordinates of Failure Assessment Diagram (FAD). So، desired levels that minimize the coordinates and rises the possibility of safety are derived for each parameter. The variation in FAD coordinates according to the changes in each parameter are also found. Finally، comparisons between the optimum design and all other experiments and simulations have shown a good safety situation. It is also concluded that the more design parameters close to optimum levels، the better safety condition will occur in FAD. A verification study is performed on the safety of longitudinal semielliptical crack and the results has shown a good agreement between numerical and experimental results.
Keywords: Semi, elliptical crack; Finite element analysis; Taguchi method; Failure assessment diagram
  
 On the Stability of an ElectrostaticallyActuated Functionally Graded MagnetoElectroElastic MicroBeams Under MagnetoElectric Conditions A Amiri * , G Rezazadeh , R Shabani , A Khanchehgardan Pages 756772 Abstract Full Text [PDF 861KB]   In this paper، the stability of a functionally graded magnetoelectroelastic (FGMEE) microbeam under actuation of electrostatic pressure is studied. For this purpose EulerBernoulli beam theory and constitutive relations for magnetoelectroelastic (MEE) materials have been used. We have supposed that material properties vary exponentially along the thickness direction of the microbeam. Governing motion equations of the microbeam are derived by using of Hamilton’s principle. Maxwell’s equation and magnetoelectric boundary conditions are used in order to determine and formulate magnetic and electric potentials distribution along the thickness direction of the microbeam. By using of magnetoelectric potential distribution، effective axial forces induced by external magnetoelectric potential are formulated and then the governing motion equation of the microbeam under electrostatic actuation is obtained. A Galerkinbased step by step linearization method (SSLM) has been used for static analysis. For dynamic analysis، the Galerkin reduced order model has been used. Static pullin instability for 5 types of MEE microbeam with different gradient indexes has been investigated. Furthermore، the effects of external magnetoelectric potential on the static and dynamic stability of the microbeam are discussed in detail.
Keywords: Functionally graded; MEE; MEMS; Maxwell’s Equation; Pull, in instability
  
 Analyzing Frequency of Conical (∆ shaped) Tanks F Saljughi * Pages 773780 Abstract Full Text [PDF 758KB]   A finite element analysis is presented for sloshing and impulsive motion of liquidfilled conical tanks during lateral antisymmetric excitation. The performed analyses led to the development of a number of charts which can be used to identify the natural frequency، the mode shapes of conical tanks for both fundamental and the cos(θ)modes of vibration. Conical tank geometry was described with several parameters namely، bottom radius( Rb) total height of liquid (h)، angle of inclination of the tanks(θi)، as variables. Numerical result of the free vibration was obtained for the cases of conical tanks with θi=0 and compared with existing experiments and other predicated results، showing a good agreement between the experiment and numerical results.
Keywords: Conical shell; Modal characteristic; Finite element method; Apex angle; Natural frequency
  
 Dynamic Simulation and Mechanical Properties of Microtubules M Motamedi * , M Mosavi Mashhadi Pages 781787 Abstract Full Text [PDF 640KB]   This work is conducted to obtain mechanical properties of microtubule. For this aim، interaction energy in alphabeta، betaalpha، alphaalpha، and betabeta dimers was calculated using the molecular dynamic simulation. Forcedistance diagrams for these dimers were obtained using the relation between potential energy and force. Afterwards، instead of each tubulin، one sphere with 55 KDa weight connecting to another tubulin with a nonlinear connection such as nonlinear spring could be considered. The mechanical model of microtubule was used to calculate Young’s modulus based on finite element method. Obtained Young’s modulus has good agreement with previous works. Also، natural frequency of microtubules was calculated based on finite element method.
Keywords: Microtubules; Finite element; Molecular dynamic; Mechanical properties
  
 ThermoMechanical Vibration Analysis of FG Circular and Annular Nanoplate Based on the ViscoPasternak Foundation M Goodarzi * , M Mohammadi , M Khooran , F Saadi Pages 788805 Abstract Full Text [PDF 951KB]   In this study، the vibration behavior of functional graded (FG) circular and annular nanoplate embedded in a ViscoPasternak foundation and coupled with temperature change is studied. The effect of inplane preload and temperature change are investigated on the vibration frequencies of FG circular and annular nanoplate. To obtain the vibration frequencies of the FG circular and annular nanoplate، two different size dependent theories are utilized. The material properties of the FGM nanoplates are assumed to vary in the thickness direction and are estimated through the Mori–Tanaka homogenization technique. The FG circular and annular nanoplate is coupled by an enclosing viscoelastic medium which is simulated as a Visco Pasternak foundation. By using the modified strain gradient theory (MSGT) and the modified couple stress theory (MCST)، the governing equation is derived for FG circular and annular nanoplate. The differential quadrature method (DQM) and the Galerkin method (GM) are utilized to solve the governing equation to obtain the frequency vibration of FG circular and annular nanoplate. The results are subsequently compared with valid result reported in the literature. The effects of the size dependent، the inplane preload، the temperature change، the power index parameter، the elastic medium and the boundary conditions on the natural frequencies are investigated. The results show that the size dependent parameter has an increasing effect on the vibration response of circular and annular nanoplate. The temperature change also play an important role in the mechanical behavior of the FG circular and annular nanoplate. The present analysis results can be used for the design of the next generation of nanodevices that make use of the thermal vibration properties of the nanoplate
Keywords: Circular and annular nanoplate; Functional graded nanoplate; Modified strain gradient theory; Modified couple stress theory
  
 Effects of Gravitational and Hydrostatic Initial Stress on a TwoTemperature FiberReinforced Thermoelastic Medium for ThreePhaseLag S.M Said * , M.I.A Othman Pages 806822 Abstract Full Text [PDF 848KB]   The threephaselag model and Green–Naghdi theory without energy dissipation are employed to study the deformation of a twotemperature fiberreinforced medium with an internal heat source that is moving with a constant speed under a hydrostatic initial stress and the gravity field. The modulus of the elasticity is given as a linear function of the reference temperature. The exact expressions for the displacement components، force stresses، thermal temperature and conductive temperature are obtained by using normal mode analysis. The variations of the considered variables with the horizontal distance are illustrated graphically. A comparison is made with the results of the two theories for two different values of a hydrostatic initial stress. Comparisons are also made with the results of the two theories in the absence and presence of the gravity field as well as the linear temperature coefficient.
Keywords: Fiber, reinforced; Gravity field; Green, Naghdi theory; Hydrostatic initial stress; Three, phase, lag model; Two, temperature
  
 Coupled Vibration of Partially FluidFilled Laminated Composite Cylindrical Shells M.R Saviz * Pages 823839 Abstract Full Text [PDF 1261KB]   In this study، the free vibration of partially fluidfilled laminated composite circular cylindrical shell with arbitrary boundary conditions has been investigated by using RayleighRitz method. The analysis has been carried out with straindisplacement relations based on Love’s thin shell theory and the contained fluid is assumed irrotational، incompressible and inviscid. After determining the kinetic and potential energies of fluid filled laminated composite shell، the eigenvalue problem has been obtained by means of RayleighRitz method. To demonstrate the validity and accuracy of the results، comparison has been made with the results of similar works for the empty and partially fluidfilled shells. Finally، an extensive parameter study on a typical composite tank is accomplished and some conclusions are drawn.
Keywords: Laminated composite; Rayleigh, Ritz; Partially fluid, filled; Cylindrical shell; Vibration analysis
  
 Thermomechanical Interactions Due to Hall Current in Transversely Isotropic Thermoelastic with and Without Energy Dissipation with Two Temperatures and Rotation R Kumar , N Sharma , P Lata* Pages 840858 Abstract Full Text [PDF 1131KB]   The present paper is concerned with the investigation of disturbances in a homogeneous transversely isotropic thermoelastic rotating medium with two temperatures، in the presence of the combined effects of Hall currents and magnetic field due to thermomechanical sources. The formulation is applied to the thermoelasticity theories developed by GreenNaghdi Theories of TypeII and TypeIII. Laplace and Fourier transform technique is applied to solve the problem. As an application، the bounding surface is subjected to concentrated and distributed sources (mechanical and thermal sources). The analytical expressions of displacement، stress components، temperature change and current density components are obtained in the transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerical simulated results are depicted graphically to show a comparison of effect of Hall current on the two theories GNII and GNIII on resulting quantities. Some special cases are also deduced from the present investigation.
Keywords: Transversely isotropic thermoelastic; Laplace and fourier transform; Concentrated and distributed sources; Rotation; Hall current
  
 NonLocal ThermoElastic Buckling Analysis of MultiLayer Annular/Circular NanoPlates Based on First and Third Order Shear Deformation Theories Using DQ Method Sh Dastjerdi , M Jabbarzadeh* Pages 859874 Abstract Full Text [PDF 872KB]   In present study، thermoelastic buckling analysis of multilayer orthotropic annular/circular graphene sheets is investigated based on Eringen’s theory. The moderately thick and also thick nanoplates are considered. Using the nonlocal first and third order shear deformation theories، the governing equations are derived. The van der Waals interaction between the layers is simulated for multilayer sheets. The stability governing equations are obtained according to the adjacent equilibrium estate method. The constitutive equations are solved by applying the differential quadrature method (DQM). Applying the differential quadrature method، the ordinary differential equations are transformed to algebraic equations. Then، the critical temperature is obtained. Since there is not any research in thermoelastic buckling analysis of multilayer graphene sheets، the results are validated with available single layer articles. The effects of nonlocal parameter، the values of van der Waals interaction between the layers، third to first order shear deformation theory analyses، nonlocal to local analyses، different values of Winkler and Pasternak elastic foundation and analysis of bilayer and triple layer sheets are investigated. It is concluded that the critical temperature increases and tends to a constant value along the rise of van der Waals interaction between the layers.
Keywords: Multi, layer orthotropic annular,circular graphene sheets; Non, local first and third order shear deformation theories; Thermo, elastic buckling analysis; Differential quadrature method (DQM)
  
 Lateral Vibrations of SingleLayered Graphene Sheets Using Doublet Mechanics A Fatahi , Vajari , A. Imam* Pages 875894 Abstract Full Text [PDF 949KB]   This paper investigates the lateral vibration of singlelayered graphene sheets based on a new theory called doublet mechanics with a length scale parameter. After a brief reviewing of doublet mechanics fundamentals، a sixth order partial differential equation that governs the lateral vibration of singlelayered graphene sheets is derived. Using doublet mechanics، the relation between natural frequency and length scale parameter is obtained in the lateral mode of vibration for singlelayered graphene. It is shown that length scale parameter plays a significant role in the lateral vibration behavior of singlelayered graphene sheets. Such effect decreases the natural frequency compared to the predictions of the classical continuum mechanics models. However with increasing the length of the plate، the effect of scale parameter on the natural frequency decreases. For validating the results of this method، the results obtained herein are compared with the existing nonlocal and molecular dynamics results and good agreement with the latter is observed.
Keywords: Doublet mechanics; Natural frequency; Length scale parameter; Lateral vibration; Single, layered graphene sheets
  
 Free and Forced Transverse Vibration Analysis of Moderately Thick Orthotropic Plates Using Spectral Finite Element Method M.R Bahrami , S Hatami * Pages 895915 Abstract Full Text [PDF 1602KB]   In the present study، a spectral finite element method is developed for free and forced transverse vibration of Levytype moderately thick rectangular orthotropic plates based on firstorder shear deformation theory. Levy solution assumption was used to convert the twodimensional problem into a onedimensional problem. In the first step، the governing outofplane differential equations are transformed from time domain into frequency domain by discrete Fourier transform theory. Then، the spectral stiffness matrix is formulated، using frequencydependent dynamic shape functions which are obtained from the exact solution of the governing differential equations. An efficient numerical algorithm، using drawing method is used to extract the natural frequencies. The frequency domain dynamic responses are obtained from solution of the spectral element equation. Also، the time domain dynamic responses are derived by using inverse discrete Fourier transform algorithm. The accuracy and excellent performance of the spectral finite element method is then compared with the results obtained from closed form solution methods in previous studies. Finally، comprehensive results for outofplane natural frequencies and transverse displacement of the moderately thick rectangular plates with six different combinations of boundary conditions are presented. These results can serve as a benchmark to compare the accuracy and precision of the numerical methods used.
Keywords: Spectral finite element method; First, order shear deformation theory; Orthotropic plate; Exact solution; Dynamic stiffness matrix; Discrete Fourier transform; Transverse vibration
  
 Calculation of Collision Speed Corresponded to Maximum Penetration Using Hydrodynamic Theory A.R Nezamabadi * Pages 916922 Abstract Full Text [PDF 757KB]   One of the most valid and efficient models of long rod projectile penetration in homogeneous targets is Tate and Alekseevskii’s (A&t) model. Based on Tate’s model، the present research tries to calculate the optimum speeds to achieve the maximum penetration depth in the homogeneous targets. The proposed collision speedpenetration depth diagrams are developed using Tate’s model. In this way، various collision speedpenetration depth diagrams for different projectile dynamic resistances and targets are calculated and the optimum speed envelope is derived. According to Tate’s diagrams، the increase of collision speed is not followed by the increase of penetration depth; instead، it causes erosion phenomenon to happen. The comparison of the resulted optimum penetration speeds and the available data confirms the findings. Speed and rigidity both have a positive impact on the increase of penetration depth. With the increase of speed، the erosion issue finds a higher significance due to the increase of pressure on the projectile tip. Therefore، higher speed and erosion are opposed to each other; for the case of Y>R، there are some maximum points which indicate the optimum reciprocity of the two mentioned factors to obtain a maximum penetration depth. In the present research، an equation is developed indicating the optimum speeds resulting in the maximum penetration rate in the case of Y>R. For the reciprocity of speed and erosion، the target resistance against an erosive projectile should be 4 to 5 fold higher than the same target resistance against a rigid projectile penetration. [1]
Keywords: Hydrodynamic theory; Tate and Alekseevskii’s theory; Erosion; Rigidity; Optimum speed; Maximum penetration depth
  
تاريخ انتشار: 10/10/95 تلفن: 34134025 (086)
تاريخ درج در سايت: 18/10/95
شمار بازديدکنندگان اين شماره: 127




