2017
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224
Evaluation of Fatigue Life Reduction Factors at Bolt Hole in Double Lap Bolted Joints Using Volumetric Method
2
2
In this research, the influence of bolt preload on the fatigue strength of 2024T3 aluminium alloy double lap bolted joints has been studied experimentally and numerically. To do so, three sets of the specimens were prepared and each of them subjected to tightening torque of 1,2.5 and 5 Nm and then fatigue tests were conducted under various cyclic axial load levels. In the numerical method, the influence of bolt preload on the fatigue life of double lap bolted joints were studied using the values of fatigue notch factor obtained by volumetric approach. In order to obtain stress distribution around the notch (hole) which is required for volumetric approach, nonlinear finite element simulations were carried out. To estimate the fatigue life, the SN curve of plain (unnotched) specimen and the fatigue notch factors obtained from volumetric method were used. The estimated fatigue life was compared with those obtained from the experiments. The investigation reveals that there is a good agreement between the life predicted by the volumetric approach and the experimental results for various specimens with different amounts of bolt preload. The volumetric approach and experimental results showed that the fatigue strength of specimens were improved by increasing the bolt preload as the result of compressive stresses which appeared around the bolt hole.
1

1
11


F
Esmaeili
Department of Mechanical Engineering, University College of Nabi Akram (UCNA),Tabriz, Iran
Department of Mechanical Engineering, University
Iran
esmaeili@ucna.ac.ir


S
Barzegar
Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran
Faculty of Mechanical Engineering, University
Iran


H
Jafarzadeh
Department of Mechanical Engineering, Tabriz Branch, Islamic Azad University ,Tabriz, Iran
Department of Mechanical Engineering, Tabriz
Iran
Clamping force
Bolted joint
Hybrid joint
Tightening torque
[[1] Huda Z., Zaharinie T., Min G., 2010, Temperature effects on material behavior of aerospace aluminum alloys for subsonic and supersonic aircraft, Journal of Aerospace Engineering 23(2): 124128.##[2] Mahadevan S., Shi P., 2001, Corrosion fatigue reliability of aging aircraft structures, Progress in Structural Engineering and Materials 3(2): 188197.##[3] Buyuk M., Kan S., Loikkanen M., 2009, Explicit finiteelement analysis of 2024t3/t351 aluminum material under impact loading for airplane engine containment and fragment shielding, Journal of Aerospace Engineering 22(3): 287295.##[4] Mao J., Kang S.B., Park J.O., 2005, Grain refinement, thermal stability and tensile properties of 2024 aluminum alloy after equalchannel angular pressing, Journal of Materials Processing Technology 159(3): 314320.##[5] Pratt J., Pardoen G., 2002, Numerical modeling of bolted lap joint behavior, Journal of Aerospace Engineering 15(1): 2031.##[6] Ireman T., 1998, Threedimensional stress analysis of bolted singlelap composite joints, Composite Structures 43(3): 195216.##[7] Pratt J., Pardoen G., 2002, Comparative behavior of singlebolted and dualbolted lap joints, Journal of Aerospace Engineering 15(2): 5563.##[8] Esmaeili F., Chakherlou T.N., Zehsaz M., Hasanifard S., 2013, Investigating the effect of clamping force on the fatigue life of bolted plates using volumetric approach, Journal of Mechanical Science and Technology 27(12): 36573664.##[9] Valtinat G., Hadrych I., Huhn H., 2000, Strengthening of riveted and bolted steel constructions under fatigue loading by preloaded fasteners experimental and theoretical investigations, Connections in Steel Structures IV.##[10] Chakherlou T.N., Abazadeh B., Vogwell J., 2009, The effect of bolt clamping force on the fracture strength and the stress intensity factor of a plate containing a fastener hole with edge cracks, Engineering Failure Analysis 16(1): 242253.##[11] Chakherlou T.N., AlvandiTabrizi Y., Kiani A., 2011, On the fatigue behavior of cold expanded fastener holes subjected to bolt tightening, International Journal of Fatigue 33(6): 800810.##[12] Budynas R.G., Nisbett J.K., 2011, Shigley’s Mechanical Engineering Design, 9rd ed, McGrawHill.##[13] Dowling N., 2012, Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture and Fatigue, Prentice Hall Inc, New Jersey.##[14] Esmaeili F., Hassanifard S., Zehsaz M., 2011, Fatigue life prediction of notched specimens using the volumetric approach, Journal of Solid Mechanics and Materials Engineering 5(9): 508518.##[15] Hassanifard S., Zehsaz M., Esmaeili F., 2011, Spot weld arrangement effects on the fatigue behavior of multispot welded joints, Journal of Mechanical Science and Technology 25(3): 647653.##[16] Adib H., Pluvinage G., 2003, Theoretical and numerical aspects of the volumetric approach for fatigue life prediction in notched components, International Journal of Fatigue 25(1): 6776.##[17] Tryon R. G., Dey A., 2003, Reliabilitybased model for fatigue notch effect, SAE International 1: 010462.##[18] Pluvinage G., 2004, Fracture and Fatigue Emanating From Stress Concentrators, Kluwer Academic Publishers, Dordrecht.##[19] Peterson R. E., 1974, Stress Concentration Factors, John Wiley & Sons, New York.##[20] Neuber H., 1961, Theory of Notch Stresses: Principles for Exact Calculation of Strength with Reference to Structural Form and Material, USAEC Office of Technical Information, Oak Ridge, Tenn.##[21] Heywood R.B., 1962, Design Against Fatigue, London, Chapman and Hall.##[22] Pluvinage G., 1997, Application of notch fracture mechanics to fracture emanating from stress concentrators. Advances in Computational Engineering Congress of Computational Engineering Sciences 97: 213218.##[23] Swanson Analysis Systems Inc, 2004, ANSYS, Release 9.##]
Bending Analysis of MultiLayered Graphene Sheets Under Combined NonUniform Shear and Normal Tractions
2
2
Bending analysis of multilayer graphene sheets (MLGSs) subjected to nonuniform shear and normal tractions is presented. The constitutive relations are considered to be nonclassical based on nonlocal theory of elasticity. Based on the differential transformation method, numerical illustrations are carried out for circular and annular geometries. The effects of nano scale parameter, radius of circular and annular graphene sheet, number of layers as well as distance between layers in the presence of van der Waals interaction forces are investigated. In addition, the effects of different boundary conditions are also examined. The numerical results show that above mentioned parameters have significant effects on the bending behavior of MLGSs under the action of nonuniform shear and normal tractions.
1

12
23


M.M
Alipour
Department of Mechanical Engineering, University of Mazandaran, Babolsar, Iran
Department of Mechanical Engineering, University
Iran


M
Shaban
Mechanical Engineering Department, Faculty of Engineering, BuAli Sina University, Hamadan, Iran
Mechanical Engineering Department, Faculty
Iran
m.shaban@basu.ac.ir
Graphene
Multilayer
Nonlocal
Shear and normal traction
[[1] Chang W. J., Lee H. L., 2014, Mass detection using a doublelayer circular graphenebased nanomechanical resonator, Journal of Applied Physics 116(3): 034303.##[2] Gheshlaghi B., Hasheminejad S. M., 2013, Size dependent damping in axisymmetric vibrations of circular nanoplates, Thin Solid Films 537: 212216.##[3] Gibson R. F., Ayorinde E. O., Wen Y. F., 2007, Vibrations of carbon nanotubes and their composites: A review, Composites Science and Technology 67(1): 128.##[4] Behfar K., Naghdabadi R., 2005, Nanoscale vibrational analysis of a multilayered graphene sheet embedded in an elastic medium, Composites Science and Technology 65(78): 11591164.##[5] Behfar K., Seifi P., Naghdabadi R., Ghanbari J., 2006, An analytical approach to determination of bending modulus of a multilayered graphene sheet, Thin Solid Films 496(2): 475480.##[6] Eringen A. C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54(9): 4703.##[7] Rafiee R., Moghadam R. M., 2014, On the modeling of carbon nanotubes : A critical review, Composites Part B 56: 435449.##[8] Eringen A. C., 2002, Nonlocal Continuum Field Theories, Springer.##[9] Lim C. W., 2010, On the truth of nanoscale for nanobeams based on nonlocal elastic stress field theory: equilibrium, governing equation and static deflection, Applied Mathematics and Mechanics 31(1):3754.##[10] Babaei H., Shahidi A. R., 2011, Vibration of quadrilateral embedded multilayered graphene sheets based on nonlocal continuum models using the Galerkin method, Acta Mechanica Sinica 27: 967976.##[11] Duan W. H., Wang C. M., 2007, Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory, Nanotechnology 18: 385704.##[12] Lim C. W., Li C., Yu J. L., 2012, Free torsional vibration of nanotubes based on nonlocal stress theory, Journal of Sound and Vibration 331(12): 27982808.##[13] Murmu T., Pradhan S. C., 2009, Smallscale effect on the free inplane vibration of nanoplates by nonlocal continuum model, Physica E: LowDimensional Systems and Nanostructures 41(8):16281633.##[14] Pradhan S. C., Phadikar J. K., 2009, Nonlocal elasticity theory for vibration of nanoplates, Journal of Sound and Vibration 325: 206223.##[15] Radić N., Jeremić D., Trifković S., Milutinović M., 2014, Buckling analysis of doubleorthotropic nanoplates embedded in Pasternak elastic medium using nonlocal elasticity theory, Composites Part B 61: 162171.##[16] Zenkour A. M., Sobhy M., 2013, Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium, Physica E: LowDimensional Systems and Nanostructures 53: 251259.##[17] Wang Y. Z., Li F. M., 2012, Static bending behaviors of nanoplate embedded in elastic matrix with small scale effects, Mechanics Research Communications 41: 4448##[18] Narendar S., Gopalakrishnan S., 2011, Scale effects on buckling analysis of orthotropic nanoplates based on nonlocal twovariable refined plate theory, Acta Mechanica 223(2):395413.##[19] Bedroud M., Nazemnezhad R., 2015, Axisymmetric / asymmetric buckling of functionally graded circular / annular Mindlin nanoplates via nonlocal elasticity, Physica E: LowDimensional Systems and Nanostructures 43(10):18201825.##[20] Farajpour A., Danesh M., Mohammadi M., 2011, Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics, Physica E: LowDimensional Systems and Nanostructures 44(3): 719727.##[21] Malekzadeh P., Farajpour A., 2012, Axisymmetric free and forced vibrations of initially stressed circular nanoplates embedded in an elastic medium, Acta Mechanica 223(11): 23112330.##[22] Bedroud M., HosseiniHashemi S., Nazemnezhad R., 2013, Buckling of circular/annular Mindlin nanoplates via nonlocal elasticity, Acta Mechanica 224(11): 26632676.##[23] Bedroud M., Nazemnezhad R., 2015, Axisymmetric / asymmetric buckling of functionally graded circular / annular Mindlin nanoplates via nonlocal elasticity, Meccanica 50:17911806.##[24] Shaban M., Alibeigloo A., 2014, Static analysis of carbon nanotubes based on shell model by using threedimensional theory of elasticity, Journal of Computational and Theoretical Nanoscience 11: 19541961.##[25] Shaban M., Alibeigloo A., 2014, Three dimensional vibration and bending analysis of carbon nano tubes embedded in elastic medium based on theory of elasticity, Latin American Journal of Solids and Structures 11: 21222140.##[26] Shaban M., Alipour M. M., 2011, Semianalytical solution for free vibration of thick functionally graded plates rested on elastic foundation with elastically restrained edge, Acta Mechanica Sinica 24(4): 340354.##[27] Alipour M. M., Shariyat M., Shaban M., 2010, A semisnalytical solution for free vibration and modal stress analyses of circular plates resting on twoparameter elastic foundations, Journal of Solid Mechechanics 2(1): 6378.##[28] Alipour M. M., Shariyat M., 2010, Stress analysis of twodirectional FGM moderately thick constrained circular plates with nonuniform load and substrate stiffness distributions, Journal of Solid Mechechanics 2(4): 316331.##[29] Alipour M. M., Shariyat M., 2011, A power series solution for free vibration of variable thickness mindlin circular plates with twodirectional material heterogeneity and elastic foundations, Journal of Solid Mechechanics 3(2): 183197.##[30] Saidi A. R., Rasouli A., Sahraee S., 2009, Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained thirdorder shear deformation plate theory, Composite Structures 89(1):110119.##]
Thermomechanical Response in Thermoelastic Medium with Double Porosity
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2
A dynamic two dimensional problem of thermoelasticity with double porous structure has been considered to investigate the disturbance due to normal force and thermal source. Laplace and Fourier transform technique is applied to the governing equations to solve the problem. The transformed components of stress and temperature distribution are obtained .The resulting expressions are obtained in the physical domain by using numerical inversion technique. Numerically computed results for these quantities are depicted graphically to study the effect of porosity. Results of Kumar & Rani [42] and Kumar & Ailawalia [43] have also been deduced as special cases from the present investigation.
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24
38


R
Kumar
Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana,India
Department of Mathematics, Kurukshetra University,
India
rajneesh_kuk@rediffmail.com


R
Vohra
Department of Mathematics& Statistics, H.P.University, Shimla, HP, India
Department of Mathematics& Statistics,
India


M.G
Gorla
Department of Mathematics& Statistics, H.P.University, Shimla, HP, India
Department of Mathematics& Statistics,
India
Thermoelasticity
Thermomechanical sources
Double porosity
Laplace and Fourier transforms
[[1] De Boer R., 2000, Theory of Porous Media , SpringerVerleg, New York.##[2] De Boer R., EhlersW.,1988, A historical review of the foundation of porous media theories, Acta Mechanica 74: 18.##[3] Biot M. A., 1941, General theory of threedimensional consolidation, Journal of Applied Physics 12: 155164.##[4] Bowen R.M.,1980, Incompressible porous media models by use of the theory of mixtures, International Journal of Engineering Science 18: 11291148.##[5] De Boer R., Ehlers W., 1990, Uplift, friction and capillaritythree fundamental effects for liquid saturated porous solids, International Journal of Solids and Structures 26: 4357.##[6] Barenblatt G.I., Zheltov I.P., Kochina I.N., 1960, Basic concept in the theory of seepage of homogeneous liquids in fissured rocks (strata), Journal of Applied Mathematics and Mechanics 24: 12861303.##[7] Wilson R. K., Aifantis E. C.,1982, On the theory of consolidation with double porosity, International Journal of Engineering Science 20(9): 10091035.##[8] Khaled M.Y., Beskos D. E., Aifantis E. C.,1984, On the theory of consolidation with double porosityIII, International Journal for Numerical and Analytical Methods in Geomechanics 8: 101123.##[9] Wilson R. K., Aifantis E. C., 1984, A double porosity model for acoustic wave propagation in fractured porous rock, International Journal of Engineering Science 22(810): 12091227.##[10] Beskos D. E., Aifantis E. C.,1986., On the theory of consolidation with double porosityII, International Journal of Engineering Science 24(111): 16971716.##[11] Khalili N., Valliappan S., 1996, Unified theory of flow and deformation in double porous media, European Journal of Mechanics  A/Solids 15: 321336.##[12] Aifantis E. C., 1977, Introducing a multi –porous medium, Developments in Mechanics 8: 209211.##[13] Aifantis E. C.,1979, On the response of fissured rocks, Developments in Mechanics 10: 249253.##[14] Aifantis E.C., 1980, On the problem of diffusion in solids, Acta Mechanica 37: 265296.##[15] Aifantis E.C., 1980, The Mechanics of Diffusion in Solids, T.A.M. Report No. 440, Department of Theoretical and Applied Mechanics, University of Illinois, Urbana, Illinois.##[16] Moutsopoulos K. N., Eleftheriadis I. E., Aifantis E. C.,1996, Numerical simulation of transport phenomena by using the double porosity/ diffusivity Continuum model, Mechanics Research Communications 23(6): 577582.##[17] Khalili N., Selvadurai A. P. S., 2003, A fully coupled constitutive model for thermohydro –mechanical analysis in elastic media with double porosity, Geophysical Research Letters 30: 22682271.##[18] Pride S. R., Berryman J. G., 2003, Linear dynamics of double –porosity dualpermeability materialsI, Physical Review E 68: 036603.##[19] Straughan B., 2013, Stability and uniqueness in double porosity elasticity, International Journal of Engineering Science 65:18.##[20] Svanadze M., 2005, Fundamental solution in the theory of consolidation with double porosity, Journal of the Mechanical Behavior of Materials 16:123130.##[21] Svanadze M., 2010, Dynamical problems on the theory of elasticity for solids with double porosity, Applied Mathematics and Mechanics 10: 209310.##[22] Svanadze M., 2012, Plane waves and boundary value problems in the theory of elasticity for solids with double porosity, Acta Applicandae Mathematicae 122: 461470.##[23] Svanadze M., 2014, On the theory of viscoelasticity for materials with double porosity, Discrete and Continuous Dynamical Systems  Series B 19(7): 23352352.##[24] Svanadze M., 2014, Uniqueness theorems in the theory of thermoelasticity for solids with double porosity, Meccanica 49: 20992108.##[25] Scarpetta E., Svanadze M., Zampoli V., 2014, Fundamental solutions in the theory of thermoelasticity for solids with double porosity, Journal of Thermal Stresses 37(6): 727748.##[26] Scarpetta E., Svanadze M., 2014 ,Uniqueness theorems in the quasistatic theory of thermo elasticity for solids with double porosity, Journal of Elasticity 120: 6786.##[27] Kumar R., Ailawalia P., 2005, Elastodynamics of inclined loads in an micropolar cubic crystal, Mechanics and Mechanical Engineering 9(2): 5775.##[28] Kumar R., Kaushal S., Miglani A., 2010, Analysis of deformation due to various sources in micropolar thermodiffusive elastic medium, International Journal for Computational Methods in Engineering Science and Mechanics 11:196210.##[29] Kumar R., Singh D., Kumar A.,2014, A problem in microtstetch thermoelastic diffusion medium, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering 8(1): 2427.##[30] Iesan D., Quintanilla R., 2014, On a theory of thermoelastic materials with a double porosity structure, Journal of Thermal Stresses 37: 10171036.##[31] Sherief H., Saleh H., 2005, A half space problem in the theory of generalized thermoelastic diffusion, International Journal of Solids and Structures 42: 44844493.##[32] Khalili N., 2003, Coupling effects in double porosity media with deformable matrix, Geophysical Research Letters 30(22): 21532155.##[33] Nowacki W., 1967, On the completeness of stress functions in thermoelasticity, Bulletin De L’academie Polonaise des Sciences 15(9): 583591.##[34] Wang W., Wang M.Z., 1992, Constructivity and completeness of the general solutions in elastodynamics, Acta Mechanica 91: 209214.##[35] EskandarGhadi M., 2005, A complete solution of the wave equations for transversely isotropic media, Journal of Elasticity 81:119.##[36] EskandariGhadi M., Pak Ronald Y.S., 2008, Elastodynamics and elastostatic by a unified method of potentials for convex domains, Journal of Elasticity 92:187194.##[37] Hayati Y., EskandariGhadi M., Raoofian M., Rahimian M., Ardalan A.A., 2013, Frequency domain analysis of an axisymmetric thermoelastic transversely isotropic halfspace, Journal of Engineering Mechanics 139:14071418.##[38] Hayati Y., EskandariGhadi M., Raoofian M., Rahimian M., Ardalan A.A., 2013, Domain Green’s functions of an axisymmetric thermoelastic halfspace by a method of potentials, Journal of Engineering Mechanics 139:11661177.##[39] EskandariGhadi M., Rahimian M., Sture S., Forati M., 2014, Thermoelastodynamics in transversely isotropic media with scalar potential functions, Journal of Applied Mechanics 81: 021013.##[40] Raoofian Naeeni M., EskandriGhadi M., Ardalan A.A., Strure S., Rahimian M., 2015, Transient response of a thermoelastic halfspace to mechanical and thermal buried source, Zeitschrift für Angewandte Mathematik und Mechanik 95(4): 354376.##[41] Kumar R., Rani L., 2004, Response of Generalized thermoelastic halfspcae with voids dut to mechanical and thermal sources, Meccanica 39: 563584.##[42] Kumar R., Rani L., 2005, Interaction due to mechanical and thermal sources in thermoelastic halfspace with voids, Journal of Vibration and Control 11: 499517.##[43] Kumar R., Ailawalia P, 2006, Deformations due to mechanical sources in elastic solid with voids, International Journal of Applied Mechanics and Engineering 11(4): 865880.##[44] Unger D.J., Aifantis E.C.,1988, Completeness of solutions in the double porosity theory, Acta Mechanica 75:269274.##[45] Honig G., Hirdes U., 1984, A method for the numerical inversion of the Laplace transform, Journal of Computational and Applied Mathematics 10:113132.##[46] Press W.H., Teukolsky S.A., Vellerlig W.T., Flannery B.P., 1986, Numerical Recipes in Fortran , Cambridge University Press, Cambridge.##[47] Raoofian Naeeni M., Campagna R., EskandriGhadi M., Ardalan A.A., 2015,Performance comparison of numerical inversion methods for Laplace and Hankel integral transforms in engineering problems, Applied Mathematics and Computation 250: 759775.##[48] Sharma J.N., Chauhan R.S., 2001, Mechanical and thermal sources in a generalized thermoelastic halfspace, Journal of Thermal Stresses 24: 651675.##[49] Bradie B., 2007, A Friendly Introduction to Numerical Analysis, Pearson Education/Prentice Hall, New Delhi, India.##]
Free Vibration and Buckling Analysis of Sandwich Panels with Flexible Cores Using an Improved Higher Order Theory
2
2
In this paper, the behavior of free vibrations and buckling of the sandwich panel with a flexible core was investigated using a new improved highorder sandwich panel theory. In this theory, equations of motion were formulated based on shear stresses in the core. Firstorder shear deformation theory was applied for the procedures. In this theory, for the first time, incompatibility problem of velocity and acceleration field existing in Frostig's first theory was solved using a simple analytical method. The main advantage of this theory is its simplicity and less number of equations than the second method of Frostig's highorder theory. To extract dynamic equations of the core, threedimensional elasticity theory was utilized. Also, to extract the dynamic equations governing the whole system, Hamilton's principle was used. In the analysis of free vibrations, the panel underwent primary pressure plate forces. Results demonstrated that, as plate preloads got closer to the critical buckling loads, the natural frequency of the panel tended zero. The results obtained from the present theory were in good correspondence with the results of the most recent papers.
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K
Malekzadeh Fard
Department of Mechanical Engineering, Malek Ashtar University, Tehran, Iran
Department of Mechanical Engineering, Malek
Iran


H
MalekMohammadi
Department of Mechanical Engineering BuAli Sina University, Hamedan, Iran
Department of Mechanical Engineering BuAli
Iran
h.malekmohamadi93@basu.ac.ir
Free vibration
Buckling
Plate sandwich
Flexible core
Navier’s methods
[[1] Kameswara Rao M., Desai Y.M., Chitnis M.R., 2001, Free vibrations of laminated beams using mixed theory, Composite Structures 52(2): 149160.##[2] Kant T., Swaminathan K., 2001, Free vibrations of laminated beams using mixed theory, Composite Structures 53(1): 7385.##[3] Meunier M., Shenoi R.A., 2001, Dynamic analysis of composite sandwich plates with damping modelled using highorder shear deformation theory, Composite Structures 54(23): 243254.##[4] Nayak A.K., Moy S. S. J., Shenoi R.A., 2002, Free vibration analysis of composite sandwich plates based on Reddy's higherorder theory, Composites Part B: Engineering 33(7): 505519.##[5] Frostig Y., Thomsen O.H., 2004, Highorder free vibration of sandwich panels with a flexible core, International Journal of Solids and Structures 41(56): 16971724.##[6] Malekzadeh K., Khalili K. M. R., Mittal R. K., 2005, Local and global damped vibrations of plates with a viscoelastic soft flexible core: an improved highorder approach, Journal of Sandwich Structures and Materials 7(5): 431456.##[7] Frostig Y., Baruch M., 1990, Bending of sandwich beams with transversely flexible core, American Institute of Aeronautics and Astronautics 28(3): 523531.##[8] Frostig Y., Baruch M., 1994, Free vibrations of sandwich beams with a transversely flexible core: a high order approach, Journal of Sound and Vibration 176(2): 195208.##[9] Frostig Y., 1998, Buckling of sandwich panels with a flexible core—highorder theory, International Journal of Solids and Structures 35(3): 183204.##[10] Frostig Y., Thomsen O.H., 2007, Buckling and nonlinear response of sandwich panels with a compliant core and temperaturedependent mechanical properties, Journal of Mechanics of Materials and Structures 2(7): 13551380.##[11] Dafedar J.B., Desai Y.M., Mufti A. A., 2003, Stability of sandwich plates by mixed, higherorder analytical formulation, International Journal of Solids and Structures 40(17): 45014517.##[12] Pandit M.K., Singh B.N., Sheikh A.H., 2008, Buckling of laminated sandwich plates with soft core based on an improved higher order zigzag theory, ThinWalled Structures 46(11): 11831191.##[13] Ćetković M., Vuksanović D.J., 2009, Bending, free vibrations and buckling of laminated composite and sandwich plates using a layer wise displacement model, Composite Structures 88(2): 219227.##[14] Yao S., Kuo., LeChung Shiau., 2009, Buckling and vibration of composite laminated plates with variable fiber spacing, Composite Structures 90(2): 196200.##[15] Fiedler L., Lacarbonara W., Vestroni F., 2010, A generalized higherorder theory for buckling of thick multilayered composite plates with normal and transverse shear strains, Composite Structures 92(12): 30113019.##[16] Shariyat M., 2010, A generalized highorder global–local plate theory for nonlinear bending and buckling analyses of imperfect sandwich plates subjected to thermomechanical loads, Composite Structures 92(1): 130143.##[17] Dariushi S., Sadighi M., 2015, Analysis of composite sandwich beam with enhanced nonlinear high order sandwich panel theory, Modares Mechanical Engineering 14(16): 18.##[18] Rao M.K., Scherbatiuk K., Desai Y.M., Shah A.H., 2004, Natural vibrations of laminated and sandwich plates, Journal of Engineering of Mechanics 130(11): 12681278.##[19] Zhen W., Wanji C., Xiaohui R., 2010, An accurate higherorder theory and C0 finite element for free vibration analysis of laminated composite and sandwich plates, Composite Structures 92(6): 12991307.##[20] Zhen W., Wanji C., 2007, Thermo mechanical buckling of laminated composite and sandwich plates using global–local higher order theory, International Journal of Mechanical Sciences 49(6): 712721.##]
Surface Degradation of Polymer Matrix Composites Under Different Low Thermal Cycling Conditions
2
2
The principal effects of mass degradation on polymer matrix composites (PMCs) are the decay of mechanical properties such as strength, elongation, and resilience. This degradation is a common problem of the PMCs under thermal cycling conditions. In this article, composite degradation was investigated by measurement of total mass loss (TML) using the Taguchi approach. Thermal cycling tests were performed using a developed thermal cycling apparatus. Weight loss experiments were performed on the glass fiber/epoxy laminates under different number of thermal cycles and temperature differences. Also, The specimens had various fiber volume fractions and stacking sequences. Statistical analysis is performed to study contribution of each factor. Based on weight loss rates, a regression model was presented to evaluate the TML of laminated composite materials samples. It was found that the temperature differences and fiber volume fraction are the most effective factors of surface degradation with 61 and 22 percent contribution. Also, under the similar experimental conditions, the [0]8 layups exhibits 44 and 35.7 percent more mass loss than the [0/±45/90]s and [02/902]s layups, respectively.
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62


A.R
Ghasemi
Faculty of Mechanical Engineering, Department of Solid Mechanics, University of Kashan, Kashan, Iran
Faculty of Mechanical Engineering, Department
Iran
ghasemi@kashanu.ac.ir


M
Moradi
Faculty of Mechanical Engineering, Department of Solid Mechanics, University of Kashan, Kashan, Iran
Faculty of Mechanical Engineering, Department
Iran
Thermal cycling
Total mass loss
Polymer matrix composites (PMCs)
Taguchi Method
Stacking sequence
[[1] Sethi S., Ray B.Ch., 2014, Environmental effects on fibre reinforced polymeric composites: Evolving reasons and remarks on interfacial strength and stability, Advances in Colloid and Interface Science 217: 4367.##[2] Chung K., Seferis J.C., Nam J.D., 2000, Investigation of thermal degradation behavior of polymeric composites: prediction of thermal cycling effect from isothermal data, Composites: Part A 31: 945957.##[3] Meyer M.R., Friedman R.J., Schutte H.D.J., Jr L.R.A., 1994, Longterm durability of the interface in FRP composites after exposure to simulated physiologic saline environments, Journal of Biochemical Materials Research 28: 12211231.##[4] Yu Q., Chen P., Gao Y., Mu J., Chen Y., Lu Ch., Liu D., 2011, Effects of vacuum thermal cycling on mechanical and physical properties of high performance carbon/bismaleimide composite, Materials Chemistry and Physics 130: 10461053.##[5] Moon J.B., Kim M. G., Kim Ch. G., Bhowmik Sh., 2011, Improvement of tensile properties of CFRP composites under LEO space environment by applying MWNTs and thinply, Composites: Part A 42: 694701.##[6] Paillous A. Pailler C., 1994, Degradation of multiply polymer–matrix composites induced by space environment, Composites 25(4): 287295.##[7] Chao Zh., Binienda K.W., Morscher G.N., Martin R.E., Kohlman L.W., 2013, Experimental and FEM study of thermal cycling induced microcracking in carbon/epoxy triaxial braided composites, Composites Part A: Applied Science and Manufacturing 46: 3444.##[8] Nam J.D., Seferis J.C., 1992, Anisotropic thermooxidative stability of carbon fiber reinforced polymeric composites, SAMPE Quarterly 24: 1018.##[9] Shin K.B., Kim C.G., Hong C.S., Lee H.H., 2000, Prediction of failure thermal cycles in graphite/epoxy composite materials under simulated low earth orbit environments, Composites Part B 31(3): 223235.##[10] LafarieFrenot M.C., 2006, Damage mechanisms induced by cyclic plystresses in carbon–epoxy laminates: Environmental effects, International Journal of Fatigue 28(10): 12021216.##[11] LafarieFrenot M.C., Grandidier J.C., Gigliotti M., Olivier L., Colin X., Verdu J., Cinquin J., 2010, Thermooxidation behaviour of composite materials at high temperatures: A review of research activities carried out within the COMEDI program, Polymer Degradation and Stability 95(6): 965974.##[12] Taguchi G., Konishi S., 1987, Taguchi Methods, Orthogonal Arrays and Linear Graphs, Tools for Quality Engineering, American Supplier Institute Dearborn.##[13] Dobrzañski L.A., Domaga J., Silva J.F., 2007, Application of taguchi method in the optimization of filament winding of thermoplastic composites, Archives of Materials Science and Engineering 28(3): 133140.##[14] Ghasemi A.R., Baghersad R., Sereshk M.R.V., 2011, Nonlinear behavior of polymer based composite laminates under cyclic thermal shock and its effects on residual stresses, Journal of Polymer Science and Technology 24(2): 133140.##[15] Ghasemi A.R., Baghersad R., 2012, Analytical and experimental studies of cyclic thermal shock effects on nonlinear behavior of composite laminates, Journal of Aeronautical Engineering 14(2): 1116.##[16] ASTM, D. D 3039M95a, 1997, Standard test method for tensile properties of polymer matrix composite materials.##[17] MINITAB 17 statistical software, Minitab Inc, 2013.##[18] Colin X., Marais C., Verdu J., 2002 , Kinetic modelling and simulation of gravimetric curves: application to the oxidation of bismaleimide and epoxy resins, Polymer Degradation and Stability 78: 545553.##]
ThermoElastic Analysis of NonUniform Functionally Graded Circular Plate Resting on a Gradient Elastic Foundation
2
2
Present paper is devoted to stress and deformation analyses of heated variable thickness functionally graded (FG) circular plate with clamped supported, embedded on a gradient elastic foundation and subjected to nonuniform transverse load. The plate is coupled by an elastic medium which is simulated as a Winkler Pasternak foundation with gradient coefficients in the radial and circumferential directions during the plate deformation. The temperature distribution is assumed to be a function of the thickness direction. The governing state equations are derived in terms of displacements and temperature based on the 3D theory of thermoelasticity. These equations are solved using a semianalytical method to evaluate the deformation and stress components in the plate. Material properties of the plate except the Poisson's ratio are assumed to be graded continuously along the thickness direction according to an exponential distribution. A parametric study is accomplished to evaluate the effects of material heterogeneity indices, foundation parameters, temperature difference between the top and bottom surfaces of the plate and thickness to radius ratio on displacements and stresses. The results are reported for the first time and the new results can be used as a benchmark solution for the future researches.
1

63
85


A
Behravan Rad
Engineering Department ,Zamyad Company,15Km Karaj Old Road, P.O 1386183741, Tehran, Iran
Engineering Department ,Zamyad Company,15Km
Iran
abehravanrad@aol.com
Functionally graded
Circular plate
Gradient foundation
Thermomechanical
Semianalytical
Nonuniform
[[1] Reddy J.N., Wang C.M., Kitipornchai S., 1999, Axisymmetric bending of functionally graded circular and annular plates, European Journal of Mechanics A/Solids 18(2): 185189.##[2] Najafizadeh M. M., Heydari H. R., 2008, An exact solution for buckling of functionally graded circular plates based on higher order shear deformation plate theory under uniform radial compression, International Journal of Mechanical Science 50(3): 603612.##[3] Ma L. s., Wang T. J., 2003, Nonlinear bending and post buckling of functionally graded circular plates under mechanical and thermal loadings, International Journal of Solids & Structures 40: 33113330.##[4] Khorshidvand A. R., Jabbari M., Eslami M. R., 2012, Thermo elastic buckling analysis of functionally graded circular plates integrated with oiezoelectric layers, Journal of Thermal Stress 35: 695717.##[5] Kiani Y., Eslami M. R., 2013, An exact solution for thermal buckling of annular FGM plates on an elastic medium, Composites Part: B Engineering 45: 101110.##[6] Gaikwad K. R., 2013, Analysis of thermoelastic deformation of a thin hollow circular disk due to partially distributed heat supply, Journal of Thermal Stress 36: 207224.##[7] Golmakani M.E., Kadkhodayan M., 2014, An investigation into the thermo elastic analysis of circular and annular FGM plates, Mechanics of Advanced Materials and Structures 21(1): 113.##[8] Fallah F., Noseir A., 2015, Thermo  mechanical behavior of functionally graded circular sector plates, Acta Mechanica 226: 3754.##[9] Gunes R., Reddy J. N., 2008, Nonlinear analysis of functionally graded circular plates under different loads and boundary conditions, International Journal of Structural Stability and Dynamic 8(1): 131159.##[10] Prakash T., Ganapathi M., 2006, Asymmetric flexural vibration and thermoelastic stability of functionally graded circular plates using finite element method, Composite Part: B Engineering 37(78): 642649.##[11] Gomshei M. M., abbasi V., 2013, Thermal buckling analysis of annular FGM plate having variable thickness under thermal load of arbitrary distribution by finite element method, Journal of Mechanical Science and Technology 27 (4): 10311039.##[12] Afsar A. M., Go J., 2010, Finite element analysis of thermoelastic field in a rotating FGM circular disk, Applied Mathematical Modeling 34: 33093320.##[13] Leu SY., Chien Lc., 2015, Thermoelastic analysis of functionally graded rotating disks with variable thickness involving nonuniform heat source, Journal of Thermal Stress 38: 415426.##[14] Safaeian Hamzehkolaei N., Malekzadeh P., Vaseghi J., 2011, Thermal effect on axisymmetric bending of functionally graded circular and annular plates using DQM, Steel and Composite Structures 11(4): 341358.##[15] Malekzadeh P., Golbahar Haghighi M.R., Atashi M.M., 2011, Free vibration analysis of elastically supported functionally graded annular plates subjected to thermal environment, Meccanica 47(2): 321333.##[16] Sepahi O., Forouzan M.R., Malekzadeh P., 2011, Thermal buckling and post buckling analysis of functionally graded annular plates with temperature dependent material properties, Materials & Design 32(7): 40304041.##[17] Sepahi O., Forouzan M.R., Malekzadeh P., 2010, Large deflection analysis of thermomechanical loaded annular FGM plates on nonlinear elastic foundation via DQM, Composite Structures 92: 23692378.##[18] Jabbari M., Shahryari E., Haghighat H., Eslami M.R., 2014, An analytical solution for steady state three dimensional thermo elasticity of functionally graded circular plates due to axisymmetric loads, European Journal of Mechanics A/Solids 47: 124142.##[19] Nie G.J., Zhong Z., 2007, Semianalytical solution for threedimensional vibration of functionally graded circular plates, Computational Methods in Applied Mechanics and Engineering 196: 49014910.##[20] Yu Li X., Li P.D., Kang G.Z., Pan D.Z., 2013, Axisymmetric thermoelasticity field in a functionally graded circular plate of transversely isotropic material, Mathematics and Mechanics of Solid 18(5): 464475.##[21] Behravan Rad A., 2012, Semianalytical solution for functionally graded solid circular and annular plates resting on elastic foundations subjected to axisymmetric transverse loading, Advances in Applied Mathematics and Mechanics 4(2): 205 222.##[22] Behravan Rad A., Alibeigloo A., 2013, Semianalytical solution for the static analysis of 2D functionally graded circular and annular circular plates resting on elastic foundation, Mechanics of Advanced Materials and Structures 20(7): 515528.##[23] Behravan Rad A., 2012, Static response of 2D functionally graded circular plate with gradient thickness and elastic foundations to compound loads, Structural Engineering and Mechanics 44(2):139161.##[24] Shu C., 2000, Differential Quadrature and Its Application in Engineering, Springer, New York.##[25] Zong Z., Zhang Y., 2009, Advanced Differential Quadrature Methods, CRC Press, New York.##]
Analysis of Plane Waves in Anisotropic MagnetoPiezothermoelastic Diffusive Body with Fractional Order Derivative
2
2
In this paper the propagation of harmonic plane waves in a homogeneous anisotropic magnetopiezothermoelastic diffusive body with fractional order derivative is studied. The governing equations for a homogeneous transversely isotropic body in the context of the theory of thermoelasticity with diffusion given by Sherief et al. [1] are considered as a special case. It is found that three types of waves propagate in one dimension anisotropic magnetopiezothermoelastic diffusive body, namely quasilongitudinal wave (QP), quasithermal wave (QT) and quasidiffusion wave (QD). The different characteristics of waves like phase velocity, attenuation coefficient, specific heat loss and penetration depth are computed numerically and presented graphically for Cadmium Selenide (CdSe) material. The effect of fractional order parameter on phase velocity, attenuation coefficient, specific heat loss and penetration depth has been studied.
1

86
99


R
Kumar
Department of Mathematics, Kurukshetra University Kurukshetra136119, Haryana , India
Department of Mathematics, Kurukshetra University
India
rajneesh_kuk@rediffmail.com


P
Sharma
Department of Mathematics, Kurukshetra University Kurukshetra136119, Haryana , India
Department of Mathematics, Kurukshetra University
India
Piezothermoelastic
Magneto
Harmonic plane wave
Phase velocity
Attenuation coefficient
[[1] Sherief H. H., Hamza F.A., Saleh H.A., 2004, The theory of generalised thermoelastic diffusion, International Journal of Engineering Science 42(5): 591608.##[2] Sherief H.H., ElSayed A.M., ElLatief A.M., 2010, Fractional order theory of thermoelasticity, International Journal of Solids and Structures 47: 269275.##[3] Mindlin R.D.,1974, Equation of high frequency of thermopiezoelectric crystals plates, International Journal of Solids and Structures 10: 625637.##[4] Nowacki W., 1978, Some general theorems of thermopiezoelectricity, Journal of Thermal Stresses 1:171182.##[5] Nowacki W., 1979 , Foundation of Linear Piezoelectricity, In Parkus, Interactions in Elastic Solids, Springer, Wein.##[6] Chandrasekharaiah D.S., 1984, A generalised linear thermoelasticity theory of piezoelectric media, Acta Mechanica 71: 293349.##[7] Sharma M.D., 2010, Propagation of inhomogeneous waves in anisotropic piezothermoelastic media, Acta Mechanica 215: 307318.##[8] Sharma J .N., Kumar M., 2000, Plane harmonic waves in piezothermoelastic materials, Indian Journal of Engineering & Materials Sciences 7: 434442.##[9] Sharma J.N., Walia V., 2007, Further investigation on Rayleigh waves in piezothermoelastic materials, Journal of Sound and Vibration 301:189206.##[10] Sharma J.N., Pal M., Chand D., 2005, Propagation characteristics of Rayleigh waves in transversely isotropic piezothermoelastic materials, Journal of Sound and Vibration 284: 227248.##[11] Alshaikh F. A., 2012, The mathematical modelling for studying the influence of the initial stresses and relaxation times on reflection and refraction waves in piezothermoelastic halfspace, Applied Mathematics 3: 819832.##[12] Singh B., 2005, Reﬂection of P and SV waves from free surface of an elastic solid with generalized thermodiﬀusion, Journal of Earth System Science 114(2): 159168.##[13] Singh B., 2006, Reﬂection of SV waves from free surface of an elastic solid in generalized thermodiffusion, Journal of Sound and Vibration 291: 764778.##[14] Aouadi M., 2006, Variable electrical and thermal conductivity in the theory of generalized thermodiffusion, Zeitschrift für Angewandte Mathematik und Physik 57(2): 350366.##[15] Aouadi M., 2006, A generalized thermoelastic diﬀusion problem for an inﬁnitely long solid cylinder, International Journal of Mathematics and Mathematical Sciences 2006:115.##[16] Aouadi M., 2007, A problem for an inﬁnite elastic body with a spherical cavity in the theory of generalized thermoelastic diﬀusion, International Journal of Solids and Structures 44: 57115722.##[17] Aouadi M., 2007, Uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion, Journal of Thermal Stresses 30: 665678.##[18] Aouadi M.,2008, Generalized theory of thermoelastic diﬀusion for anisotropic media, Journal of Thermal Stresses 31: 270285.##[19] Sharma J.N., Singh D., Sharma R., 2003, Generalized thermoelastic waves in transversely isotropic plates, Indian Journal of Pure and Applied Mathematics 34(6): 841852.##[20] Sharma J.N., 2007, Generalized thermoelastic diﬀusive waves in heat conducting materials, Journal of Sound and Vibration 301: 979993.##[21] Sharma J.N., Sharma Y.D., Sharma P.K., 2008, On the propagation elastothermodiﬀusive surface waves in heatconducting materials, Journal of Sound and Vibration 315(4): 927938.##[22] Kumar R., Kansal T., 2012, Analysis of plane waves in anisotropic thermoelastic diffusive body, Mechanics of solids 47(3): 337352.##[23] Van Run A. M. J. G., Terrell D.R., Scholing J.H., 1974, An in situ grown eutectic magnetoelectric composite material, Journal of Materials Science 9: 17101714.##[24] Li J.Y., Dunn M.L., 1998, Micromechanics of mgnetoelectrostatic composites: average fields and effective behaviour, Journal of Intelligent Material Systems and Structures 9: 404416.##[25] Oatao Y., Ishihara M., 2013, Transient thermoelastic analysis of a laminated hollow cylinder constructed of isotropic elastic and magnetoelectrothermoelastic material, Advances in Materials Science and Applications 2(2): 4859.##[26] Pang Y., Li J. X., 2014, SH interfacial waves between piezoelectric/piezomagnetic halfspaces with magnetoelectroelastic imperfect bonding, Piezoelectricity, Acoustic Waves, and Device Applications .##[27] Li L., Wei P.J., 2014, The piezoelectric and piezomagnetic effect on the surface wave velocity of magnetoelectroelastic solids, Journal of Sound and Vibration 333(8): 23122326.##[28] Abdalla Aboelnour N., Alshaikh F., Giorgio I., Della Corte A., 2015, A mathematical model for longitudinal wave propagation in a magnetoelastic hollow circular cylinder of anisotropic material under the influence of initial hydrostatic stress, Mathematics and Mechanics of Solids 21: 104118.##[29] Kumar R., Gupta V., 2013, Plane wave propagation in an anisotropic thermoelastic body with fractional order derivative and void, Journal of Thermoelasticity 1(1): 2134.##[30] Bassiouny E., Sabry R., 2013, Fractional order two temperature thermoelastic behavior of piezoelectric materials, Journal of Applied Mathematics and Physics 1(5):110120 .##[31] Meerschaert M. M., McGough R. J., 2014, Attenuated fractional wave equations with anisotropy, Journal of Vibration and Acoustics 136:051004.##[32] Kumar R., Gupta V., 2015, Plane wave propagation and domain of influence in fractional order thermoelastic materials with three phase lag heat transfer, Mechanics of Advanced Materials and Structures 23(8): 896908.##[33] Meral F. C., Royston T.J., Magin R.L., 2009, Surface response of a fractional order viscoelastic halfspace to surface and subsurface sources, Journal of the Acoustical Society of America 126(6): 32783285.##[34] Meral F.C., Royston T. J., Magin R. L., 2011, RayleighLamb wave propagation on a fractional order viscoelastic plat, Journal of the Acoustical Society of America 129(2): 10361045.##[35] Li J. Y., 2003, Uniqueness and reciprocity theorems for linear thermoelectromagnetoelasticity, Journal of Mechanics and Applied Mathematics 56(1): 3543.##[36] Kuang Z.B., 2010, Variational principles for generalised thermodiffusion theory in pyroelectricity, Acta Mechanica 214: 275289.##[37] Slaughter W.S., 2002, The Linearized Theory of Elasticity, Birkhauser Boston.##]
Stress Analysis of Rotating Thick Truncated Conical Shells with Variable Thickness under Mechanical and Thermal Loads
2
2
In this paper, thermoelastic analysis of a rotating thick truncated conical shell subjected to the temperature gradient, internal pressure and external pressure is presented. Given the existence of shear stress in the conical shell due to thickness change along the axial direction, the governing equations are obtained based on firstorder shear deformation theory (FSDT). These equations are solved by using multilayer method (MLM). The model has been verified with the results of finite element method (FEM). Finally, some numerical results are presented to study the effects of thermal and mechanical loading, geometry parameters of truncated conical shell.
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100
114


M
Jabbari
Mechanical Engineering Department, Yasouj University, P.O.Box: 75914353, Yasouj, Iran
Mechanical Engineering Department, Yasouj
Iran


M
Zamani Nejad
Mechanical Engineering Department, Yasouj University, P.O.Box: 75914353, Yasouj, Iran
Mechanical Engineering Department, Yasouj
Iran
m_zamani@yu.ac.ir


M
Ghannad
Mechanical Engineering Faculty, Shahrood University, Shahrood, Iran
Mechanical Engineering Faculty, Shahrood
Iran
Pressurized conical shells
Variable thickness
Thermoelastic analysis
Rotation
Multilayer method (MLM)
[[1] Eipakchi H. R., Khadem S. E., Rahimi G. H., 2008, Axisymmetric stress analysis of a thick conical shell with varying thickness under nonuniform internal pressure, Journal of Engineering Mechanics 134(8): 601610.##[2] Nejad M. Z., Jabbari M., Ghannad M., 2015, Elastic analysis of axially functionally graded rotating thick cylinder with variable thickness under nonuniform arbitrarily pressure loading, International Journal of Engineering Science 89: 8699.##[3] Ghasemi A. R., Kazemian A., Moradi M., 2014, Analytical and numerical investigation of FGM pressure vessel reinforced by laminated composite materials, Journal of Solid Mechanics 6(1): 4353.##[4] Nejad M. Z., Jabbari M., Ghannad M., 2015, Elastic analysis of rotating thick cylindrical pressure vessels under nonuniform pressure: linear and nonlinear thickness, Periodica Polytechnica Engineering, Mechanical Engineering 59(2): 6573.##[5] Witt F.J., 1965, Thermal stress analysis of conical shells, Nuclear Structure Engineering 1(5): 449456.##[6] Panferov I. V., 1991, Stresses in a transversely isotropic conical elastic pipe of constant thickness under a thermal load, Journal of Applied Mathematics and Mechanics 56(3): 410415.##[7] Sundarasivarao B. S. K., Ganesan N. 1991, Deformation of varying thickness of conical shells subjected to axisymmetric loading with various end conditions, Engineering Fracture Mechanics 39(6): 10031010.##[8] Jane K. C., Wu Y. H., 2004, A generalized thermoelasticity problem of multilayered conical shells, International Journal of Solids Structures 41: 22052233.##[9] Vivio F., Vullo V., 2007, Elastic stress analysis of rotating converging conical disks subjected to thermal load and having variable density along the radius, International Journal of Solids Structures 44: 77677784.##[10] Naj R., Boroujerdy M. B., Eslami M. R., 2008, Thermal and mechanical instability of functionally graded truncated conical shells, Thin Walled Structures 46: 6578.##[11] Eipakchi H. R., 2009, Errata for axisymmetric stress analysis of a thick conical shell with varying thickness under nonuniform internal pressure, Journal of Engineering Mechanics 135(9): 10561056.##[12] Sladek J., Sladek V., Solek P., Wen P. H., Atluri A. N., 2008, Thermal analysis of reissnermindlin shallow shells with FGM properties by the MLPG, CMES: Computer Modelling in Engineering and Sciences 30(2): 7797.##[13] Nejad M. Z., Rahimi G. H., Ghannad M., 2009, Set of field equations for thick shell of revolution made of functionally graded materials in curvilinear coordinate system, Mechanika 77(3): 1826.##[14] Ghannad M., Nejad M. Z., Rahimi G. H., 2009, Elastic solution of axisymmetric thick truncated conical shells based on firstorder shear deformation theory, Mechanika 79(5): 1320.##[15] Eipakchi, H. R., 2010, Thirdorder shear deformation theory for stress analysis of a thick conical shell under pressure, Journal of Mechanics of materials and structures 5(1): 117.##[16] Jabbari M., Meshkini M., Eslami M. R., 2011, Mechanical and thermal stresses in a FGPM hollow cylinder due to nonaxisymmetric loads, Journal of Solid Mechanics 3(1): 1941.##[17] Ray S., Loukou A., Trimis D., 2012, Evaluation of heat conduction through truncated conical shells, International Journal of Thermal Sciences 57: 183191.##[18] Ghannad M., Gharooni H., 2012, Displacements and stresses in pressurized thick FGM cylinders with varying properties of power function based on HSDT, Journal of Solid Mechanics 4(3): 237251.##[19] Ghannad M., Nejad M. Z., Rahimi G. H., Sabouri H., 2012, Elastic analysis of pressurized thick truncated conical shells made of functionally graded materials, Structural Engineering and Mechanics 43(1): 105126.##[20] Nejad M. Z., Jabbari M., Ghannad M., 2014, A semianalytical solution of thick truncated cones using matched asymptotic method and disk form multilayers, Archive of Mechanical Engineering 3: 495513.##[21] Nejad M. Z., Jabbari M., Ghannad M. 2014, Elastic analysis of rotating thick truncated conical shells subjected to uniform pressure using disk form multilayers, ISRN Mechanical Engineering 764837: 110.##[22] Jabbari M., Meshkini M., 2014, Mechanical and thermal stresses in a FGPM hollow cylinder due to radially symmetric loads, Encyclopedia of Thermal Stresses 29382946.##[23] Nejad M. Z., Jabbari M., Ghannad M., 2015, Elastic analysis of FGM rotating thick truncated conical shells with axiallyvarying properties under nonuniform pressure loading, Composite Structures 122: 561569.##[24] Sofiyev A. H., Huseynov S. E., Ozyigit P., Isayev, F. G., 2015, The effect of mixed boundary conditions on the stability behavior of heterogeneous orthotropic truncated conical shells, Meccanica 50: 21532166.##[25] Jabbari M., Nejad M. Z., Ghannad M., 2016, Thermoelastic analysis of rotating thick truncated conical shells subjected to nonuniform pressure, Journal of Solid Mechanics 8(3): 481466.##[26] Vlachoutsis S., 1992, Shear correction factors for plates and shells, International Journal for Numerical Methods in Engineering 33: 15371552.##[27] Buchanan G. R., Yii C. B. Y., 2002, Effect of symmetrical boundary conditions on the vibration of thick hollow cylinders, Applied Acoustics 63(5): 547566.##]
Generalized Thermoelastic Problem of a Thick Circular Plate with Axisymmetric Heat Supply Due to Internal Heat Generation
2
2
A two dimensional generalized thermoelastic problem of a thick circular plate of finite thickness and infinite extent subjected to continuous axisymmetric heat supply and an internal heat generation is studied within the context of generalized thermoelasticity. Unified system of equations for classical coupled thermoelasticity, LordShulman and GreenLindsay theory is considered. An exact solution of the problem is obtained in the transform domain. Inversion of Laplace transforms is done by employing numerical scheme. Mathematical model is prepared for Copper material plate and the numerical results are discussed and represented graphically.
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115
125


J.J
Tripathi
Department of mathematics, Dr. Ambedkar College, Deekshabhoomi, Nagpur 440010, Maharashtra, India
Department of mathematics, Dr. Ambedkar College,
India
tripathi.jitesh@gmail.com


G.D
Kedar
Department of mathematics, R.T.M. Nagpur University, Nagpur440033 Maharashtra, India
Department of mathematics, R.T.M. Nagpur
India


K.C
Deshmukh
Department of mathematics, R.T.M. Nagpur University, Nagpur440033 Maharashtra, India
Department of mathematics, R.T.M. Nagpur
India
Thermoelasticity
Classical coupled
Lordshulman
Greenlindsay
Internal heat generation
Axisymmetric heat supply
[[1] Biot M. A., 1956, Thermoelasticity and irreversible thermodynamics, Journal of Applied Physics 27: 240253.##[2] Nowacki W., 1966, Couple stresses in the theory of thermoelasticity , Bulletin L'Academie Polonaise des Science, Serie des Sciences Technology 14: 129138.##[3] Lord H., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15: 299309.##[4] Green A. E., Lindsay K. A, 1972, Thermoelasticity, Journal of Elasticity 2: 17.##[5] Nowacki W., 1975, Dynamic Problems of Thermoelasticity, Noordhoff International Publishing, Leyden, The Netherlands.##[6] Hetnarski R. B., Eslami M. R., 2009, Thermal StressesAdvanced Theory and Applications, Springer.##[7] Chandrasekariah D. S., 1986, Thermoelasticity with second sound: a review, Applied Mechanics Review 39: 355376.##[8] Hetnarski R. B., Ignaczak J., 1999, Generalized thermoelasticity, Journal of Thermal Stresses 22: 451476.##[9] Tripathi J. J., Kedar G. D., Deshmukh K. C., 2014, Dynamic problem of generalized thermoelasticity for a semiinfinite cylinder with heat sources, Journal of Thermoelasticity 2(1): 0108.##[10] Maghraby N. M., Abdel Halim A. A., 2010, A generalized thermoelastic problem for a half space with heat sources under axisymmetric distribution, Australian Journal of Basic and Applied Science 4(8): 38033814.##[11] Aouadi M., 2005, Discontinuities in a axisymmetric generalized thermoelastic problem, International Journal of Mathematics and Mathematical Sciences 7: 10151029##[12] Tripathi J. J., Kedar G. D., Deshmukh K. C., 2015, Generalized thermoelastic diffusion problem in a thick circular plate with axisymmetric heat supply, Acta Mechanica 226(7): 21212134.##[13] Youssef H. M., 2006, Twodimensional generalized thermoelasticity problem for a half space subjected to ramptype heating, European Journal of Mechanics A/Solids 25: 745763.##[14] Tripathi J. J., Kedar, G. D., Deshmukh K. C., 2015, Two dimensional generalized thermoelastic diffusion in a half space under axisymmetric distributions, Acta Mechanica 226: 32633274.##[15] Tripathi J. J., Kedar G. D., Deshmukh K. C., 2015, Theoretical study of disturbances due to mechanical source in a generalized thermoelastic diffusive half space, Proceeding of the Third International Conference on Advances in Applied Science and Environmental Engineering  ASEE 2015: 5761.##[16] Gaver D. P., 1966, Observing stochastic processes and approximate transform inversion, Operations Research 14: 444459.##[17] Stehfast H., 1970, Algorithm 368: Numerical inversion of Laplace transforms, Communications of the ACM 13: 4749.##[18] Stehfast H., 1970, Remark on algorithm 368, Numerical inversion of Laplace transforms, Communications of the ACM 13: 624.##[19] Press W. H., Flannery B. P., Teukolsky S. A., Vetterling W. T., 1986, Numerical Recipes, Cambridge University Press, Cambridge, The Art of Scientific Computing.##]
Comparison of Stiffness and Failure Behavior of the Laminated Grid and Orthogrid Plates
2
2
The present paper investigates the advantages of a new class of composite grid structures over conventional grids. Thus far, a known grid structure such as orthogrid or isogrid has been used as an orthotropic layer with at most inplane anisotropy. The present laminated grid is composed of various numbers of thin composite grid layers. The stiffness of the structure can be adjusted by choosing proper stacking sequences. This concept yields to a large variety of laminated grid configurations with different coupling effects compare to conventional grids. To illustrate the advantages of the laminated grids, the stiffness matrices and the bending response of the laminated and conventional grids are compared. Furthermore, a progressive failure analysis is implemented to compare the failure resistance of laminated and conventional grids. The results indicate that, thoughtful selection of stacking sequences of the laminated grid enhances the stiffness and response of the laminated grids without significant effect on the failure index.
1

126
137


A
Ehsani
Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Mechanical Engineering, Ferdowsi
Iran


J
Rezaeepazhand
Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad,Iran.
Department of Mechanical Engineering, Faculty
Iran
jrezaeep@um.ac.ir
Laminated grid
Composite
Stiffness
Orthogrid
Plate bending
progressive failure
[[1] Huybrechts S.M., Hahn S.E., Meink T.E., 1999, Grid stiffened structures: survey of fabrication, analysis and design methods, Proceedings of the 12th International Conference on Composite Materials (ICCM/12).##[2] Chen H.J., Tsai S.W., 1996, Analysis and optimum design of composite grid structures, Journal of Composite Materials 30: 503534.##[3] Gürdal Z., Gendron G., 1993, Optimal design of geodesically stiffened composite cylindrical shells, Composites Engineering 3: 11311147.##[4] Oliveira J.G., Christopoulos D.A., 1981, A practical method for the minimum weight design of stiffened plates under uniform lateral pressure, Computers & Structures 14: 409421.##[5] Kidane S., Li G., Helms J., Pang S.S., Woldesenbet E., 2003, Buckling load analysis of grid stiffened composite cylinders, Composites Part B: Engineering 34: 19.##[6] Ambur D.R., Jaunky N., 2001, Optimal design of gridstiffened panels and shells with variable curvature, Composite Structures 52: 173180.##[7] Chen C.J., Liu W., Chern S.M., 1994, Vibration analysis of stiffened plates, Computers & Structures 50: 471480.##[8] Shi S., Sun Z., Ren M., Chen H., Hu X., 2013, Buckling resistance of gridstiffened carbonfiber thinshell structures, Composites Part B: Engineering 45: 888896.##[9] Lai C., Wang J., Liu C., 2014, Parameterized finite element modeling and buckling analysis of six typical composite grid cylindrical shells, Applied Composite Materials 21: 739758.##[10] Huang L., Sheikh A.H., Ng C. T., Griffith M.C., 2015, An efficient finite element model for buckling analysis of grid stiffened laminated composite plates, Composite Structures 122: 4150.##[11] Anyfantis K.N. , Tsouvalis N.G., 2012, Post buckling progressive failure analysis of composite laminated stiffened panels, Applied Composite Materials 19: 219236.##[12] Pietropaoli E., 2012, Progressive failure analysis of composite structures using a constitutive material model (USERMAT) developed and implemented in ANSYS, Applied Composite Materials 19: 657668.##[13] Kollar L.P., Springer G.S., 2003, Mechanics of Composite Structures, Cambridge University Press.##[14] Naik N.K., Chandra Sekher Y., Meduri S., 2000, Damage in wovenfabric composites subjected to lowvelocity impact, Composites Science and Technology 60: 731744.##[15] Barbero E.J., 1999, Introduction to Composite Materials Design, Taylor & Francis.##[16] Chang F. K., Chang K.Y., 1987, A progressive damage model for laminated composites containing stress concentrations, Journal of Composite Materials 21: 834855.##[17] Lessard L.B., Shokrieh M.M., 1995, Twodimensional modeling of composite pinnedjoint failure, Journal of Composite Materials 29: 671697.##[18] Ambur D.R., Jaunky N., Hilburger M.W., 2004, Progressive failure studies of stiffened panels subjected to shear loading, Composite Structures 65: 129142.##]
Whirling Analysis of AxialLoaded MultiStep Timoshenko Rotor Carrying Concentrated Masses
2
2
In this paper, exact solution for twoplane transverse vibration analysis of axialloaded multistep Timoshenko rotor carrying concentrated masses is presented. Each attached element is considered to have both translational and rotational inertia. Forward and backward frequencies and corresponding modes are obtained using transfer matrix method (TMM). The effect of the angular velocity of spin, value of the translational and rotational inertia, position of the attached elements and applied axial force on the natural frequencies are investigated for various boundary conditions.
1

138
156


K
Torabi
Faculty of Mechanical Engineering, University of Isfahan, Isfahan, Iran
Faculty of Mechanical Engineering, University
Iran
k.torabi@eng.ui.ac.ir


H
Afshari
Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Faculty of Mechanical Engineering, University
Iran


H
Najafi
Department of Solid Mechanics, Faculty of Mechanical Engineering, Politecnico di Milano, Milan, Italy
Department of Solid Mechanics, Faculty of
Italy
Whirling analysis
Timoshenko rotor
Multistep
Axial load
Concentrated mass
Rotational inertia
Transfer matrix method (TMM)
[[1] Chen Y., 1963, On the vibration of beams or rods carrying a concentrated mass, Journal of Applied Mechanics 30: 310311.##[2] Laura P., Maurizi M.J., Pombo J.L., 1975, A note on the dynamics analysis of an elastically restrainedfree beam with a mass at the free end, Journal of Sound and Vibration 41: 397405.##[3] Rossit C.A., Laura P., 2001, Transverse vibrations of a cantilever beam with a spring mass system attached on the free end, Ocean Engineering 28: 933939.##[4] Rao G.V., Saheb K.M., Janardhan G.R., 2006, Fundamental frequency for large amplitude vibrations of uniform Timoshenko beams with central point concentrated mass using coupled displacement field method, Journal of Sound and Vibration 298: 221232.##[5] Rossit C.A., Laura P., 2001, Transverse normal modes of vibration of a cantilever Timoshenko beam with a mass elastically mounted at the free end, Journal of the Acoustical Society of America 110: 28372840.##[6] Laura P., Filipich C.P., Cortinez V.H., 1987, Vibrations of beams and plates carrying concentrated masses, Journal of Sound and Vibration 117: 459465.##[7] Rossi R.E., Laura P., 1990, Vibrations of a Timoshenko beam clamped at one end and carrying a finite mass at the other, Applied Acoustics 30: 293301.##[8] Maiz S., Bambill D., Rossit C., Laura P., 2007, Transverse vibration of Bernoulli–Euler beams carrying point masses and taking into account their rotary inertia, Journal of Sound and Vibration 303: 895908.##[9] Lin H.Y., 2009, On the natural frequencies and mode shapes of a multispan Timoshenko beam carrying a number of various concentrated elements, Journal of Sound and Vibration 319: 593605.##[10] Gutierrez R.H., Laura P., Rossi R.E., 1991, Vibrations of a Timoshenko beam of nonuniform crosssection elastically restrained at one end and carrying a finite mass at the other, Ocean Engineering 18: 129145.##[11] Nelson H.D., 1980, A finite rotating shaft element using Timoshenko beam theory, Journal of Mechanical Design 102: 793803.##[12] Edney S.L., Fox C.H.J., Williams E.J., 1990, Tapered Timoshenko finite elements for rotor dynamics analysis, Journal of Sound and Vibration 137: 463481.##[13] Zu J.W.Z., Han R.P.S., 1992, Natural frequencies and normal modes of a spinning Timoshenko beam with general boundary conditions, Journal of Applied Mechanics 59: 197204.##[14] Jun O.S., Kim J.O., 1999, Free bending vibration of a multistep rotor, Journal of Sound and Vibration 224: 625642.##[15] Banerjee J.R., Su H., 2006, Dynamic stiffness formulation and free vibration of a spinning composite beam, Computers & Structures 84: 12081214.##[16] Hosseini S.A.A., Khadem S.E., 2009, Free vibrations analysis of a rotating shaft with nonlinearities in curvature and inertia, Mechanism and Machine Theory 44: 272288.##[17] Hosseini S.A.A., Zamanian M., Shams Sh., Shooshtari A., 2014, Vibration analysis of geometrically nonlinear spinning beams, Mechanism and Machine Theory 78: 1535.##[18] Afshari H., Irani M., Torabi K., 2014, Free whirling analysis of multistep Timoshenko rotor with multiple bearing using DQEM, Modares Mechanical Engineering 14: 109120.##[19] Wu J.S., Chen C.T., 2007, A lumpedmass TMM for free vibration analysis of a multistep Timoshenko beam carrying eccentric lumped masses with rotary inertias, Journal of Sound and Vibration 301: 878897.##[20] Wu J.S., Chen C.T., 2008, A continuousmass TMM for free vibration analysis of a nonuniform beam with various boundary conditions and carrying multiple concentrated elements, Journal of Sound and Vibration 311: 14201430.##[21] Wu J.S., Chang B.H., 2013, Free vibration of axialloaded multistep Timoshenko beam carrying arbitrary concentrated elements using continuousmass transfer matrix method, European Journal of Mechanics  A/Solids 38: 2037.##[22] Khaji N., Shafiei M., Jalalpour M., 2009, Closedform solutions for crack detection problem of Timoshenko beams with various boundary conditions, International Journal of Mechanical Sciences 51: 667681.##[23] Torabi K., Afshari H., Najafi H., 2013, Exact solution for free vibration analysis of multistep BernoulliEuler and Timoshenko beams carrying multiple attached masses and taking into account their rotary inertia, Journal of Solid Mechanics 5: 336349.##[24] Genta G., 2005, Dynamics of Rotating Systems, Springer, New York.##[25] Hutchinson J.R., 2001, Shear coefficients for Timoshenko beam theory, Journal of Applied Mechanics 68: 8792.##]
Axisymmetric Problem of Thick Circular Plate with Heat Sources in Modified Couple Stress Theory
2
2
The main aim is to study the two dimensional axisymmetric problem of thick circular plate in modified couple stress theory with heat and mass diffusive sources. The thermoelastic theories with mass diffusion developed by Sherief et al. [1] and kumar and Kansal [2] have been used to investigate the problem. Laplace and Hankel transforms technique is applied to obtain the solutions of the governing equations. The displacements, stress components, temperature change and chemical potential are obtained in the transformed domain. Numerical inversion technique has been used to obtain the solutions in the physical domain. Effects of couple stress on the resulting quantities are shown graphically. Some particular cases of interest are also deduced.
1

157
171


R
Kumar
Department of Mathematics, Kurukshetra University , Kurukshetra, Haryana, India
Department of Mathematics, Kurukshetra University
India
rajneesh_kuk@rediffmail.com


Sh
Devi
Department of Mathematics & Statistics, Himachal Pradesh University Shimla, Shimla, India
Department of Mathematics & Statistics,
India


V
Sharma
Department of Mathematics & Statistics, Himachal Pradesh University Shimla, Shimla, India
Department of Mathematics & Statistics,
India
Modified couple stress
Axisymmetric heat sources
Heat generation
Laplace and Hankel transforms
[Sherief H. H., Saleh H., Hamza F., 2004, The theory of generalized thermoelastic diffusion, International Journal of Engineering Science 42: 591608.##[2] Kumar R., Kansal T., 2008, Propagation of Lamb waves in transversely isotropic thermoelastic diffusion plate, International Journal of Solids and Structures 45: 58905913.##[3] Voigt W., 1887, Theoretische Studien über die Elasticitätsverhältnisse der krystalle, Göttingen Dieterichsche Verlags uchhandlung.##[4] Cosserat E., Cosserat F., 1909, Theory of Deformable Bodies, Hermann et Fils, Paris.##[5] Mindlin R. D., Tiersten H. F., 1962, Effects of couplestresses in linear elasticity, Archive for Rational Mechanics and Analysis 11: 415448.##[6] Toupin R. A., 1962, Elastic materials with couplestresses, Archive for Rational Mechanics and Analysis 11: 385414.##[7] Koiter W. T., 1964, Couplestresses in the theory of elasticity, Proceedings of the Royal Netherlands Academy of Arts and Science 67: 1744.##[8] Lakes R. S., 1982, Dynamical study of couple stress effects in human compact bone, Journal of Biomechanical Engineering 104: 611.##[9] Lam D. C. C., Yang F., Chong A. C. M., Wang J., Tong P., 2003, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids 51: 14771508.##[10] Yang F., Chong A. C. M., Lam D. C. C., Tong P., 2002, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures 39: 27312743.##[11] Park S. K., Gao X. L., 2006, Bernoulli–Euler beam model based on a modified couple stress theory, Journal of Micromechanics and Microengineering 16: 2355.##[12] Simsek M., Reddy J. N., 2013, Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory, International Journal of Engineering Science 64: 3753.##[13] Shaat M., Mahmoud F. F., Gao X. L., Faheem A. F., 2014, Sizedependent bending analysis of Kirchhoff nanoplates based on a modified couplestress theory including surface effects, International Journal of Mechanical Sciences 79: 3137.##[14] Ghorbanpour A. Arani, Abdollahian M., Jalaei H. M., 2015, Vibration of bioliquidfilled microtubules embedded in cytoplasm including surface effects using modified couple stress theory, Journal of Theoretical Biology 367: 2938.##[15] Darijani H., Shahdadi A. H., 2015, A new shear deformation model with modified couple stress theory for microplates, Acta Mechanica 226: 27732788.##[16] Wang Y. G., Lin W. H., Ning L., 2015, Nonlinear bending and postbuckling of extensible microscale beams based on modified couple stress theory, Applied Mathematical Modelling 39: 117127.##[17] Podstrigach I. S., 1961, Differential equations of the problem of thermodiffusion in isotropic deformed solid bodies, Dop Akad Nauk Ukr SSR 169172.##[18] Nowacki W., 1974a, Dynamical problems of thermo diffusion in solids I. Bulletin de l'Academie Polonaise des Sciences, Serie des Sciences Techniques 22: 5564.##[19] Nowacki W., 1974b, Dynamical problems of thermo diffusion in solids II. Bulletin de l'Academie Polonaise des Sciences, Serie des Sciences Techniques 22: 129135.##[20] Nowacki W., 1974c, Dynamical problems of thermo diffusion in solids III. Bulletin de l'Academie Polonaise des Sciences, Serie des Sciences Techniques 22: 257266.##[21] Nowacki W., 1976, Dynamical problems of thermo diffusion in solids, Engineering Fracture Mechanics 8: 261266.##[22] Sherief H. H., Saleh H., 2005, A halfspace problem in the theory of generalized thermoelastic diffusion, International Journal of Solids and Structures 42: 44844493.##[23] ElMaghraby N. M., AbdelHalim A. A., 2010, A generalized thermoelsticity problem for a half space with heat sources under axisymmetric distributions, Australian Journal of Basic and Applied Sciences 4: 38033814.##[24] Lord H. W., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15: 299309.##[25] Tripathi J. J., Kedar G. D., Deshmukh K. C., 2014, Dynamic problem of generalizedthermoelasicity for a semiinfinite cylinder with heat sources, Journal of Thermoelasticity 2: 18.##[26] Tripathi J. J., Kedar G. D., Deshmukh K. C., 2015, Generalized thermoelastic diffusion problem in a thick circular plate with axisymmetric heat supply, Acta Mechanica 226: 21212134.##[27] Honig G., Hirdes U., 1984, A method for the numerical inversion of the Laplace transform, Journal of Computational and Applied Mathematics 10: 113132.##[28] Press W. H., Teukolsky S. A., Vellerling W. T., Flannery B. P., 1986, Numerical Recipes , Cambridge University Press.##]
Numerical Investigation of the MixedMode Stress Intensity Factors in FGMs Considering the Effect of Graded Poisson’s Ratio
2
2
In this paper, the interface crack of two nonhomogenous functionally graded materials is studied. Subsequently, with employing the displacement method for fracture of mixedmode stress intensity factors, the continuous variation of material properties are calculated. In this investigation, the displacements are derived with employing of the functional graded material programming and analysis of isoparametric finite element; then, with using of displacement fields near crack tip, the mixedmode stress intensity factors are defined. In this present study, the problems are divided into homogenous and nonhomogenous materials categories; and in order to verify the accuracy of results, the analytical and numerical methods are employed. Moreover, the effect of Poisson's ratio variation on mixedmode stress intensity factors for interface crack be examined and is shown in this study. Unlike the homogenous material, the effect of Poisson’s ratio variations on mixedmode stress intensity factors at interface crack between two nonhomogenous is considerable.
1

172
185


R
Ghajar
Department of Mechanical Engineering, K.N. Toosi University ,Tehran, Iran
Department of Mechanical Engineering, K.N.
Iran
ghajar@kntu.ac.ir


S
Peyman
Department of Mechanical Engineering, K.N. Toosi University ,Tehran, Iran
Department of Mechanical Engineering, K.N.
Iran


J
Sheikhi
Department of Civil Engineering ,Razi University , Kermanshah, Iran
Department of Civil Engineering ,Razi University
Iran


M
Poorjamshidian
Department of Mechanical Engineering, Kashan University ,Kashan, Iran
Department of Mechanical Engineering, Kashan
Iran
Interface crack
Displacement method
Nonhomogeneous materials
[[1] Williams M.L., 1959, The stresses around a fault or crack in dissimilar media, Bulletin of the Seismological Society of America 49 (2): 199204.##[2] England A.H., 1965, A crack between dissimilar media, Journal of Applied Mechanics 32: 400402.##[3] Erdogan F., 1965, Stress distribution in bonded dissimilar materials with cracks, Journal of Applied Mechanics 32: 403 410.##[4] Rice J.R., Sih G.C., 1965, Plane problems of cracks in dissimilar media, Journal of Applied Mechanics 32: 418423.##[5] Rice J.R., 1988, Elastic fracture mechanics concepts for interfacial cracks, Journal of Applied Mechanics 55: 98103.##[6] Hutchinson J.W., Mear M.E., Rice J.R., 1987, Crack paralleling an interface between dissimilar materials, Journal of Applied Mechanics 54: 828832.##[7] Hutchinson J.W., Suo Z., 1992, Mixed mode cracking in layered materials, Advances in Applied Mechanics 29: 63191.##[8] Rice J.R., 1968, A path independent integral and the approximate analysis of strain concentration by notches and cracks, Journal of Applied Mechanics 35: 379386.##[9] Smelser R.E., Gurtin M.E., 1977, On the Jintegral for bimaterial bodies, International Journal of Fracture 13: 382384.##[10] Nagashima T., Omoto Y., Tani S., 2003, Stress intensity factor analysis of interface cracks using XFEM, International Journal for Numerical Methods in Engineering 56: 11511173.##[11] Sukumar N., Huang Z.Y., Prévost J.H., Suo Z., 2004, Partition of unity enrichment for bimaterial interface cracks, International Journal for Numerical Methods in Engineering 59: 10751102.##[12] Matsumto T., Tanaka M., Obara R., 2000, Computation of stress intensity factors of interface cracks based on interaction energy release rates and BEM sensitivity analysis, Engineering Fracture Mechanics 65: 683702.##[13] Cisilino A.P., Ortiz J.E., 2005, Threedimensional boundary element assessment of a fibre/matrix interface crack under transverse loading, Computers and Structures 83: 856869.##[14] Ortiz J.E., Cisilino A.P., 2005, Boundary element method for Jintegral and stress intensity factor computations in threedimensional interface cracks, International Journal of Fracture 133: 197222.##[15] Johnson J., Qu J.M., 2007, An interaction integral method for computing mixed mode stress intensity factors for curved bimaterial interface cracks in nonuniform temperature fields, Engineering Fracture Mechanics 74: 22822291.##[16] Merzbacher M.J., Horst P., 2009, A model for interface cracks in layered orthotropic solids: convergence of modal decomposition using the interaction integral method, International Journal for Numerical Methods in Engineering 77: 10521071.##[17] Eischen J.W., 1987, Fracture of nonhomogeneous materials, International Journal of Fracture 34: 322.##[18] Erdogan F., 1995, Fracture mechanics of functionally graded materials, Composites Engineering 5 (7): 753770.##[19] Chen Y.F., Erdogan F., 1996, The interface crack problem for a nonhomogeneous coating bonded to a homogeneous substrate, Journal of the Mechanics and Physics of Solids 44: 771787.##[20] Noda N., 1999, Thermal stresses in functionally graded materials, Journal of Thermal Stresses 22 (45):477512.##[21] Guler M.A., Erdogan F., 2006, Contact mechanics of two deformable elastic solids with graded coatings, Mechanics of Materials 38 (7): 633647.##[22] Guo L.C., Noda N., 2007, Modeling method for a crack problem of functionally graded materials with arbitrary properties – piece wise exponential model, International Journal of Solids and Structures 44(21): 67686790.##[23] Guo L.C., Noda N., 2008, Fracture mechanics analysis of functionally graded layered structures with a crack crossing the interface, Mechanics of Materials 40 (3):8199.##[24] Dolbow J.E., Gosz M., 2002, On the computation of mixedmode stress intensity factors in functionally graded materials, International Journal of Solids and Structures 39: 25572574.##[25] Paulino G.H., Kim J.H., 2004, A new approach to compute Tstress in functionally graded materials by means of the interaction integral method, Engineering Fracture Mechanics 71: 19071950.##[26] Kim J.H., Paulino G.H., 2003, Tstress, mixedmode stress intensity factors, and crack initiation angles in functionally graded materials: a unified approach using the interaction integral method, Computer Methods in Applied Mechanics and Engineering 192: 14631494.##[27] Kim J.H., Paulino G.H., 2005, Consistent formulations of the interaction integral method for fracture of functionally graded materials, Journal of Applied Mechanics 72: 351364.##[28] Hongjun Yu., Linzhi Wu ., Licheng Guo., Qilin He., Shanyi Du., 2009, Interaction integral method for the interfacial fracture problems of two nonhomogeneous materials, Journal of Applied Mechanics of Materials 42: 435 450.##[29] Yildrim B., Dag S., Erdogan F., 2005, Three dimensional fracture analysis of FGM coatings under thermomechanical loading, International Journal of Fracture 132: 369395.##[30] Ghajar R., Moghaddam A.S., 2010, Numerical investigation of the mode III stress intensity factors in FGMs consideringthe effect of graded Poisson’s ratio, Engineering Fracture Mechanics 78: 14781486.##[31] Paulino G.H., Kim J.H., 2004, On the poisson's ratio effect on mixedmode stress intensity factors and Tstress in##functionally graded materials, International Journal of Computational Engineering Science 5: 833861.##[32] Malyshev B.M., Salganik R.L., 1965, The strength of adhesive joints using the theory of cracks, International Journal of Fracture 1: 114128.##[33] Suo Z., 1989, Mechanics of Interface Fracture, Ph.D. Thesis, Division of Applied Sciences, Harvard University,##Cambridge, MA, U.S.A.##[34] Dundurs J., 1969, Edgebonded dissimilar orthogonal elastic wedges, Journal of Applied Mechanics 36:##[35] Walters M. C., Paulino G. H., Dodds R. H., 2006, Computation of mixedmode stress intensity factors for cracks in threedimensional functionally graded solids, Journal of Engineering Mechanics 132: 115.##[36] Kim J.H., Paulino G.H.,2002, Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials, Journal of Applied Mechanics 69: 502514.##[37] Hughes T. J. R., 1987, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, PrenticeHall, Englewood Cliffs, NJ.##]
An Exact Solution for Vibration Analysis of Soft Ferromagnetic Rectangular Plates Under the Influence of Magnetic Field with Levy Type Boundary Conditions
2
2
In this paper vibration of ferromagnetic rectangular plates which are subjected to an inclined magnetic field is investigated based on classical plate theory and Maxwell equations. Levy type solution and Finite element method using Comsol software are used to obtain the frequency of the plate subjected to different boundary conditions, good agreements is obtained when computed results are compared with those obtained by Comsol software, the results have shown that the frequency of the plates increases with the magnetic field and the effect of magnetic field is similar to the Winkler’s foundation.
1

186
197


S.A
Mohajerani
Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
Department of Mechanical Engineering, Science
Iran


A
Mohammadzadeh
Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
Department of Mechanical Engineering, Science
Iran
amohamadzadeh@srbiau.ac.ir


M
Nikkhah Bahrami
Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
Department of Mechanical Engineering, Science
Iran
Free vibration
magnetic field
Ferromagnetic plate
Exact solution
Levy type
[[1] Moon F. C., 1984, MagnetoSolid Mechanics, Wiley New York etc.##[2] Eringen A. C., 1989 ,Theory of electromagnetic elastic plates , International Journal of Engineering Science 27(4): 363375.##[3] Liang W., Soh Ai K., Hu R., 2007 ,Vibration analysis of a ferromagnetic plate subjected to an inclined magnetic field , International Journal of Mechanical Sciences 49(4): 440446.##[4] Moon F.C., Pao Y.H., 1968, Magnetoelastic buckling of a thin plate, Journal of Applied Mechanics 35(8):5358.##[5] Yang W., Pan H., Zheng D., Cai Q., 1999, An energy method for analyzing magnetoelastic buckling and bending of ferromagnetic plates in static magnetic fields, Journal of applied mechanics 66(4): 913917.##[6] Ohj T ., Shinkai T., Amei K., Sakui M ., 2007, Application of Lorentz force to a magnetic levitation system for a nonmagnetic thin plate , Journal of Materials Processing Technology 181(13):4043.##[7] Hoffmann T., ChudzickaAdamczak M., 2009, The Maxwell stress tensor for magnetoelastic materials, International Journal of Engineering Science 47(5): 735739.##[8] Eringen C., 1989 , Theory of electromagnetic elastic plates, International Journal of Engineering Science 27(4):365375.##[9] Griffiths D. J., College R., 1999, Introduction to Electrodynamics, Prentice Hall New Jersey.##[10] Wang X., Sehlee J., 2006, Dynamic stability of ferromagnetic plate under transverse magnetic field and inplane periodic compression , International Journal of Mechanical Sciences 48(8): 889898.##[11] Liang W., Soh Ai K., Hu R., 2007 , Vibration analysis of a ferromagnetic plate subjected to an inclined magnetic field, International Journal of Mechanical Sciences 49(4): 440446.##[12] Goudjo C., Maugin G., 1983, On the static and dynamic stability of softferromagnetic elastic plates, Journal de Mécaniquethéorique et Appliquée 2(6): 947975.##[13] Chen W., Kang Yong L., Ding H.J., 2005, On free vibration of nonhomogeneous transversely isotropic magnetoelectroelastic plates, Journal of Sound and Vibration 279(1): 237251.##[14] YihHsing P., ChauShioung Y., 1973, A linear theory for soft ferromagnetic elastic solids, International Journal of Engineering Science 11(4): 415436.##[15] Ven A., 1978, Magnetoelastic buckling of thin plates in a uniform transverse magnetic field , Journal of Elasticity 8(3): 297312.##[16] Yuda H., Jing L. , 2009, The magnetoelastic subharmonic resonance of currentconducting thin plate in magnetic filed , Journal of Sound and Vibration 319(3): 11071120.##[17] Wang X., Lee J.S., Zheng X., 2003, Magnetothermoelastic instability of ferromagnetic plates in thermal and magnetic fields , International Journal of Solids and Structures 40(22): 61256142.##[18] Goudjo C., Maugin G., 1983, On the static and dynamic stability of softferromagnetic elastic plates, Journal de Mécaniquethéorique et Appliquée 2(6): 947975.##[19] Li X.Y., Ding H.J., Chen W.Q., 2008 , Threedimensional analytical solution for functionally graded magneto–electroelastic circular plates subjected to uniform load ,Composite Structures 83(4): 381390.##[20] Golubeva T. N., Korobkov Y. S., Khromatov V. E., 2013, Influence of a longitudinal magnetic field on the vibration frequencies of ferromagnetic plates, Russian Electrical Engineering 84(3): 155159.##]
The Effects of Carbon Nanotube Orientation and Aggregation on Static Behavior of Functionally Graded Nanocomposite Cylinders
2
2
In this paper, the effects of carbon nanotube (CNT) orientation and aggregation on the static behavior of functionally graded nanocomposite cylinders reinforced by CNTs are investigated based on a meshfree method. The used nanocomposites are made of the straight CNTs that are embedded in an isotropic polymer as matrix. The straight CNTs are oriented, randomly or aligned or local aggregated into some clusters. The volume fractions of the CNTs and clusters are assumed variable along the thickness, so mechanical properties of the carbon nanotube reinforced composite cylinders are variable and are estimated based on the Eshelby–Mori–Tanaka approach. The obtained mechanical properties are verified by experimental and theoretical results that are reported in literatures. In the meshfree analysis, moving least squares (MLSs) shape functions are used for approximation of displacement field in the weak form of equilibrium equation. Also, the effects of CNT distribution type and cylinder thickness are investigated on the stress distribution and displacement field of these cylinders.
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198
212


R
MoradiDastjerdi
School of Mechanical Engineering, Shahid Rajaee Teacher Training University (SRTTU), Tehran, Iran
School of Mechanical Engineering, Shahid
Iran


G
Payganeh
School of Mechanical Engineering, Shahid Rajaee Teacher Training University (SRTTU), Tehran, Iran
School of Mechanical Engineering, Shahid
Iran
g.payganeh@srttu.edu


M
Tajdari
Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran
Department of Mechanical Engineering, Arak
Iran
m.tajdari@srbiau.ac.ir
Nanocomposite cylinder
Aggregation
Mori–Tanaka
Static behavior
Functionally graded
MeshFree
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study of the stress–strain behavior of carbonnanotube reinforced Epon 862 composites, Materials Science and Engineering A 447: 5157.##[8] Manchado M.A.L., Valentini L., Biagiotti J., Kenny J.M., 2005, Thermal and mechanical properties of singlewalled carbon nanotubespolypropylene composites prepared by melt processing, Carbon 43: 14991505.##[9] Qian D., Dickey E.C., Andrews R., Rantell T., 2000, Load transfer and deformation mechanisms in carbon nanotube–polystyrene composites, Applied Physics Letters 76: 28682870.##[10] Mokashi V.V., Qian D., Liu Y.J., 2007, A study on the tensile response and fracture in carbon nanotubebased composites using molecular mechanics, Composites Science and Technology 67: 530540.##[11] Montazeri A., Javadpour J., Khavandi A., Tcharkhtchi A., Mohajeri A., 2010, Mechanical properties of multiwalled carbon nanotube/epoxy composites, Material & Design 31: 42024208.##[12] Barai P., Weng G.J., 2011, A theory of plasticity for carbon nanotube reinforced 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Torsional Surface Wave Propagation in Anisotropic Layer Sandwiched Between Heterogeneous HalfSpace
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The present paper studies the possibility of propagation of torsional surface waves in an inhomogeneous anisotropic layer lying between two heterogeneous halfspaces (upper and lower halfspace). Both the halfspaces are assumed to be under compressive initial stress. The study reveals that under the assumed conditions, a torsional surface wave propagates in the medium. The dispersion relation of torsional surface wave has been obtained in the presence of heterogeneity, initial stress and anisotropic, and it is observed that the inhomogeneity factor due to quadratic and hyperbolic variations in rigidity, density and initial stress of the medium decreases the phase velocity as it increases. The result also shows that the initial stresses have a pronounced influence on the propagation of torsional surface waves. In the absence of anisotropy, Initial stress, inhomogeneity and rigidity of the upper halfspace, then the dispersion relation coincide with the classical dispersion relation of Love wave.
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P.K
Vaishnav
Department of Applied Mathematics, Indian School of Mines, Dhanbad826004, India
Department of Applied Mathematics, Indian
India
pvaishnav.ism@gmail.com


S
Kundu
Department of Applied Mathematics, Indian School of Mines, Dhanbad826004, India
Department of Applied Mathematics, Indian
India


S.M
AboDahab
Department, Qena Faculty of Science, Egypt
Department, Qena Faculty of Science, Egypt
Egypt


A
Saha
Department of Applied Mathematics, Indian School of Mines, Dhanbad826004, India
Department of Applied Mathematics, Indian
India
Torsional wave
Heterogeneity
Initial stress
Phase velocity
Dispersion relation
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