2013
5
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106
Plane Wave Propagation Through a Planer Slab
2
2
An approximation technique is considered for computing transmission and reflection coefficients for propagation of an elastic pulse through a planar slab of finite width. The propagation of elastic pulse through a planar slab is derived from first principles using straightforward timedependent method. The paper ends with calculations of enhancement factor for the elastic plane wave and it is shown that it depends on the velocity ratio of the wave in two different media but not the incident wave form. The result, valid for quite arbitrary incident pulses and quite arbitrary slab inhomogeneities, agrees with that obtained by timeindependent methods, but uses more elementary methods.
1

1
13


R
Kakar
Principal, DIPS Polytechnic College, Hoshiarpur
Principal, DIPS Polytechnic College, Hoshiarpur
Iran
rkakar_163@rediffmail.com
Inhomogeneous media
Plane waves
timeindependent methods
Navier’s equations
[[1] Poisson S. D., 1829, Memoire sur I’equilibre et le movement des corps e’lastiques, Mem de I’Acad Roy des Science I’Inst 8: 357570. ##[2] Kelvin L., 1863, On the rigidity of the earth, Philosophical Transactions of the Royal Society A 153: 573582. ##[3] Rayleigh L., 1877, On progressive waves, Proceedings of the London Mathematical Society 19: 2126. ##[4] Rayleigh L., 1885, On waves propagation on the plane surface of an elastic solid, Proceedings of the London Mathematical Society 17: 411. ##[5] Rayleigh L., 1912, On the propagation of waves through a stratified medium with special reference to the question of reflection, Proceedings of the Royal Society A 86 (586): 207226. ##[6] Stoneley R., 1924, Elastic waves at the surface of separation of two solids, Proceedings of the Royal Society A 106(738): 416428. ##[7] Spencer A. J. M., 1974, Boundary layers in highly anisotropic plane elasticity, International Journal of Solids and Structures 10(10): 11031123. ##[8] Biot M. A., 1965, Mechanics of Incremental Deformations, Wiley, New York. ##[9] Love A.E.H., 1944, Mathematical Theory of Elasticity, Dover Publications, 4th edition. ##[10] Epstien P.S., 1930, Reflection of waves in an inhomogeneous absorbing medium, Proceedings of the National Academy of Sciences 16: 627637. ##[11] Sinha S.B., 1999, Transmission of elastic waves through a homogenous layer sandwiched in homogenous media, Journal of Physics of the Earth 12: 14. ##[12] Tooly R.D., Spencer T.W., Sagoci H.F., 1965, Reflection and Transmission of plane compressional waves, Geophysics 30: 552570. ##[13] Gupta RN., 1966, Reflection of elastic waves from a linear transition layer, Bulletin of the Seismological Society of America 56: 511526. ##[14] Agemi R., 2000, Global existence of nonlinear elastic waves, Inventiones mathematicae 142: 225250. ##[15] Kakar R., Kakar S., 2012, Propagation of Love waves in a nonhomogeneous elastic media,Journal of Academia and Industrial Research 1(6): 323328. ##[16] Sokolnikoff I. S., 1956, Mathematical Theory of Elasticty, McGrawHill, New York. ## ##]
Double Cracks Identification in Functionally Graded Beams Using Artificial Neural Network
2
2
This study presents a new procedure based on Artificial Neural Network (ANN) for identification of double cracks in Functionally Graded Beams (FGBs). A cantilever beam is modeled using Finite Element Method (FEM) for analyzing a doublecracked FGB and evaluation of its first four natural frequencies for different cracks depths and locations. The obtained FEM results are verified against available references. Furthermore, four MultiLayer Perceptron (MLP) neural networks are employed for identification of locations and depths of both cracks of FGB. BackError Propagation (BEP) method is used to train the ANNs. The accuracy of predicted results shows that the proposed procedure is suitable for double cracks identification detection in FGBs.
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14
21


F
Nazari
Department of Mechanical Engineering, Ferdowsi University of Mashhad
Department of Mechanical Engineering, Ferdowsi
Iran


M.H
Abolbashari
Department of Mechanical Engineering, Lean Production Engineering Research Center, Ferdowsi University of Mashhad
Department of Mechanical Engineering, Lean
Iran
abolbash@um.ac.ir
Double cracks
Functionally graded beam
Artificial Neural Network
Model analysis
[ [1] Douka E., Loutridis S., Trochidis A., 2003, Crack identification in beams using wavelet analysis, International Journal of Solid Structures 40(1314): 35573569. ##[2] Dimarogonas A.D., 1996, Vibration of cracked structures: A state of the art review, Engineering Fracture Mechanic ##55(5): 831857. ##[3] Dimarogonas A.D., 1976, Vibration Engineering, West Publishers, St Paul, Minnesota. ##[4] Paipetis S.A., Dimarogonas A.D., 1986, Analytical Methods in Rotor Dynamics, Elsevier Applied Science, London. ##[5] Adams A.D., Cawley P., 1979, The location of defects in structures from measurements of natural frequencies, Journal of Strain Analysis for Engineering Design14(2): 4957. ##[6] Chondros T.G., Dimarogonas A.D., 1980, Identification of cracks in welded joints of complex structures, Journal of Sound and Vibration 69(11): 531538. ##[7] Goudmunson P., 1982, Eigen frequency change of structures: a state of the art review, Engineering Fracture Mechanic 55(5): 831857. ##[8] Shen M.H.H., Taylor J.E., 1991, An identification problem for vibrating cracked beams, Journal of Sound and Vibration 150(3): 457484. ##[9] Masoud A., Jarrad M.A., AlMaamory M., 1998, Effect of crack depth on the natural frequency of a prestressed fixedfixed beam, Journal of Sound and Vibration 214(2): 201212. ##[10] Sekhar A.S., 2008, Multiple cracks effects and identification, Journal of Mechanical Systems and Signal Processing 22(4): 845878. ##[11] Lee J., 2009, Identification of multiple cracks in a beam using natural frequencies, Journal of Sound and Vibration 320(3): 482490. ##[12] Patil D.P., Maiti S.K., 2003, Detection of multiple cracks using frequency measurements, Engineering Fracture Mechanic 70(12): 15531572. ##[13] Mazanoglu K., Yesilyurt I., Sabuncu M., 2009, Vibration analysis of multiplecracked nonuniform beams, Journal of Sound and Vibration 320(45): 977989. ##[14] Binici B., 2005, Vibration of beams with multiple open cracks subjected to axial force, Journal of Sound and Vibration 287(12): 277295. ##[15] Khiem N.T., Lien T.V., 2001, A simplified method for natural frequency analysis of a multiple cracked beam, Journal of Sound and Vibration 245(4): 737751. ##[16] Cam E., Sadettin O., Murat L., 2008, An analysis of cracked beam structure using impact echo method, Independent Nondestructive Testing and Evaluation 38(5): 368373. ##[17] Wu X., Ghaboussi J., Garret Jr J.H., 1992, Use of neural networks in detection of structural damage, Computers and Structures 42(4): 649659. ##[18] Wang B.S., He Z.C., 2007, Crack detection of arch dam using statistical neural network based on the reductions of natural frequencies, Journal of Sound and Vibration 302(45): 10371047. ##[19] Kao C.Y., Hung S.L., 2003, Detection of structural damage via free vibration responses generated by approximating artificial neural networks, Computers and Structures 81(2829): 26312644. ##[20] Chen Q., Chan Y.W., Worden K., 2003, Structural fault diagnosis and isolation using neural networks based on responseonly data, Computers and Structures 81(2223): 21652172. ##[21] Yu Z., Chu F., 2009, Identification of crack in functionally graded material beams using the pversion of finite element method, Journal of Sound and Vibration 325(12): 6984. ##[22] Kitipornchai S., Ke L.L, Yang J., Xiang Y., 2009, Nonlinear vibration of edge cracked functionally graded Timoshenko beams, Journal of Sound and Vibration 324(35): 962982. ##[23] Yang J., Chen Y., 2008, Free vibration and buckling analyses of functionally graded beams with edge cracks, Computers and Structures 83(1): 4860. ##[24] Simsek M., 2010, Nonlinear vibration analysis of a functionally graded Timoshenko beam under action of a moving harmonic load, Computers and Structures 92(10): 25322546. ##[25] Broek D., 1986, Elementary Engineering Fracture Mechanics, Martinus Nijhoff Publishers, Dordrecht. ##[26] Erdogan F., Wu B.H., 1997, The surface crack problem for a plate with functionally graded properties, Journal of Applied Mechanics 64(3): 448456. ##[27] Yang J., Chen Y., Xiang Y., Jia X.L., 2008, Free and forced vibration of cracked inhomogeneous beams under an axial force and a moving load, Journal of Sound and Vibration 312(12): 166181. ##[28] ANSYS Release 8.0. ANSYS, Inc. Southpointe 275 Technology Drive Canonsburg, PA 15317. ##[29] Wu J.D., Chan. J.J., 2009, Faulted gear identification of a rotating machinery based on wavelet transform and artificial neural network, Expert Systems with Applications 36:88628875. ##[30] McClelland J.L., Rumelhart D.E., 1986, Explorations in the Microstructure of Cognition, Parallel Distributed Processing: Vol.I and II, MIT Press. ##[31] The Math works Inc, Version 2009, MATLAB. ## ##]
FlowInduced Instability Smart Control of Elastically Coupled DoubleNanotubeSystems
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2
Flow induced vibration and smart control of elastically coupled doublenanotubesystems (CDNTSs) are investigated based on Eringen’s nonlocal elasticity theory and EulerBernoulli beam model. The CDNTS is considered to be composed of Carbon Nanotube (CNT) and BoronNitride Nanotube (BNNT) which are attached by Pasternak media. The BNNT is subjected to an applied voltage in the axial direction which actuates on instability control of CNT conveying nanofluid. Polynomial modal expansions are employed for displacement components and electric potential and discretized governing equations of motion are derived by minimizing total energies of the CDNTS with respect to timedependent variables of the modal expansions. The statespace matrix is implemented to solve the eigenvalue problem of motion equations and examine frequencies of the CDNTS. It is found that Pasternak media and applied voltage have considerable effects on the vibration behavior and stability of the system. Also, it is found that trend of figures have good agreement with the other studies. The results of this study can be used for design of CDNTS in nano / Micro electromechanical systems.
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22
34


V
Atabakhshian
Department of Mechanical Engineering, Faculty of Engineering, BuAli Sina University
Department of Mechanical Engineering, Faculty
Iran


A
Ghorbanpour Arani
Faculty of Mechanical Engineering, University of Kashan
Institute of Nanoscience & Nanotechnology, University of Kashan
Faculty of Mechanical Engineering, University
Iran
aghorban@kashanu.ac.ir


A.R
Shajari
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University
Iran


S
Amir
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University
Iran
Doublenanotube system
Instability smart control
Pasternak media
Conveying nanofluid
[[1] Vaccarini L., Goze C., Henrard L., Herna´ndez E., Bernier P., Rubio A., 2000, Mechanical and electronic properties of carbon and boron–nitride nanotubes, Carbon 38: 1681–1690. ##[2] Lahiri D., Rouzaud F., Richard T., Keshri A.K., Bakshi S.R., Kos L., Agarwal A., 2010, Boron nitride nanotube reinforced polylactide–polycaprolactone copolymer composite: Mechanical properties and cytocompatibility with osteoblasts and macrophages in vitro, Acta Biomaterialia 6: 35243533. ##[3] Ghorbanpour Arani A., Shajari A.R., Atabakhshian V., Amir S., Loghman A., 2013, Nonlinear dynamical response of embedded fluidconveyed microtube reinforced by BNNTs, Composites Part B 44: 424–432. ##[4] Ghorbanpour Arani A., Shajari A.R., Amir S., Loghman A., 2012, Electrothermomechanical nonlinear nonlocal vibration and instability of embedded microtube reinforced by BNNT, conveying fluid, Physica E 45: 109121. ##[5] SalehiKhojin A., Jalili N., 2008, Buckling of boron nitride nanotube reinforced piezoelectric polymeric composites subject to combined electrothermomechanical, Loadings Composites Science and Technology 68: 14891501. ##[6] Ghorbanpour Arani A., Atabakhshian V., Loghman A., Shajari A.R., Amir S., 2012, Nonlinear vibration of embedded SWBNNTs based on nonlocal Timoshenko beam theory using DQ method, Physica B 407: 25492555. ##[7] Kuang Y.D., He X.Q., Chen C.Y., Li G.Q., 2009, Analysis of nonlinear vibrations of doublewalled carbon nanotubes conveying fluid, Computation Materials Science 45: 875880. ##[8] Fu Y.M., Hong J.W., Wang X.Q., 2006, Analysis of nonlinear vibration for embedded carbon nanotubes, Journal of Sound and Vibration 296: 746756. ##[9] Narasimhan M.N.L., 2010, On the flow of an electrically conducting nonlocal viscous fluid in a circular pipe in the presence of a transverse magnetic field in magneto hydro dynamics, International Journal of Fluid Mechanics Research 37 (2): 190199. ##[10] Vu H.V., Ordonez A.M., Karnopp B.H., 2000, Vibration of a doublebeam system, Journal of Sound and Vibration 229 (4): 807822. ##[11] Lin Q., Rosenberg J., Chang D., Camacho R., Eichenfield M., Vahala K.J., Painter O., 2010, Coherent mixing of mechanical excitations in nanooptomechanicalstructures, Nature Photonics 4: 236242. ##[12] Murmu T., Adhikari S., 2010, Nonlocal effects in the longitudinal vibration of doublenanorod systems, Physica E 43: 415422. ##[13] Ke L.L., Wang Y.Sh., Wang Zh.D., 2012, Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory, Composite Structures 94: 20382047. ##[14] Han J.H., Lee I., 1998, Analysis of composite plates with piezoelectric actuators for vibration control using layerwise displacement theory, Composites Part B 29: 621632. ##[15] Reddy J.N., 2004, Wang C.M., Dynamics of Fluid Conveying Beams: Governing Equations and Finite Element Models, Centre for offshore research and engineering national university of singapore. ##[16] Rashidi V., Mirdamadi H.R., Shirani E., 2012, A novel model for vibrations of nanotubes conveying nanoflow, Computation Materials Science 51: 347352. ##[17] Shokouhmand H., Isfahani A.H.M., Shirani E., 2010, Friction and heat transfer coefficient in micro and nano channels filled with porous media for wide range of Knudsen number, International Communications in Heat and Mass Transfer 37: 890894. ##[18] Ke L.L., Yang J., Kitipornchai S., 2010, Nonlinear free vibration of functionally gradedcarbon nanotubereinforced composite beams, Composite Structures 92: 676683. ##[19] Nirmala V., Kolandaivel P., 2007, Structure and electronic properties of armchair boron nitride nanotubes, Journal of Molecular Structure: Theochem 817: 137145. ##[20] Yang, J. Ke L.L., Kitipornchai S., 2010, Nonlinear free vibration of singlewalled carbonnanotubes using nonlocal Timoshenko beam theory, Physica E 42: 17271735. ##[21] Kaviani F., Mirdamadi H.R., 2012, Influence of Knudsen number on fluid viscosity for analysis of divergencein fluid conveying nanotubes, Computation Materials Science 61: 270277. ## ##]
Thermal Vibration of Composites and Sandwich Laminates Using Refined Higher Order Zigzag Theory
2
2
Vibration of laminated composite and sandwich plate under thermal loading is studied in this paper. A refined higher order theory has been used for the purpose. In order to avoid stress oscillations observed in the implementation of a displacement based finite element, the stress field derived from temperature (initial strains) have been made consistent with total strain field. So far no study has been reported in literature on the thermal vibration problem based on the refined higher order theory using a FE model. Numerical results are presented for thermal vibration problems to study the influence of boundary conditions, ply orientation and plate geometry on the natural frequencies of these structures.
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35
46


A
Chakrabarti
Department of Civil Engineering, Indian Institute of Technology
Department of Civil Engineering, Indian Institute
Iran
anupam1965@yahoo.co.uk


S.K
Singh
Department of Civil Engineering, School of Engineering, Shiv Nadar University, Dadri
Department of Civil Engineering, School of
Iran
sushilbit@yahoo.co.in


A.H
Sheikh
School of Civil, Environment and Mining Engineering, University of Adelaide,
School of Civil, Environment and Mining Engineerin
Iran
Finite Element
Higher order
Laminated composites
Thermal load
[[1] Noor A.K., Burton W.S., 1992, Threedimensional solutions for the free vibrations and buckling of thermally stressed multilayered angleply composite plates, ASME Journal of Applied Mechanics 59(12): 868877. ##[2] Matsunaga H., 2007, Free vibration and stability of angleply laminated composite and sandwich plates under thermal loading, Composite Structures 77: 249262. ##[3] Reddy J.N., Phan N.D., 1985, Stability and vibration of isotropic, orthotropic and laminated plates according to a higherorder shear deformation theory, Journal of Sound and Vibration 98: 157170. ##[4] Putcha N.S. Reddy J.N., 1986, Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory, Journal of Sound and Vibration 104 (2): 285300. ##[5] Tessler A., Saether E., Tsui T., 1995, Vibration of thick laminated composite plates, Journal of Sound and Vibration 179: 475498. ##[6] Ganapathi M., Makhecha D.P., 2001, Free vibration analysis of multilayered composite laminates based on an accurate higherorder theory, Composites: Part B 32: 535543. ##[7] Shi J.W., Nakatani A., Kitagawa H., 2004, Vibration analysis of fully clamped arbitrarily laminated plate, Composite Structures 63:115122. ##[8] Khare R.K., Kant T., Garg A.K., 2004, Free vibration of composite and sandwich laminates with a higherorder facet shell element, Composite Structures 65: 405418. ##[9] Carrera E., 1998, Layerwise mixed models for accurate vibrations analysis of multilayered plates, ASME Journal of Applied Mechanics 65: 820828. ##[10] Nosier A., Kapania R.K., Reddy J.N., 1993, Free vibration analysis of laminated plates using a layer wise theory, Journal of American Institute of Aeronautics and Astronautics 31(12):23352346. ##[11] Cho K.N., Bert C.W., Striz A.G., 1991, Free vibrations of laminated rectangular plates analyzed by higher order individuallayer theory, Journal of Sound and Vibration 145(3): 429442. ##[12] Khdeir A.A., Reddy J.N., 1999, Free vibration of laminated composite plates using secondorder shear deformation theory, Computers and Structures 71: 617626. ##[13] Messina A., 2001, Two generalized higher order theories in free vibration studies of multilayered plates, Journal of Sound and Vibration 242(1): 125150. ##[14] Shu X., 2001, Vibration and bending of anti symmetrically angleply laminated plates with perfectly and weakly bonded layers, Composite Structures 53: 245255. ##[15] Singh B.N., Yadav D., Iyengar N.G.R., 2001, Natural frequencies of composite plates with random material properties using higher order shear deformation theory, International Journal of Mechanical Science 43: 21932214. ##[16] Kapuria S., Achary G.G.S., 2004, An efficient higherorder zigzag theory for laminated plates subjected to thermal loading, International Journal of Solids and Structures 41: 46614684. ##[17] Matsunaga H., 2004, A comparison between 2D singlelayer and 3D layer wise theories for computing inter laminar stresses of laminated composite and sandwich plates subjected to thermal loadings, Composite Structures 64(2): 161177. ##[18] Wang X., Dong K., Wang X.Y., 2005, Hygro thermal effect on dynamic inter laminar stresses in laminated plates with piezoelectric actuators, Composite Structures 71: 220228. ##[19] Zhen W., Wanji C., 2006, An efficient higherorder theory and finite element for laminated plates subjected to thermal loading, Composite Structures 73: 99109. ##[20] Matsunaga H., 2005, Thermal buckling of crossply laminated composite and sandwich plates according to a global higherorder deformation theory, Composite Structures 68(4): 439454. ##[21] Matsunaga H., 2006, Thermal buckling of angleply laminated composite and sandwich plates according to a global higherorder deformation theory, Composite Structures 72(2): 177192. ##[22] Matsunaga H., 2007, Free vibration and stability of angleply laminated composite and sandwich plates under thermal loading. Composite Structures 77: 249262. ##[23] Naganarayana B.P., Rama Mohan P., Prathap G., 1997, Accurate thermal stress predictions using C0 continuous higherorder shear deformable elements. Computer Methods in Applied Mechanics and Engineering 144: 6175. ## ##]
An Efficient Co Finite Element Approach for Bending Analysis of Functionally Graded CeramicMetal Skew Shell Panels
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2
In this article, the prominence has been given to study the influence of skew angle on bending response of functionally graded material shell panels under thermomechanical environment. Derivation of governing equations is based on the Reddy’s higherorder shear deformation theory and Sander’s kinematic equations. To circumvent the problem of C1 continuity requirement coupled with the finite element implementation, C0 formulation is developed. A nine noded isoparametric Lagrangian element has been employed to mesh the proposed shell element in the framework of finite element method. Bending response of functionally graded shell under thermal field is accomplished by exploiting temperature dependent properties of the constituents. Arbitrary distribution of the elastic properties follows linear distribution law which is a function of the volume fraction of ingredients. Different combinations of ceramicmetal phases are adopted to perform the numerical part. Different types of shells (cylindrical, spherical, hyperbolic paraboloid and hypar) and shell geometries are concerned to engender newfangled results. Last of all, the influence of various parameters such as thickness ratio, boundary condition, volume fraction index and skew angle on the bending response of FGM skew shell is spotlighted. Some new results pertain to functionally graded skew shells are reported for the first time, which may locate milestone in future in the vicinity of functionally graded skew shells.
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47
62


G
Taj
Department of Civil Engineering, Indian Institute of Technology
Department of Civil Engineering, Indian Institute
Iran
gulshantaj19@yahoo.co.in


A
Chakrabarti
Department of Civil Engineering, Indian Institute of Technology
Department of Civil Engineering, Indian Institute
Iran
anupam1965@yahoo.co.uk
Functionally graded material
Skew shell
Higher order shear deformation theory
Bending Analysis
Thermal field
[[1] Gasik M.M., 2010, Functionally graded materials: bulk processing techniques, International Journal of Materials and Production Technology 39(1–2):20–29. ##[2] Jha D.K., Tarun Kant R.K., Singh., 2013, A critical review of recent research on functionally graded plates, Composite Structures 96: 833849. ##[3] Praveen G.N., Reddy J.N., 1998, Nonlinear transient thermoelastic analysis of functionally graded ceramic–metal plates, International Journal of Solids and Structures 35:4457–4471. ##[4] Reddy J.N., Wang C.M., Kitipornchai S., 1999, Axisymmetric bending of functionally graded circular and annular plates, European Journal of Mechanics A/Solids 18:185–99. ##[5] Reddy J.N., 2000, Analysis of functionally graded plates, International Journal of Numerical Methods in Engineering 47:663–684. ##[6] Vel S.S., Batra R.C., 2002, Exact solutions for thermoelastic deformations of functionally graded thick rectangular plates, AIAA Journal 40(7):1421–33. ##[7] Shen H.S., 2005, Postbuckling of FGM plates with piezoelectric actuators under thermoelectromechanical loadings, International Journal of Solids and Structures 42:6101–6121. ##[8] Tsukamoto H., 2003, Analytical method of inelastic thermal stresses in a functionally graded material plate by a combination of a micro and macromechanical approaches, Composites Part B 34(6):561–8. ##[9] Qian L.F., Batra R.C., Chen L.M., 2004, Analysis of cylindrical bending thermoelastic deformations of functionally graded plates by a meshless local Petrov– Galerkin method, Computational Mechanics 33:263–73. ##[10] Lanhe W., 2004, Thermal buckling of a simply supported moderately thick rectangular FGM plate, Composite Structures 64:211–218. ##[11] Ferreira A.J.M., Batra R.C., Roque C.M.C., Qian L.F., Martins P.A.L.S., 2005, Static analysis of functionally graded plates using thirdorder shear deformation theory and a meshless method, Composite Structures 69:449–457. ##[12] Zenkour A.M., 2007, Benchmark trigonometric and 3D elasticity solutions for an exponentially graded thick rectangular plate, Archive of Applied Mechanics 77:197–214. ##[13] Kim Y.W., 2005, Temperature dependent vibration analysis of functionally graded rectangular plates, Journal of Sound and Vibration 284:531–549. ##[14] Javaheri R, Eslami M.R., 2003, Thermal buckling of functionally graded plates based on higher order theory, Journal of Thermal Stresses 25:603–625. ##[15] Na K.S., Kim J.H., 2004, Threedimensional thermal buckling analysis of functionally graded materials, Composites Part B 35:429–437. ##[16] Neves A.M.A., Ferreira A.J.M., Carrera E, Roque C.M.C., Cinefra M, Jorge R.M.N., 2012, A quasi3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates, Composites Part B 43:711–725. ##[17] Naghdi P.M., 1956, A survey of recent progress in the theory of elastic shells, Applied Mechanics Reviews 9: 365368. ##[18] Bert C.W., 1976, Dynamics of composite and sandwich panelsPart I, Journal of Shock and Vibration 8: 3748. ##[19] Bert C.W., 1980, Analysis of Shells. Analysis and Performance of Composites, Wiley, New York . ##[20] Hildebrand F.B., Reissner E, Thomas G.B., 1949, Note on the foundations of the theory of small displacements of orthotropic shells, Advisory Committee for Aeronautics Techical Notes, No. 1833. ##[21] Lure A.I., 1947, Statics of Thin Elastic Shells , Gostekhizdat, Moscow . ##[22] Reissner E., 1952, Stressstrain relations in the theory of thin elastic shells, Journal of Mathematical Physics 31: 109 119. ##[23] Whitney J.M., Sun C.T., 1973, A higher order theory for extensional motion of laminated anisotropic shells and plates, Journal of Sound and Vibration 30: 8589. ##[24] Whitney J.M., Sun C.T., 1974, A refined theory for laminated anisotropic cylindrical shells, Journal of Applied Mechanics 41(2):471476. ##[25] Reddy J.N., 1983, Exact solutions of moderately thick laminated shells, Journal of Engineering Mechanics 110 (5): 794809. ##[26] Reddy J.N., Arciniega R.A., 2004, Shear deformation plate and shell theories: From Stavsky to present, Journal of Mechanics of Advanced Materials and Structures 11: 535582. ##[27] Ferreira A.J.M., Roque C.M.C., Carrera E., Cinefra M., Polit O, 2011, Two higher order zigzag theories for the accurate analysis of bending, vibration and buckling response of laminated plates by radial basis functions collocation and a unified formulation, Journal of Composite Materials 45(24):2523–2536. ##[28] Ferreira A.J.M, Roque C.M.C., Carrera E, Cinefra M, Polit O, 2011, Radial basis functions collocation and a unified formulation for bending, vibration and buckling analysis of laminated plates, according to a variation of murakami’s zigzag theory, European Journal of Mechanics A/Solids 30(4):559–570. ##[29] Carrera E., Brischetto S., Robaldo A., 2008, Variable kinematic model for the analysis of functionally graded material plates, AIAA Journal 46:194–203. ##[30] Carrera E., Brischetto S., Cinefra M., Soave M., 2011, Effects of thickness stretching in functionally graded plates and shells, Composite Part B 42:23–133. ##[31] Qian L.F., Batra R.C., Chen L.M., 2004, Analysis of Cylindrical Bending Thermoelastic Deformations of Functionally Graded Plates by a Meshless Local PetrovGalerkin Method, Computational Mechanics 33: 263–273. ##[32] Pradyumna S., Namit Nanda, Bandyopadhyay J.N., 2010, Geometrically nonlinear analysis of functionally graded shell panels using a higher order finite element formulation, Journal of Mechanical Engineering and Research 2(2): 3951. ##[33] Zhao X., Liew K.M., 2009, Geometrically nonlinear analysis of functionally graded shells, Journal of Mechanical Sciences 51: 131144. ##[34] Zhao X., Lee Y., Liew K.M., 2009, Thermoelastic and vibration analysis of functionally graded cylindrical shells, Journal of Mechanical Sciences 51: 694707. ##[35] Naghdabadi R., Hosseini Kordkheni, S.A., 2005, A finite element formulation for analysis of functionally graded plates and shells, Archive of Applied Mechanics 74: 375386. ##[36] Cinefra M., Carrera E., Brischetto S., Belouettar S., 2010, ThermoMechanical analysis of functionally graded shells, Journal of Thermal Stresses 33: 942963. ##[37] Najafizadeh M.M., Isvandzibaei M.R., 2007, Vibration of functionally graded cylindrical shells based on higher order shear deformation plate theory with ring support, Acta Mechanica 191: 7591. ##[38] Najafizadeh M.M., Hasani A., Khazaeinejad P., 2009, Mechanical stability of functionally graded stiffened cylindrical shells, Applied Mathematical Modelling 33: 11511157. ##[39] Najafizadeh M.M., Isvandzibaei M.R., 2009, Vibration of functionally graded cylindrical shells based on different shear deformation shell theories with ring support under various boundary conditions, Journal of Mechanical Science and Technology 23: 113. ##[40] Khazaeinejad P., Najafizadeh M.M., 2010, Mechanical buckling of cylindrical shells with varying material properties, Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science 224(8): 15511557. ##[41] Khazaeinejad P., Najafizadeh M.M., Jenabi J., Isvandzibaei M.R., 2010, On the buckling of functionally graded cylindrical shells under combined external pressure and axial compression, ASME Journal of Pressure Vessel and Technology 132(6): 06450116. ##[42] Najafizadeh M.M., Khazaeinejad P., 2010, An analytical solution for buckling of nonhomogeneous cylindrical shells under combined loading, Journal of Applied Mechanics Research 2(2):1120. ##[43] Woo S, Meguid, S.A., 2001, Non linear analysis of functionally graded plates and shallow shells, Journal of Solids and Structures 38: 74097421. ##[44] Liew K.M., Kitipornchai S., Zhang X.Z., Lim C.W., 2003, Analysis of the thermal stress behavior of functionally graded hollow circular cylinders, International Journal of Solids and Structures 40: 23552380. ##[45] Jacob L.P., Vel. S.S., 2006, An exact solution for the steadystate thermoelastic response of functionally graded orthotropic cylindrical shells, International Journal of Solids and Structures 43: 11311158. ##[46] Woo J., Meguid, S.A., Stranata, J.C, Liew, K.M., 2005, Thermomechanical post buckling analysis of moderately thick functionally graded plates and shallow shells, International Journal of Mechanical Sciences 47: 11471171. ##[47] Bahtui A., and Eslami M.R., 2007, Generalized coupled thermoelasticity of functionally graded cylindrical shells, International Journal of Numerical Methods in Engineering 69: 676697. ##[48] Reddy J.N., 1984, A simple higherorder theory for laminated composite plate, Journal of Applied Mechanics 51: 745752. ##[49] Hill R., 1965, A selfconsistent mechanics of composite materials, Journal of Mechanics and Physics of Solids 13:213–222. ##[50] Hashin Z., 1968, Assessment of the self consistent scheme approximation: conductivity of composites, Journal of Composite Materials 4:284–300. ##[51] Bhaskar K., Varadan T.K, 2001, Assessment of the self consistent scheme approximation: conductivity of composites, ASME Journal of Applied Mechanics 68(4):660–2. ##[52] Mori T., Tanaka T., 1973, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metallaugica 21:571–574. ##[53] Benveniste Y., 1987, A new approach to the application of Mori–Tanaka’s theory in composite materials, Mechanics of Materials 6:147–157. ##[54] Hashin Z., 1962, The elastic moduli of heterogeneous materials, ASME Journal of Applied Mechanics 29:143–150. ##[55] Hashin Z., Shtrikman S., 1964, A variational approach to the theory of elastic behaviour of multiphase materials, Journal of mechanics and physics of solids 11:127–140. ##[56] Hashin Z., Rosen B.W., 1964, The elastic moduli of fiberreinforced materials, ASME Journal of Applied Mechanics 4:223–232. ##[57] Hashin Z., 1979, Analysis of properties of fiber composites with anisotropic constituents, ASME Journal of Applied Mechanics 46:543–450. ##[58] Chamis C.C., Sendeckyj G.P., 1968, Critique on theories predicting thermoelastic properties of fibrous composites, Journal of Composite Materials 2(3):332–358. ##[59] Gibson R.F., 1991, Principles of composite material mechanics, McGrawHill. ##[60] Aboudi J., 1991, Mechanics of composite materials: a unified micromechanical approach, Amsterdam, Elsevier. ##[61] Suresh S., Mortensen A., 1998, Fundamentals of Functionally Graded Material, London, IOM Communications. ## ##]
A Semianalytical Approach to Elasticplastic Stress Analysis of FGM Pressure Vessels
2
2
An analytical method for predicting elastic–plastic stress distribution in a cylindrical pressure vessel has been presented. The vessel material was a ceramic/metal functionally graded material, i.e. a particle–reinforcement composite. It was assumed that the material’s plastic deformation follows an isotropic strainhardening rule based on the vonMises yield criterion, and that the vessel was under planestress conditions. The mechanical properties of the graded layer were modelled by the modified rule of mixtures. By assuming small strains, Hencky’s stress–strain relation was used to obtain the governing differential equations for the plastic region. A numerical method for solving those differential equations was then proposed that enabled the prediction of stress state within the structure. Selected finite element results were also presented to establish supporting evidence for the validation of the proposed analytical modelling approach. Similar analyses were performed and solutions for spherical pressure made of FGMs were also provided.
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63
73


A.T
Kalali
Mechanical Engineering Department, Ferdowsi University of Mashhad
Mechanical Engineering Department, Ferdowsi
Iran


S
HadidiMoud
Mechanical Engineering Department, Ferdowsi University of Mashhad
Mechanical Engineering Department, Ferdowsi
Iran
hadidi@um.ac.ir
Functionally graded material
Elastic–plastic analysis
Pressure vessel
Modified rule of mixtures
[[1] Chakraborty A., Gopalakrishnan S., Reddy J.N., 2003, A new beam finite element for the analysis of functionally graded materials, International Journal of Mechanical Sciences 45:519–539. ##[2] Jin ZH., Paulino GH., Dodds Jr RH., 2003, Cohesive fracture modeling of elastic–plastic crack growth in functionally graded materials, Engineering Fracture Mechanics 70:1885–912. ##[3] Figueiredo F., Borges L., Rochinha F., 2008, Elastoplastic stress analysis of thickwalled FGM pipes, American Institute of Physics Conference Proceedings 973:147_52. ##[4] Haghpanah Jahromi B., Farrahi GH., Maleki M., NayebHashemi H., Vaziri A., 2009, Residual stresses in autofrettaged vessel made of functionally graded material, Engineering Structures 31:2930–5. ##[5] Haghpanah Jahromi B., Ajdari A., NayebHashemi H., Vaziri A., 2010, Autofrettage of layered and functionally graded metal–ceramic composite vessels, Composite Structures 92:1813–22. ##[6] Jahed H., Dubey RN., 1997, An axisymmetric method of elasticplastic analysis capable of predicting residual stress field, Journal of Pressure Vessel Technology 119:264–73 ##[7] Jahed H., Farshi B., Karimi M., 2006, Optimum autofrettage and shrinkfit combination in multilayer cylinders, Journal of Pressure Vessel Technology 128:196–201. ##[8] Jahed H., Farshi B., Bidabadi J., 2005, Minimum weight design of inhomogeneous rotating discs, International Journal of Pressure Vessels and Piping 82:35–41. ##[9] Jahed H., Shirazi R., 2001, Loading and unloading behaviour of a thermoplastic disc, International Journal of Pressure Vessels and Piping 78:637–45. ##[10] You LH., Zhang JJ., You XY., 2005, Elastic analysis of internally pressurized thickwalled spherical pressure vessels of functionally graded materials, International Journal of Pressure Vessels and Piping 82:374–345. ##[11] Dai HL., Fu YM., Dong ZM., 2006, Exact solutions for functionally graded pressure vessels in a uniform magnetic field, International Journal of Solids and Structures 43:5570–80. ##[12] Chen YZ., Lin XY., 2008, Elastic analysis for thick cylinders and spherical pressure vessels made of functionally graded materials, Computational Materials Science 44:581–587. ##[13] Sadeghian M., Ekhteraei H., 2011, Axisymmetric yielding of functionally graded spherical vessel under thermomechanical loading, Computational Materials Science 50:975–81. ##[14] Dunne F., Petrinic N., 2006, Introduction to Computational Plasticity, Oxford University Press. ##[15] Chakrabarty J., 2006, Theory of Plasticity, UK, Elsevier Butterworth Heinemann, 3rd Edition. ##[16] Mendelson A., 1968, Plasticity: Theory and Application, New York, Macmillan. ##[17] Suresh S., Mortensen A., 1998, Fundamentals of Functionally Graded Materials, IOM Communications Ltd. ##[18] Carpenter RD., Liang WW., Paulino GH., Gibeling JC., Munir ZA., 1999, Fracture testing and analysis of a layered functionally graded Ti/TiB beam in 3point bending, Materials Science Forum 308–311:837–42. ##[19] Jamshidi N., Abouei A., Molaei R., Rezaei R., Jamshidi M., 2011, Applied Guide on MATLAB, Tehran, Abed. ##[20] Karlsson., Hibbitt., Sorensen., 2008, ABAQUS/CAE, Version 6.81. ##[21] Setoodeh A., Kalali A., Hosseini A., 2008, Numerical analysis of FGM plate by applying virtual temperature distribution, 7 th conference of Iranian aerospace society, Tehran. ## ##]
AxiSymmetric Deformation Due to Various Sources in Saturated Porous Media with Incompressible Fluid
2
2
The general solution of equations of saturated porous media with incompressible fluid for two dimensional axisymmetric problem is obtained in the transformed domain. The Laplace and Hankel transforms have been used to investigate the problem. As an application of the approach concentrated source and source over circular region have been taken to show the utility of the approach. The transformed components of displacement, stress and pore pressure are obtained. Numerical inversion technique is used to obtain the resulting quantities in physical domain. Effect of porosity is shown on the resulting quantities. A particular case of interest is also deduced from the present investigation.
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74
91


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


S
Kumar
Department of Mathematics, Govt. Degree College Indora (Kangra), Himachal Pradesh
Department of Mathematics, Govt. Degree College
Iran


M.G
Gourla
Department of Mathematics, Himachal Pradesh University
Department of Mathematics, Himachal Pradesh
Iran
Axisymmetric
Incompressible porous medium
Pore pressure
Laplace transform
Hankel transform
Concentrated source and source over circular region
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Vibration and Stability Analysis of a Pasternak Bonded DoubleGNRSystem Based on Different Nonlocal Theories
2
2
This study deals with the vibration and stability analysis of doublegraphene nanoribbonsystem (DGNRS) based on different nonlocal elasticity theories such as Eringen's nonlocal, strain gradient, and modified couple stress within the framework of Rayleigh beam theory. In this system, two graphene nanoribbons (GNRs) are bonded by Pasternak medium which characterized by Winkler modulus and shear modulus. An analytical approach is utilized to determine the frequency and critical buckling load of the coupled system. The three vibrational states including outofphase vibration, inphase vibration and one GNR being stationary are discussed. A detailed parametric study is conducted to elucidate the influences of the small scale coefficients, stiffness of the internal elastic medium, mode number and axial load on the vibration of the DGNRS. The results reveal that the dimensionless frequency and critical buckling load obtained by the strain gradient theory is higher than the Eringen's and modified couple stress theories. Moreover, the small scale effect in the case of inphase vibration is higher than that in the other cases. This study might be useful for the design of nanodevices in which GNRs act as basic elements.
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92
106


A
Ghorbanpour Arani
Faculty of Mechanical Engineering, University of Kashan
Institute of Nanoscience & Nanotechnology, University of Kashan
Faculty of Mechanical Engineering, University
Iran
aghorban@kashanu.ac.ir


R
Kolahchi
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University
Iran


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


M
Abdollahian
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University
Iran
GNR
Strain gradient theory
Rayleigh beam theory
Coupled system
Modified couple stress theory
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2011, Nonlocal elasticity theory for the buckling of doublelayer graphene nanoribbons based on a continuum model, Computational Material Science 50: 30853090. ##[7] Eringen A.C., 1972, Nonlocal polar elastic continua, International Journal of Engineering Science 10: 1–16. ##[8] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54: 47034710. ##[9] Eringen A.C., 2002, Nonlocal Continuum Field Theories, SpringerVerlag, New York. ##[10] Ghorbanpour Arani A., Mosallaie Barzoki A.A., Kolahchi R., Loghman A., 2011, Pasternak foundation effect on the axial and torsional waves propagation in embedded DWCNTs using nonlocal elasticity cylindrical shell theory, Journal of Mechanical Science and Technology 25: 23852391. ##[11] Mindlin R.D., 1965, Second gradient of strain and surface tension in linear elasticity, International Journal of Solids and Structures 1: 417438. ##[12] Lam D.C.C., Yang F., Chong A.C.M., Wang J., Tong P., 2003, Experiments and theory in strain gradient elasticity, Journal of Mechanics and Physics of Solid 51: 14771508. ##[13] Kong S.L., Zhou S.J., Nie Z.F., Wang K., 2009, Static and dynamic analysis of micro beams based on strain gradient elasticity theory, International Journal of Engineering Science 47: 487498. ##[14] Yin L., Qian Q., Wang, L., 2011, Strain gradient beam model for dynamics of microscale pipes conveying fluid, Applied Mathematical Modeling 35: 28642873. ##[15] 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. ##[16] Şimşek S., 2010, Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory, International Journal of Engineering Science 48: 17211732. ##[17] Shi J.X., Ni Q.Q., Lei X.W., Natsuki T., 2012, Nonlocal vibration of embedded doublelayer graphene nanoribbonsinphase and antiphase modes, Physica E 44:1136–1141. ##[18] Shi J.X., Ni Q.Q., Lei X.W., Natsuki T., 2011, Nonlocal elasticity theory for the buckling of doublelayer graphene nanoribbons based on a continuum model, Computational Material Science 50: 30853090. ##[19] Murmu T., Adhikari S., 2011, Axial instability of doublenanobeamsystem, Physics Letters A 375: 601–608. ##[20] Murmu T., Adhikari S., 2012, Nonlocal elasticity based vibration of initially prestressed coupled nanobeam systems, European Journal of Mechanics A/Solid 34: 5262. ##[21] Murmu T., Adhikari, S., 2011, Nonlocal vibration of bonded doublenanoplatesystems, Composite Part B 42: 1901–1911. ##[22] Ghorbanpour Arani A., Kolahchi R., Vossough H., 2012, Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory, Physica B 407: 44584465. ##[23] Wu J.X., Li X.F., Tang G.J. 2012, Bending wave propagation of carbon nanotubes in a biparameter elastic matrix, Physica B 407: 684–688. ##[24] Stonjanovic V., Kozic, P., 2012, Forced transverse vibration of Rayleigh and Timoshenko doublebeam system with effect of compressive axial load, International Journal of Mechanical Science 60: 5971. ##[25] Pradhan S.C., Murmu, T., 2009, Small scale effect on the buckling of singlelayered graphene sheets under biaxial compression via nonlocal continuum mechanics, Computational Material Science 47: 268274. ##[26] Kiani K., 2012, Vibration behavior of simply supported inclined singlewalled carbon nanotubes conveying viscous fluids flow using nonlocal Rayleigh beam model, Applied Mathematical Modeling 37: 18361850. ##[27] Ghorbanpour Arani A., Kolahchi R., Vossough H., 2012, Nonlocal wave propagation in an embedded DWBNNT conveying fluid via strain gradient theory, Physica B 407: 42814286. ##[28] Akgoz B., Civalek O., 2011, Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded microscaled beams, International Journal of Engineering Science 49: 12681280. ## ##]