2015
7
2
2
118
Vibration Response of an Elastically Connected DoubleSmart NanobeamSystem Based NanoElectroMechanical Sensor
2
2
Nonlocal vibration of doublesmart nanobeamsystems (DSNBSs) under a moving nanoparticle is investigated in the present study based on Timoshenko beam model. The two smart nanobeams (SNB) are coupled by an enclosing elastic medium which is simulated by Pasternak foundation. The energy method and Hamilton’s principle are used to establish the equations of motion. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, elastic medium coefficients, external voltage, length of SNB and the mass of attached nanoparticle on the frequency of piezoelectric nanobeam. The results depict that the imposed external voltage is an effective controlling parameter for vibration of the piezoelectric nanobeam. Also increase in the mass of attached nanoparticle gives rise to a decrease in the natural frequency. This study might be useful for the design and smart control of nanodevices.
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121
130


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


S.A
Mortazavi
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University
Iran


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


A.H
Ghorbanpour Arani
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University
Iran
DSNBSs
Nonlocal vibration
Pasternak foundation
Timoshenko beam model
Exact solution
[[1] Eringen A.C., 1972, Nonlocal polar elastic continua, International Journal of Engineering Science 10: 116.##[2] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54: 4703 4710.##[3] 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: Condensed Matter 407: 25492555.##[4] Wang Q., 2005, Wave propagation in carbon nanotubes via nonlocal continuum mechanics, Journal of Applied Physics 98: 124301.##[5] Wang L.F., Hu H.Y., 2005, Flexural wave propagation in singlewalled carbon nanotubes, Physical Review B 71: 195412.##[6] Narendar S., Roy Mahapatra D., Gopalakrishnan S., 2011, Prediction of nonlocal scaling parameter for armchair and zigzag singlewalled carbon nanotubes based on molecular structural mechanics, nonlocal elasticity and wave propagation, International Journal of Engineering Science 49: 509522.##[7] Yan Z., Jiang L.Y., 2011, The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects, Nanotechnology 2: 245703.##[8] Reddy J.N., 2007, Nonlocal theories for bending, buckling and vibration of beams, International Journal of Engineering Science 45: 288307.##[9] Huang G.Y., Yu S.W., 2006, Effect of surface piezoelectricity on the electromechanical behavior of a piezoelectric ring, physica Satus Solidi B 243: 2224.##[10] Yan Z., Jiang L.Y., 2008, The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects, Nanotechnology 22: 245703.##[11] Simsek M., 2011, Nonlocal effects in the forced vibration of an elastically connected doublecarbon nanotube system under a moving nanoparticle, Computational Materials Science 50: 21122123.##[12] Ke L.L., Wang Y.Sh., Wang Zh.D., 2008, Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory, Composite Structures 94: 20382047.##[13] Han J.H., Lee I., 1998, Analysis of composite plates with piezoelectric actuators for vibration control using layerwise displacement theory, Composite B: Engineering 29: 621632.##[14] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A.A., 2011, Effect of material inhomogeneity on electrothermomechanical behaviors of functionally graded piezoelectric rotating shaft, Applied Mathematical Modelling 35: 27712789.##[15] Wang Q., 2002, On buckling of column structures with a pair of piezoelectric layers, Engineering Structures 24: 199205.##[16] Mosallaie Barzoki A.A., Ghorbanpour Arani A., Kolahchi R., Mozdianfard M.R., 2012, Electrothermomechanical torsional buckling of a piezoelectric polymeric cylindrical shell reinforced by DWBNNTs with an elastic core, Applied Mathematical Modelling 36: 29832995.##[17] Mohammadimehr M., Saidi A.R., Ghorbanpour Arani A., Arefmanesh A., Han Q., 2010, Torsional buckling of a DWCNT embedded on Winkler and Pasternak foundations using nonlocal theory, Journal of Mechanical Science and Technology 24: 12891299.##[18] Ding H.J., Wang H.M., Ling D.S., 2003, Analytical solution of a pyroelectric hollow cylinder for piezothermoelastic axisymmetric dynamic problems, Journal of Thermal Stresses 26: 261276.##[19] Wang Q., 2002, Axisymmetric wave propagation in a cylinder coated with apiezoelectric layer, International Journal of Solids and Structures 39: 30233037.##[20] Shen Zh.B., Tang H.L., Li D.K., Tang G.J, 2012, Vibration of singlelayered graphene sheetbased nanomechanical sensor via nonlocal Kirchhoff plate theory, Computational Materials Science 6: 201205.##]
Semi Analytical Analysis of FGM ThickWalled Cylindrical Pressure Vessel with Longitudinal Variation of Elastic Modulus under Internal Pressure
2
2
In this paper, a numerical analysis of stresses and displacements in FGM thickwalled cylindrical pressure vessel under internal pressure has been presented. The elastic modulus is assumed to be varying along the longitude of the pressure vessel with an exponential function continuously. The Poisson’s ratio is assumed to be constant. Whereas most of the previous studies about FGM thickwalled pressure vessels are on the basis of changing material properties along the radial direction, in this research, elastic analysis of cylindrical pressure vessel with exponential variations of elastic modulus along the longitudinal direction, under internal pressure, have been investigated. For the analysis of the vessel, the stiffness matrix of the cylindrical pressure vessel has been extracted by the usage of Galerkin Method and the numerical solution for axisymmetric cylindrical pressure vessel under internal pressure have been presented. Following that, displacements and stress distributions depending on inhomogeneity constant of FGM vessel along the longitudinal direction of elastic modulus, are illustrated and compared with those of the homogeneous case. The values which have been used in this study are arbitrary chosen to demonstrate the effect of inhomogeneity on displacements and stress distributions. Finally, the results are compared with the findings of finite element method (FEM).
1

131
145


M
Shariati
Department of Mechanical Engineering, Ferdosi University
Department of Mechanical Engineering, Ferdosi
Iran
mshariati44@um.ac.ir


H
Sadeghi
Department of Mechanical Engineering, Shahrood University
Department of Mechanical Engineering, Shahrood
Iran


M
Ghannad
Department of Mechanical Engineering, Shahrood University
Department of Mechanical Engineering, Shahrood
Iran


H
Gharooni
Department of Mechanical Engineering, Shahrood University
Department of Mechanical Engineering, Shahrood
Iran
gharooni.hamed@gmail.com
Thickwalled cylinder
Cylindrical pressure vessel
FGM
Longitudinal variations of elastic modulus
Exponential
[[1] Fukui Y., Yamanaka N., 1992, Elastic analysis for thickwalled tubes of functionally graded materials subjected to internal pressure, JSME International Journal Series I 35(4): 891900.##[2] Tutuncu N., Ozturk M., 2001, Exact solution for stresses in functionally graded pressure vessel, Composites Part B: Engineering 32: 683686.##[3] Jabbari M., Sohrab pour S., Eslami M.R., 2002, Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads, International Journal of Pressure Vessel and Piping 79: 493497.##[4] 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: 601610.##[5] Eslami M.R., Babaei M.H., Poultangari R., 2005, Thermal and mechanical stresses in a functionally graded thick sphere, International Journal of Pressure Vessel and Piping 82: 522527.##[6] Dai H.L., Fu Y.M., Dong Z.M., 2006, Exact solutions for functionally graded pressure vessels in a uniform magnetic field, International Journal of Solids and Structures 43: 55705580.##[7] Naghdabadi R., Kordkheili S.A., 2005, A finite element formulation for analysis of functionally graded plates and shells, ASME Journal of Applied Mechanics 74: 375386.##[8] Hongjun X., Zhifei S., Taotao Z., 2006, Elastic analyses of heterogeneous hollow cylinders, Mechanics Research Communications 33(5): 681691.##[9] Zhifei S., Taotao Z., Hongjun X., 2007, Exact solutions of heterogeneous elastic hollow cylinders, Composite Structures 79: 140147.##[10] Tutuncu N., 2007, Stresses in thickwalled FGM cylinders with exponentiallyvarying properties, Engineering Structures 29: 20322035.##[11] Ghannad M., Nejad M.Z., 2010, Elastic analysis of pressurized thick hollow cylindrical shells with clampedclamped ends, Mechanika 5(85): 1118.##[12] Ghannad M., Rahimi G.H., Zamani Nejad M., 2012, Determination of displacements and stresses in pressurized thick cylindrical shells with variable thickness using perturbation technique, Mechanika 18(1): 1421.##[13] Gharooni H., Ghannad M., 2012, Analytical solution of rotary pressurized FGM cylinder by the usage of first order shear deformation theory, 11th Conference of Iranian Aerospace Society 15024: 195.##[14] Liu L., Li J., Ding M., Yang X., 2007, Development of SiC/(W, Ti)C gradient ceramic nozzle materials for sand blasting surface treatments, International Journal of Refractory Metals and Hard Materials 25(2): 130137.##[15] Liu L., Deng J., 2008, Study on erosion wear mechanism of SiC/(W,Ti)C gradient ceramic nozzle material, Journal of Key Engineering Materials 375(376): 440444.##[16] Asemi K., Salehi M., Akhlaghi M., 2011, Elastic solution of a twodimensional functionally graded thick truncated cone with finite length under hydrostatic combined loads, Acta Mechanica 217(12): 119134.##[17] Masoud Asgari M., Akhlaghi M., 2010, Transient thermal stresses in twodimensional functionally graded thick hollow cylinder with finite length, Archive of Applied Mechanics 80(4): 353376.##[18] Ghannad M., Rahimi G.H., Zamani Nejad M., 2013, Elastic analysis of pressurized thick cylindrical shells with variable thickness made of functionally graded materials, Composites: Part B 45: 388396.##]
An Experimental and Numerical Study of Forming Limit Diagram of Low Carbon Steel Sheets
2
2
The forming limit diagram (FLD) is probably the most common representation of sheet metal formability and can be defined as the locus of the principal planar strains where failure is most likely to occur. Low carbon steel sheets have many applications in industries, especially in automotive parts, therefore it is necessary to study the formability of these steel sheets. In this paper, FLDs, were determined experimentally for two grades of low carbon steel sheets using outofplane (dome) formability test. The effect of different parameters such as work hardening exponent (n), anisotropy (r) and thickness on these diagrams were studied. In addition, the outofplane stretching test with hemispherical punch was simulated by finite element software Abaqus. The limit strains occurred with localized necking were specified by tracing the thickness strain and its first and second derivatives versus time at the thinnest element. Good agreement was achieved between the predicted data and the experimental data.
1

146
157


M
Kadkhodayan
Department of Mechanical Engineering ,Islamic Azad University, Mashhad Branch
Department of Mechanical Engineering ,Islamic
Iran
kadkhoda@um.ac.ir


H
Aleyasin
Department of Mechanical Engineering ,Islamic Azad University, Mashhad Branch
Department of Mechanical Engineering ,Islamic
Iran
Forming Limit Diagram
Outofplane
Localized necking
Finite Element
[[1] Brun R., Chambard A., Lai M., De Luca P., 1999, Actual and virtual testing techniques for a numerical definition of materials, Numisheet 99.##[2] Cao J., Yao H., Karafillis A., Boyce M.C., 2000, Prediction of localized thinning in sheet metal using a general anisotropic yield criterion, International Journal of Plasticity 16: 11051129.##[3] Clift S.E., Hartley P., Sturgess C.E.N., Rowe G.W., 1990, Fracture prediction in plastic deformation processes, International Journal of Mechanical Sciences 32: 117.##[4] Friedman P.A., Pan J., 2000, Effects of plastic anisotropy and yield criteria on prediction of forming limit curves, International Journal of Mechanical Sciences 42: 2948.##[5] Geiger M., Merklein M., 2003, Determination of forming limit diagrams a new analysis method for characterization of materials formability, Annals of the CIRP 52: 213216.##[6] Goodwin G.M., 1968, Application of strain analysis to sheet metal forming problems in the press shop, SAE Technical Paper 680093, doi:10.4271/680093.##[7] Hecker S.S., 1975, Simple technique for determining forming limit curves, Sheetmetal Industries Ltd 52: 671676.##[8] Hill R., 1948, A theory of yielding and plastic flow of anisotropic metals, Proceedings A 193: 281297.##[9] Huang H.M., Pan J., Tang S.C., 2000, Failure prediction in anisotropic sheet metals under forming operations with consideration of rotating principal stretch directions, International Journal of Plasticity 16: 611633.##[10] Marciniak Z., Kuczynski K., 1967, Limit strains in the processes of stretch forming sheet metal, International Journal of Mechanical Sciences 9: 609620.##[11] Narayanasamy R., Sathiya Narayanan C., 2006, Forming limit diagram for Indian interstitial free steels, Materials & Design Journal 27: 882899.##[12] Ozturk F., Lee D., 2004, Analysis of forming limits using ductile fracture criteria, Journal of Materials Processing Technology 147: 397404.##[13] Pepelnjak T., Petek A., Kuzman K., 2005, Analysis of the forming limit diagram in digital environment, Advanced Material Research 6/8: 697704.##[14] Petek A., Pepelnjak T., Kuzman K., 2005, An improved method for determining a forming limit diagram in the digital environment, Journal of Mechanical Engineering 51: 330345.##[15] Raghavan K.S., 1995, A simple technique to generate inplane forming limit curves and selected applications, Metallurgical and Materials Transactions A 26(8): 20752084.##[16] Takuda H., Mori K., Takakura N., Yamaguchi K., 2000, Finite element analysis of limit strains in biaxial stretching of sheet metals allowing for ductile fracture, International Journal of Mechanical Sciences 42: 785798.##[17] Wu P.D., Jain M., Savoie J., MacEwen S.R., Tugcu P, Neale K.W., 2003, Evaluation of anisotropic yield functions for aluminum sheets, International Journal of Plasticity 19: 121138.##[18] Yoshida T., Katayama T., Usuda M., 1995, Forminglimit analysis of hemisphericalpunch stretching using the threedimensional finite element method, Journal of Materials Processing Technology 50: 226237.##]
Free Vibration Analyses of Functionally Graded CNT Reinforced Nanocomposite Sandwich Plates Resting on Elastic Foundation
2
2
In this paper, a refined plate theory is applied to investigate the free vibration analysis of functionally graded nanocomposite sandwich plates reinforced by randomly oriented straight carbon nanotube (CNT). The refined shear deformation plate theory (RSDT) uses only four independent unknowns and accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The motion equations are derived using Hamilton’s energy principle and Navier’s method and is applied to solve this equation. The sandwich plates are considered simply supported and resting on a Winkler/Pasternak elastic foundation. The material properties of the functionally graded carbon nanotube reinforced composites (FGCNTRCs) are graded along the thickness and estimated though the Mori–Tanaka method. Effects of CNT volume fraction, geometric dimensions of sandwich plate, and elastic foundation parameters are investigated on the natural frequency of the FGCNTRC sandwich plates.
1

158
172


R
MoradiDastjerdi
Young Researchers and Elite Club, Khomeinishahr Branch, Islamic Azad University
Young Researchers and Elite Club, Khomeinishahr
Iran
rasoul.moradi@iaukhsh.ac.ir


Gh
Payganeh
School of Mechanical Engineering, Shahid Rajaee Teacher Training University
School of Mechanical Engineering, Shahid
Iran


H
MalekMohammadi
School of Mechanical Engineering, Shahid Rajaee Teacher Training University
School of Mechanical Engineering, Shahid
Iran
Sandwich plates
Mori–Tanaka approach
Refined plate theory
Carbon nanotubes
Navier’s solution
[[1] Wagner H.D., Lourie O., Feldman Y., 1997, Stressinduced fragmentation of multiwall carbon nanotubes in a polymer matrix, Applied Physics Letters 72: 188190.##[2] Griebel M., Hamaekers J., 2004, Molecular dynamic simulations of the elastic moduli of polymercarbon nanotube composites, Computer Methods in Applied Mechanics and Engineering 193: 17731788.##[3] Fidelus J.D., Wiesel E., Gojny F.H., Schulte K., Wagner H.D., 2005, Thermomechanical properties of randomly oriented carbon/epoxy nanocomposites, Composite Part A 36: 15551561.##[4] Song Y.S., Youn J.R., 2006, Modeling of effective elastic properties for polymer based carbon nanotube composites, Polymer 47:17411748.##[5] Han Y., Elliott J., 2007, Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites, Computational Materials Science 39: 315323.##[6] Zhu R., Pan E., Roy A.K., 2007, Molecular dynamics study of the stress–strain behavior of carbonnanotube reinforced Epon 862 composites, Materials Science and Engineering A 447: 5157.##[7] 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.##[8] 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.##[9] 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.##[10] Wuite J., Adali S., 2005, Deflection and stress behaviour of nanocomposite reinforced beams using a multiscale analysis, Composite Structures 71: 388396.##[11] Reddy J.N., 2000, Analysis of functionally graded plates, International Journal for Numerical Methods in Engineering##47: 663684.##[12] Cheng Z.Q., Batra R.C., 2000, Deflection relationships between the homogeneous Kirchhoff plate theory and different functionally graded plate theories, Archive of Mechanics 52:143158.##[13] Cheng Z.Q., Batra R.C., 2000, Exact correspondence between eigenvalues of membranes and functionallygraded simplysupported polygonal plates, Journal of Sound and Vibration 229: 879895.##[14] Shen H.S., 2011, Postbuckling of nanotubereinforced composite cylindrical shells in thermal environments, Part I: Axiallyloaded shells, Composite Structures 93: 20962108.##[15] Ke L.L., Yang J., Kitipornchai S., 2010, Nonlinear free vibration of functionally graded carbon nanotubereinforced composite beams, Composite Structures 92: 676683.##[16] Mori T., Tanaka K., 1973, Average stress in matrix and average elastic energy of materials with Misfitting inclusions, Acta Metallurgica 21: 571574.##[17] Yas M.H., Heshmati M., 2012, Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load, Applied Mathematical Modelling 36: 13711394.##[18] Sobhani Aragh B., Nasrollah Barati A.H., Hedayati H., 2012, Eshelby–Mori–Tanaka approach for vibrational behavior of continuously graded carbon nanotube–reinforced cylindrical panels, Composites Part B 43: 19431954.##[19] Pourasghar A., Yas M.H., Kamarian S., 2013, Local aggregation effect of CNT on the vibrational behavior of fourparameter continuous grading nanotubereinforced cylindrical panels, Polymer Composites 34: 707721.##[20] MoradiDastjerdi R., Pourasghar A., Foroutan M., 2013, The effects of carbon nanotube orientation and aggregation on vibrational behavior of functionally graded nanocomposite cylinders by a meshfree method, Acta Mechanica 224: 28172832.##[21] Pasternak P.L., 1954, On a New Method of Analysis of an Elastic Foundation by Means of Two Foundation Constants, Cosudarstrennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture, Moscow, USSR.##[22] Pourasghar A., Kamarian S., 2013, Threedimensional solution for the vibration analysis of functionally graded multiwalled carbon nanotubes/phenolic nanocomposite cylindrical panels on elastic foundation, Polymer Composites 34: 20402048.##[23] Zenkour AM., 2006, Generalized shear deformation theory for bending analysis of functionally graded plates, Applied Mathematical Modelling 30: 6784.##[24] Zenkour AM., 2009, The refined sinusoidal theory for FGM plates on elastic foundations, International Journal of Mechanical Sciences 51: 869880.##[25] Merdaci S., Tounsi A., A.Houari M.S., Mechab I., Hebali H., Benyoucef S., 2011, Two new refined shear displacement models for functionally graded sandwich plates, Archive of Applied Mechanics 81:15071522.##[26] Thai H.T., Choi D.H., 2011, A refined plate theory for functionally graded plates resting on elastic foundation, Composites Science and Technology 71: 18501858.##[27] Akavci SS., 2007, Buckling and free vibration analysis of symmetric and antisymmetric laminated composite plates on an elastic foundation, Journal of Reinforced Plastics and Composites 26: 19071919.##[28] Benyoucef S., Mechab I., Tounsi A., Fekrar A., Ait Atmane H., Adda Bedia EA., 2010, Bending of thick functionally graded plates resting on WinklerPasternak elastic foundations, Mechanics of Composite Materials 46: 425434.##[29] Ait Atmane H., Tounsi A., Mechab I., Adda Bedia EA., 2010, Free vibration analysis of functionally graded plates resting on WinklerPasternak elastic foundations using a new shear deformation theory, International Journal of Mechanics and Materials in Design 6: 113121.##[30] Shi D.L., Feng X.Q., Yonggang Y.H., Hwang K.C., Gao H., 2004, The effect of nanotube waviness and agglomeration on the elasticproperty of carbon nanotube reinforced composites, Journal of Engineering Materials and Technology 126: 250257.##[31] Matsunaga H., 2008, Free vibration and stability of functionally graded plates according to a 2D higherorder deformation theory, Composite Structures 82: 499512.##[32] Akhavan H., HosseiniHashemi Sh., Rokni Damavandi Taher H., Alibeigloo A., Vahabi Sh., 2009, Exact solutions for rectangular Mindlin plates under inplane loads resting on Pasternak elastic foundation. Part II: Frequency analysis, Computational Materials Science 44: 951961.##]
Surface Stress Effect on the Nonlocal Biaxial Buckling and Bending Analysis of Polymeric Piezoelectric Nanoplate Reinforced by CNT Using EshelbyMoriTanaka Approach
2
2
In this article, the nonlocal biaxial buckling load and bending analysis of polymeric piezoelectric nanoplate reinforced by carbon nanotube (CNT) considering the surface stress effect is presented. This plate is subjected to electromagnetomechanical loadings. EshelbyMoriTanaka approach is used for defining the piezoelectric nanoplate material properties. Navier’s type solution is employed to obtain the critical buckling load of polymeric piezoelectric nanoplate for classical plate theory (CPT) and first order shear deformation theory (FSDT). The influences of various parameters on the biaxial nonlocal critical buckling load with respect to the local critical buckling load ratio () of nanoplate are examined. Surface stress effects on the surface biaxial critical buckling load to the nonsurface biaxial critical buckling load ratio () can not be neglected. Moreover, the effect of residual surface stress constant on is higher than the other surface stress parameters on it. increases by applying the external voltage and magnetic fields. The nonlocal deflection to local deflection of piezoelectric nanocomposite plate ratio () decreases with an increase in the nonlocal parameter for both theories. And for FSDT, decreases with an increase in residual stress constant and vice versa for CPT.
1

173
190


M
Mohammadimehr
Department of Solid Mechanics ,Faculty of Mechanical Engineering, University of Kashan
Department of Solid Mechanics ,Faculty of
Iran
mmohammadimehr@kashanu.ac.ir


B
Rousta Navi
Department of Solid Mechanics ,Faculty of Mechanical Engineering, University of Kashan
Department of Solid Mechanics ,Faculty of
Iran


A
Ghorbanpour Arani
Institute of Nanoscience & Nanotechnology, University of Kashan
Institute of Nanoscience & Nanotechnology,
Iran
aghorban@kashanu.ac.ir
Polymeric piezoelectric nanoplate
Buckling
Bending
Surface stress effect
EshelbyMoriTanaka approach
SWCNT
[[1] Schmidt D., Shah D., Giannelis EP., 2002, New advances in polymer/layered silicate nanocomposites, Current Opinion in Solid State and Material Science 6(3): 205212.##[2] Thostenson E., Li C., Chou T., 2005, Review nanocomposites in context, Journal Composite Science Technology 65:491516.##[3] Ghorbanpour Arani A., Hashemian M., Loghman A., Mohammadimehr M., 2011, Study of dynamic stability of the doublewalled carbon nanotube under axial loading embedded in an elastic medium by the energy method, Journal of applied mechanics and technical physics 52 (5): 815824.##[4] Mohammadimehr M., Rahmati A. H., 2013, Small scale effect on electrothermomechanical vibration analysis of singlewalled boron nitride nanorods under electric excitation, Turkish Journal of Engineering & Environmental Sciences 37: 115.##[5] Ghorbanpour Arani A., Rahnama Mobarakeh M., Shams Sh., Mohammadimehr M., 2012, The effect of CNT volume fraction on the magnetothermoelectromechanical behavior of smart nanocomposite cylinder, Journal of Mechanical Science and Technology 26 (8): 25652572.##[6] Jaffe B., Cook W.R., Jaffe H., 1971, Piezoelectric Ceramics, New York, Academic.##[7] Xu S., Yeh Y.W., Poirier G., McAlpine M.C., Register R.A., Yao N., 2013, Flexible piezoelectric PMNPT nanowirebased na nocomposite and device, Nano Letters 13: 23932398.##[8] Samaei A.T., Abbasion S., Mirsayar M.M., 2011, Buckling analysis of a singlelayer graphene sheet embedded in an elastic medium based on nonlocal Mindlin plate theory, Mechanical Resereach Communication 38: 481485.##[9] Farajpour A., Shahidi A.R., Mohammadi M., Mahzoon M., 2013, Buckling of orthotropic micro/nanoscale plates under linearly varying inplane load via nonlocal continuum mechanics, Composite Structure 94: 16051615.##[10] Aksencer T., Aydogdu M., 2011, Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory, Physica E 43: 954959.##[11] Narendar S., 2011, Buckling analysis of micro/nanoscale plates based on twovariable refined plate theory incorporating nonlocal scale effects, Composite Structure 93: 30933103.##[12] Analooei H.R., Azhari M., Heidarpour A., 2013, Elastic buckling and vibration analyses of orthotropic nanoplates using nonlocal continuum mechanics and spline finite strip method, Appllied Mathematical Modeling 37: 67036717.##[13] Murmu T., Sienz J., Adhikari S., Arnold C., 2013, Nonlocal buckling of doublenanoplatesystems under biaxial compression, Composite Part B 44: 8494.##[14] Ansari R., Sahmani S., 2013, Prediction of biaxial buckling behavior of singlelayered graphene sheets based on nonlocal plate models and molecular dynamics simulations, Appllied Mathematical Modeling 37: 73387351.##[15] 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.##[16] Murmu T., Pradhan S.C., 2009, Buckling of biaxially compressed orthotropic plates at small scales, Mechanical Research Communication 36: 933938.##[17] Farajpour A., Danesh M., Mohammadi M., 2011, Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics, Physica E 44: 719727.##[18] Gurtin M.E., Murdoch A.I., 1978, Surface stress in solids, International Journal of Solids Structure 14: 431440.##[19] Tian L., Rajapakse R.K.N.D., 2007, Finite element modelling of nanoscale inhomogeneities in an elastic matrix, Computer Material Science 41: 4453.##[20] Wang G.F., Feng X.Q., 2009, Timoshenko beam model for buckling and vibration of nanowires with surface effects, Physics D 42: 155411.##[21] Wang K.F., Wang B.L., 2013, Effect of surface energy on the nonlinear postbuckling behavior of nanoplates, International Journal of Nonlinear Mechanics 55: 1924.##[22] Alzahrani E.O., Zenkour A.M., Sobhy M., 2013, Small scale effect on hygrothermomechanical bending of nanoplates embedded in an elastic medium, Composite Structure 105: 163172.##[23] Alibeigloo A., 2013, Static analysis of functionally graded carbon nanotubereinforced composite plate embedded in piezoelectric layers by using theory of elasticity, Composite Structure 95: 612622.##[24] Zhu P., Lei Z.X., Liew K.M., 2012, Static and free vibration analyses of carbon nanotubereinforced composite plates using finite element method with first order shear deformation plate theory, Composite Structure 94: 14501460.##[25] Lei Z.X., Liew K.M., Yu J.L., 2013, Buckling analysis of functionally graded carbon nanotubereinforced composite plates using the elementfree kpRitz method, Composite Structure 98: 160168.##[26] Jafari Mehrabadi S., Sobhani Aragh B., Khoshkhahesh V., Taherpour A., 2012, Mechanical buckling of rectangular nanocomposite plate reinforced by aligned and straight singlewalled carbon nanotubes, Composite Part B 43: 20312040.##[27] Shi D.L., Feng X.Q., huang Y.Y., Hwang K.C., Gao H., 2004, The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotubereinforced composites, Journal of Engineering Material Technology 126: 250257.##[28] Rahmati A.H., Mohammadimehr M., 2014, Vibration analysis of nonuniform and nonhomogeneous boron nitride nanorods embedded in an elastic medium under combined loadings using DQM, Physica B: Condensed Matter 440: 8898.##[29] Mohammadimehr M., Saidi A. R., Ghorbanpour Arani A., Arefmanesh A., Han Q., 2011, Buckling analysis of doublewalled carbon nanotubes embedded in an elastic medium under axial compression using nonlocal Timoshenko beam theory, Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science 225: 498506.##[30] Ansari R., Sahmani S., 2011, Surface stress effects on the free vibration behavior of nanoplates, International Journal of Engineering Science 49: 12041215.##[31] Wang L., 2012, Surface effect on buckling configuration of nanobeams containing internal flowing fluid: A nonlinear analysis, Physica E 44: 808812.##[32] Kraus J., 1984, Electromagnetics, USA, McGrawHill Inc.##[33] Ghorbanpour Arani A., Amir S., Shajari A.R., Mozdianfard M.R., Khoddami Maraghi Z., Mohammadimehr M., 2012, Electrothermal nonlocal vibration analysis of embedded DWBNNTs, Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science 226: 14101422.##[34] Shen H.S., Zhu Z.H., 2012, Postbuckling of sandwich plates with nanotubereinforced composite face sheets resting on elastic foundations, European Journal of Mechanical A/Solids 35: 1021.##]
Upper Bound Analysis of Tube Extrusion Process Through Rotating Conical Dies with Large Mandrel Radius
2
2
In this paper, an upper bound approach is used to analyze the tube extrusion process through rotating conical dies with large mandrel radius. The material under deformation in the die and inside the container is divided to four deformation zones. A velocity field for each deformation zone is developed to evaluate the internal powers and the powers dissipated on all frictional and velocity discontinuity surfaces. By minimization of the total power with respect to the slippage parameter between tube and the die and equating it with the required external power, the extrusion pressure is determined. The corresponding results for rotating conical dies are also determined by using the finite element code, ABAQUS. The analytical results show a good coincidence with the results by the finite element method with a slight overestimation. Finally, the effects of various process parameters such as mandrel radius, friction factor, etc., upon the relative extrusion pressure are studied.
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191
203


H
Haghighat
Mechanical Engineering Department, Razi University, Kermanshah
Mechanical Engineering Department, Razi University
Iran
hhaghighat@razi.ac.ir


M.M
Mahdavi
Mechanical Engineering Department, Razi University, Kermanshah
Mechanical Engineering Department, Razi University
Iran
Tube extrusion
Rotating conical die
Upper bound method
[[1] Ma X., Barnett M., 2005, An upper bound analysis of forward extrusion through rotating dies, In Proceedings of the 8th ESAFORM Conference on Material Forming, Bucharest, Romania.##[2] Bochniak W., Korbel A., 1999, Extrusion of CuZn39Pb2 alloy by the KOBO method, Engineering Transactions 47: 351367.##[3] Bochniak W., Korbel A., 2000, Plastic flow of aluminum extruded, under complex conditions, Matererials Science and Technology 16: 664674.##[4] Bochniak W., Korbel A., 2003, KOBOtype forming: forging of metals under complex conditions of the process, Journal of Materials Processing Technology 134: 120134.##[5] Kim Y.H., Park J.H., 2003, Upper bound analysis of torsional backward extrusion process, Journal of Materials Processing Technology 143144: 735740.##[6] Ma X., Barnett M., Kim Y. H., 2004, Forward extrusion through steadily rotating conical dies, Part I: experiments, International Journal of Mechanical Sciences 46: 449 464.##[7] Ma X., Barnett M., Kim Y. H., 2004, Forward extrusion through steadily rotating conical dies, Part II: theoretical analysis, International Journal of Mechanical Sciences 46: 465489.##[8] Maciejewski J., Mroz Z., 2008, An upperbound analysis of axisymmetric extrusion assisted by cyclic torsion, Journal of Materials Processing Technology 206: 333344.##]
Application of Case I and Case II of Hill’s 1979 Yield Criterion to Predict FLD
2
2
Forming limit diagrams (FLDs) are calculated based on both the Marciniak and Kuczynski (MK) model and the analysis proposed by Jones and Gillis (JG). JG analysis consisted of plastic deformation approximation by three deformation phases. These phases consisted of homogeneous deformation up to the maximum load (Phase I), deformation localization under constant load (phase II) and local necking with a precipitous drop in load (phase III). In the present study, case I and case II of Hill’s nonquadratic yield function were used for the first time. It is assumed that sheets obey the powerlaw flow rule and inplane isotropy is satisfied. Calculated FLDs from this analysis are compared with the experimental data of aluminum alloys 3003O, 2036T4 and AK steel reported by other references. Calculated FLDs showed that limit strain predictions based on case I and case II of the Hill’s nonquadratic yield function are fairly well correlated to experiments when JG model is used.
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204
222


M
AghaieKhafri
Faculty of Mechanical Engineering, K.N. Toosi University of Technology
Faculty of Mechanical Engineering, K.N. Toosi
Iran
maghaei@kntu.ac.ir


M
TorabiNoori
Faculty of Mechanical Engineering, K.N. Toosi University of Technology
Faculty of Mechanical Engineering, K.N. Toosi
Iran
Yield function
Forming limit diagrams
Localization
[[1] Keeler S.P., 1969, Circular grid system: a valuable aid for evaluation sheet forming, Sheet Metal Industrial 45: 633640.##[2] Goodwin G.M., 1969, Application of strain analysis to sheet metal forming problems, Metall Ital 60: 767771.##[3] Liu J., Liu W., Xue W., 2013, Forming limit diagram prediction of 5052/polyethylene/AA5052 sandwich sheets, Materials and Design 46: 112120.##[4] AghaieKhafri M., Mahmudi R., 2005, The effect of preheating on the formability of an Al–Fe–Si alloy sheet, Journal of Materials Processing Technology 169: 3843.##[5] Friedman P.A., Pan J., 2000, Effects of plastic anisotropy and yield criteria on prediction of forming limit curves, International Journal of Mechanical Sciences 42: 2948.##[6] Zhang L., Wang J., 2012, Modeling the localized necking in anisotropic sheet metals, International Journal of Plasticity 39: 103118.##[7] Velmanirajan K., Syed Abu Thaheer A., Narayanasamy R., Ahamed Basha C., 2012, Numerical modelling of aluminium sheets formability using response surface methodology, Materials and Design 41: 239254.##[8] Hart E.W., 1967, Theory of the tensile test, Acta Metallurgica 15: 351355.##[9] Hill R., 1952, On discontinuous plastic states with special reference to localized necking in thin sheets, Journal of the Mechanics and Physics of Solids 1: 1930.##[10] Gillis P.P., Jones S.E., 1979, Tensile deformation of a flat sheet, International Journal of Mechanical Sciences 21: 109117.##[11] Marciniak Z., Kuczynski K., 1967, Limit strains in the processes of stretchforming sheet metal, International Journal of Mechanical Sciences 9: 609620.##[12] Mohebbi M.S., Akbarzadeh A., 2012, Prediction of formability of tailor welded blanks by modification of MK model, International Journal of Mechanical Sciences 61: 4451.##[13] Jones S.E., Gillis P.P., 1984, An analysis of biaxial stretching of a ﬂat sheet, Metallurgical Transactions A 15: 133138.##[14] Choi W., Gillis P.P., Jones S.E ., 1989, Calculation of the forming limit diagram, Metallurgical Transactions A 20:19751987.##[15] Choi W., Gillis P.P., Jones S.E., 1989, Forming Limit Diagrams: Concepts, Methods and Applications, edited by Wagoner R.H., Chan K.S., Keeler S.P., Published, TMS Warendale.##[16] Jones S.E., Gillis P.P., 1984, Analysis of biaxial stretching of a flat sheet, Metallurgical Transactions A 15: 133138.##[17] Jones S.E., Gillis P.P., 1984, Generalized quadratic flow law for sheet metals, Metallurgical Transactions A 15: 129132.##[18] Pishbin H., Gillis P.P., 1992, Forming limit diagrams calculated using Hill’s nonquadratic yield criterion, Metallurgical Transactions A 23: 28172831.##[19] AghaieKhafri M., Mahmudi R., 2004, Predicting of plastic instability and forming limit diagrams, International Journal of Mechanical Sciences 46: 12891306.##[20] AghaieKhafri M., Mahmudi R., Pishbin H., 2002, Role of yield criteria and hardening laws in the prediction of forming limit diagrams, Metallurgical Transactions A 33: 13631371.##[21] Noori H., Mahmudi R., 2007, Prediction of forming limit diagrams in sheet metals using different yield criteria, Metallurgical Transactions A 38: 20402052.##[22] RezaeeBazzaz A., Noori H., Mahmudi R., 2011, Calculation of forming limit diagrams using Hill’s 1993 yield criterion, International Journal of Mechanical Sciences 53: 262270.##[23] Chung K., Kim H., Lee C., 2014, Forming limit criterion for ductile anisotropic sheets as a material property and its deformation path insensitivity. Part I: Deformation path insensitive formula based on theoretical models, International Journal of Plasticity 58: 334.##[24] Avila A.F., Vieira E.L.S., 2003, Proposing a better forming limit diagram prediction: a comparative study, Journal of Materials Processing Technology 141: 101108.##[25] Chiba R., Takeuchi H., Kuroda M., Kuwabara T., 2013, Theoretical and experimental study of forminglimit strain of halfhard AA1100 aluminium alloy, Computational Materials Science 77: 6171.##[26] Panich S., Barlat F., Uthaisangsuk V., Suranuntchai S., Jirathearanat S., 2013, Experimental and theoretical formability analysis using strain and stress based forming limit diagram for advanced high strength steels, Materials & Design 51 : 756766.##[27] Assempour A., Hashemi R., Abrinia K., Ganjiani M., Masoumi E., 2009, A methodology for prediction of forming limit stress diagrams considering the strain path effect, Computational Materials Science 45: 195204.##[28] Kuroda M., Tvergaard V., 2000, Forming limit diagrams for anisotropic metal sheets with different yield criteria, International Journal of Solids and Structures 37: 50375059.##[29] Hill R., 1979, Theoretical plasticity of textured aggregates, Mathematical Proceedings of the Cambridge Philosophical Society 75: 179191.##[30] Lian J., Zhou D., Baudelet B., 1989, Application of Hill’s new yield theory to sheet metal forming part I. Hill’s 1979 criterion and its application to predicting sheet forming limit, International Journal of Mechanical Sciences 31: 237247.##[31] Considére A., 1885, Annales des Ponts et Chaussées 9: 574775.##[32] Bridgeman P.W., 1952, Studies in Large Plastic Flow and Fracture, McGrawHill, New York.##[33] Ghosh A.K., 1977, The Influence of Strain Hardening and StrainRate Sensitivity on Sheet Metal Forming, Trans ASME: Journal of Engineering Materials and Technology 99: 264274.##[34] Hecker S.S., 1975, Formability of aluminum alloy sheets, Trans ASME: Journal of Engineering Materials and Technology 97: 6673.##[35] Hill R., 1993, A userfriendly theory of orthotropic plasticity in sheet metals, International Journal of Mechanical Sciences 35:1925.##]
Wave Propagation in FibreReinforced Transversely Isotropic Thermoelastic Media with Initial Stress at the Boundary Surface
2
2
The reflection and transmission of thermoelastic plane waves at an imperfect boundary of two dissimilar fibrereinforced transversely isotropic thermoelastic solid halfspaces under hydrostatic initial stress has been investigated. The appropriate boundary conditions are applied at the interface to obtain the reflection and transmission coefficients of various reflected and transmitted waves with incidence of quasilongitudinal (qP), quasithermal (qT) & quasi transverse (qSV) waves respectively at an imperfect boundary and deduced for normal stiffness, transverse stiffness, thermal contact conductance and welded boundaries.The reflection and transmission coefficients are functions of frequency, initial stress and angle of incidence. There amplitude ratios are computed numerically and depicted graphically for a specific model to show the effect of initial stress. Some special cases are also deduced from the present investigation.
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223
238


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


S.K
Garg
Department of Mathematics, Deen Bandhu Chotu Ram Uni. of Sc. & Tech., Sonipat, Haryana,India
Department of Mathematics, Deen Bandhu Chotu
Iran


S
Ahuja
University Institute of Engg. & Tech., Kurukshetra University, Kurukshetra, Haryana, India
University Institute of Engg. & Tech.,
Iran
sanjeev_ahuja81@hotmail.com
Fibrereinforced
Hydrostatic initial stress
Reflection
Transmission
Thermoelasticity
[[1] Spencer A.J.M., 1941, Deformation of FibreReinforced Materials, Clarendon Press, Oxford.##[2] Lord H.W., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15(5):299309.##[3] Green A.E., Lindsay K.A.,1971, Thermoelasticity, Journal of Elasticity 2(1):17.##[4] Dhaliwal R.S., Sherief H.H.,1980, Generalized thermoelasticity for anisotropic media, The Quarterly of Applied Mathematics 33(1):18.##[5] Erdem A.U., 1995, Heat Conduction in fiberreinforced rigid bodies, 10 Ulusal Ist Bilimi ve Tekmgi Kongrest, 68 Eylul, Ankara.##[6] Kumar R., Rani R., 2010, Study of wave motion in an anisotropic fibrereinforced thermoelastic solid, Journal of Solid Mechanics 2(1):91100.##[7] Deresiewicz H., 1960, Effect of boundaries on waves in a thermoelastic solid, Journal of the Mechanics and Physics of Solids 8(3):164172.##[8] Sinha A.N., Sinha S.B., 1974, Reflection of thermoelastic waves at a solid halfspace with thermal relaxation, Journal of Physics of the Earth 22(2):237244.##[9] Sinha S.B., Elsibai K.A.,1966, Reflection of thermoelastic waves at a solid halfspace with two relaxation times, Journal of Thermal Stresses 19(8):763777.##[10] Sinha S.B., Elsibai K.A., 1997, Reflection and transmission of thermoelastic waves at an interface of two semiinfinite media with two relaxation times, Journal of Thermal Stresses 20(2):129146.##[11] Singh B., 2002, Reflection of thermoviscoelastic waves from free surface in the presence of magnetic field, Proceedings of the National Academy of Sciences, India,72A II,109120.##[12] AbdAlla A.N., Yahia A.A., AboDabah S.M., 2003, On reflection of the generalized magnetothermoviscoelastic plane waves, Chaos, Solitons Fractals 16(2):211231.##[13] Singh B., 2006, Reflection of SV waves from the free surface of an elastic solid in generalized thermoelastic diffusion, Journal of Sound and Vibration 291(35):764778.##[14] Song Y.Q., Zhang Y.C., Xu H.Y., Lu B.H.,2006, Magnetothermoelastic wave propagation at the interface between two micropolar viscoelastic media, Applied Mathematics and Computation 176 (2):785802.##[15] Singh S., Khurana S., 2001, Reflection and transmission of P and SV waves at the interface between two monoclinic elastic halfspaces, Proceedings of the National Academy of Sciences, India ,71(A) IV.##[16] Kumar R., Singh M., 2008, Reflection/transmission of plane waves at an imperfectly bonded interface of two orthotropic generalized thermoelastic half space, Materials Science and Engineering 472(12):8396.##[17] Biot M.A., 1965, Mechanics of Incremental Deformations, John Wiley and Sons, New York.##[18] Chattopadhyay A., Bose S., Chakraborty M., 1982, Reflection of elastic waves under initial stress at a free surface, The Journal of the Acoustical Society of America 72(1):255263.##[19] Sidhu R.S., Singh S.J., 1983, Comments on “Reflection of elastic waves under initial stress at a free surface, The Journal of the Acoustical Society of America 74(5):16401642.##[20] Dey S., Roy N., Dutta A.,1985, Reflection and transmission of Pwaves under initial stresses at an interface, Indian Journal of Pure and Applied Mathematics 16:10511071.##[21] Selim M.M., 2008, Reflection of plane waves at free surface of an initially stressed dissipative medium, Proceedings of World Academy of Sciences, Engineering and Technology.##[22] Montanaro A., 1999, On singular surface in isotropic linear thermoelasticity with initial stress, The Journal of the Acoustical Society of America 106(31):15861588.##[23] Singh B., Kumar A., Singh J.,2006, Reflection of generalized thermoelastic waves from a solid halfspace under hydrostatic initial stress, Applied Mathematics and Computation 177(1):170177.##[24] Singh B.,2008, Effect of hydrostatic initial stresses on waves in a thermoelastic solid halfspace, Applied Mathematics and Computation 198(2):494505.##[25] Othman M.I.A., Song Y., 2007, Reflection of plane waves from an elastic solid halfspace under hydrostatic initial stress without energy dissipation, International Journal Solids and Structures 44 (17):56515664.##[26] AbdAlla A.El.N., Alsheikh F.A., 2009, The effect of the initial stresses on the reflection and transmission of plane quasivertical transverse waves in piezoelectric materials, World Academy of Science, Engineering and Technology 3.##[27] Chattopadhyay A., Venkateswarlu R.L.K., Chattopadhyay A., 2007, Reflection and transmission of quasi P and SV waves at the interface of fibrereinforced media, Advanced Studies in Theoretical Physics 1(2):5773.##[28] Abbas I.A., Othman M.I.A., 2012, Generalized thermoelastic interaction in a fibrereinforced anisotropic halfspace under hydrostatic initial stress, Journal of Vibration and Control 18(2):175182##[29] Singh S. S. and Zorammuana C., 2013, Incident longitudinal wave at a fibrereinforced thermoelastic halfspace, Journal of Vibration and Control 20(12):18951906.##]