2011
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Study on the PullIn Instability of Gold MicroSwitches Using Variable Length Scale Parameter
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2
In this paper, the size dependent behavior of the gold microswitches has been studied. This behavior becomes noticeable for a structure when the characteristic size such as thickness or diameter is close to its internal lengthscale parameter. The size dependent effect is insignificant for the high ratio of the characteristic size to the lengthscale parameter, which is the case of the silicon base microbeams. On the other hand, in some types of microbeams like gold base, the size dependent effect cannot be overlooked. In such cases, ignoring this behavior in modeling will lead to incorrect results. Some previous researchers have applied classic beam theory on their models and imposed a considerable hypothetical value of residual stress to match their theoretical results with the experimental ones. In this study, by obtaining the equilibrium positions or fixed points of the gold microbeam, a considerable difference between the obtained fixed points using classic beam theory and modified couple stress theory has been shown. In addition, it has been shown that the calculated pullin voltages using modified couple stress theory are much closer to the experimental results than those obtained by classic beam theory. Finally, it has been shown that considering a unique value of length scale parameter, especially for the smallest values of the beam thicknesses, may leads to inaccurate results and variable length scale parameter should be considered.
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114
123


M
Fathalilou
Department of Mechanical Engineering, Khoy Branch, Islamic Azad University
Department of Mechanical Engineering, Khoy
Iran
m.fathalilou@tabrizu.ac.ir


M
Sadeghi
Department of Mechanical Engineering, University of Tabriz
Department of Mechanical Engineering, University
Iran


G
Rezazadeh
Department of Mechanical Engineering, Khoy Branch, Islamic Azad University
Department of Mechanical Engineering, Khoy
Iran


M
Jalilpour
Department of Mechanical Engineering, Khoy Branch, Islamic Azad University
Department of Mechanical Engineering, Khoy
Iran


A
Naghilou
Department of Mechanical Engineering, Khoy Branch, Islamic Azad University
Department of Mechanical Engineering, Khoy
Iran


S
Ahouighazvin
Department of Mechanical Engineering, Khoy Branch, Islamic Azad University
Department of Mechanical Engineering, Khoy
Iran
MEMS
Gold microswitch
Couple stress theory
Lengthscale parameter
Pullin voltage
[[1] Madou M., 2002, Fundamentals of Microfabrication, CRC Press, NewYork, USA, p. 497.##[2] Holliday R., Goodman P., 2002, Going for the gold, IEE Review, 48: 1519.##[3] Knarr R.F., Quon R.A., 1998, Direct force measurements at the smooth gold/mica interface, Langmuir 14(22): 64146418.##[4] Caol Y., Nankivil D.D., Allameh S., Soboyejo W.O., 2007, Mechanical properties of au films on silicon substrates, Materials and Manufacturing Processes 22: 187194.##[5] Younis M.I., AbdelRahman E.M., Nayfeh A., 2003, A reducedorder model for electrically actuated microbeambased MEMS, Journal of Microelectromechanical Systems 12(5): 672680.##[6] Sadeghian H., Rezazadeh G., Osterberg P.M., 2007, Application of the generalized differential quadrature method to the study of pullin phenomena of MEMS switches, Journal of Microelectromechanical Systems 16 (6): 13341340.##[7] Osterberg P.M., Senturia S.D., 1997, MTEST: a test chip for MEMS material property measurement using electrostatically actuated test structures, Journal of Microelectromechanical Systems 6: 107118.##[8] Rezazadeh G., Fathalilou M., Shabani R., 2009, Static and dynamic stabilities of a microbeam actuated by a piezoelectric voltage, Journal of Microsystem Technologies 15:17851791.##[9] PapargyriBeskou S., Tsepoura K.G., Polyzos D., Beskos D.E., 2003, Bending and stability analysis of gradient elastic beams, International Journal of solids and structures 40: 385400.##[10] Lazopoulos K.A., Lazopoulos A.K., 2010, Bending and buckling of thin strain gradient elastic beams, European Journal of mechanics A/solids 29: 837843.##[11] Asghari M., Ahmadian M.T., Kahrobaiyan M.H., Rahaeifard M., 2010, On the sizedependent behavior of functionally graded microbeams, Materials and Design 31: 23242329.##[12] Park S.K., Gao X.L., 2006, BernoulliEuler beam model based on a modified couple stress theory, Journal of Micromechanics and Microengineering 16: 23552359.##[13] Fu Y., Zhang J., 2011, Sizedependent pullin phenomena in electrically actuated nanobeams incorporating surface energies, Applied Mathematical Modelling 35: 941951.##[14] Shengli K., Shenjie Z., Zhifeng N., Kai W., 2009, Static and dynamic analysis of micro beams based on strain gradient elasticity theory, Journal of Engineering Society 47: 487498.##[15] Lam D.C.C., Chong A.C.M., 1999, Indentation model and strain gradient plasticity law for glassy polymers, Journal of Material Research 14: 37843788.##[16] Park S.K., Gao X.L., 2006, BernoulliEuler beam model based on a modified couple stress theory, Journal of Micromechanics and Microengineering 16(11): 23552359.##[17] Shengli K., Shenjie Z., Nie Z., Wang K., 2008, The sizedependent natural frequency of Bernoulli–Euler microbeams, Journal of Engineering Society 46: 427437.##[18] 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 Structure 39: 27312743.##[19] Park S.K., Gao X.L., 2006, BernoulliEuler beam model based on a modified couple stress theory, Journal of Micromechanics and Microengineering 16(11): 235523559.##[20] Zong Z., Soboyejo W.O., 2005, Indentation size effects in face centered cubic single crystal thin films, Materials Science and Engineering A 404(1–2): 281290.##[21] Zhang Y., Zhao Y., 2010, Numerical and analytical study on the pullin instability of micro structure under electrostatic loading, Journal of Sensors Actuators A: Physics 127: 366367.##[22] Samaali H., Najar F., Choura S., Nayfeh A., Masmoudi M., 2011, A double microbeam MEMS ohmic switch for RFapplications with low actuation voltage, Nonlinear Dynamics 63: 719734.##[23] Nayfeh A., Younis M.I., 2005, Dynamics of MEMS resonators under superharmonic and subharmonic excitations, Journal of Micromechanics and Microengineering 15: 18401847.##[24] Younis M.I., Miles R., Jordy D.L., 2006, Investigation of the response of microstructures under the combined effect of mechanical shock and electrostatic forces, Journal of Micromechanics and Microengineering 16: 24632474.##[25] Ballestra A., Brusa E., Pasquale G., Munteanu G., Soma A., 2010, FEM modelling and experimental characterization of microbeams in presence of residual stress, Analog Integrated Circuites Signals Process 63: 477488.##[26] Vummidia K., Khater M., AbdelRahman E., Nayfeh A., Raman S., 2009, Dynamic pullin of shunt capacitive MEMS switches, Procedia Chemistry 1: 622625.##[27] Pacheco S.P., Katehi L.P.B., Nguyen C.T.C, 2000, Design of low actuation voltage RF MEMS switch, IEEE MTTS Digest 1: 165168.##[28] Son S., Kim J., Kwon D., 2005, Tensile properties and fatigue crack growth in LIGA nickel MEMS structures, Materials Science and Engineering A 406: 274278.##[29] Nix W.D., Gao H., 1998, Indentation size effects in crystalline materials: a low for strain gradient plasticity, Journal of Mechanical and Physical Solids 46: 411425.##[30] Zong Z., Soboyejo W., 2005, Indentation size effects in face centered cubic single crystal thin films, Materials Science and Engineering A 404: 281290.##[31] Rezazadeh G., Fathalilou M., Shabani R., Tarverdilou S., Talebian S., 2009, Dynamic characteristics and forced response of an electrostatically actuated microbeam subjected to fluid loading, Journal of Microsystem Technologies 15: 13551363.##[32] Hung E.S, Senturia S.D., 1999, Generating efficient dynamical models for Microelectromechanical systems from a few finiteelement simulation runs, Journal of Microelectromechanical Systems 8: 280289.## ##]
Performance Analysis of Different Modified MR Engines Mounts
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2
Increasing current vehicle development trends for small, light, front wheel drive vehicles with low idle speeds have been forced automotive industries to use hydraulic engine mounts for further improvement in vibration, noise and harshness (NVH) performance of the vehicles. However, with the development of modern vehicle designs such as hybrid vehicles and variable engine management systems which have different operational modes, more sophisticated engine mounting systems are required to effectively response to each operational mode. Magnetorheological (MR) engine mount is a semiactive hydraulic engine mount, containing MR fluid, which can alter its dynamic behavior as a result of applying magnetic field. In this paper, design concept of two MR mounts is presented and their dynamic behavior is simulated. It is shown that the simulation methods used in this paper for simulating the dynamic behaviors of the MR mounts are effective with which the dynamic characteristic analysis and design optimization of MR mounts can be performed before its prototype development. Because of increasing demands for semiactive MR mounts in automotive industries, this can ensure their low cost and high quality for development.
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124
131


T
Feyzi
Department of Mechanical Engineering, Isfahan University of Technology
Department of Mechanical Engineering, Isfahan
Iran


R
Tikani
Department of Mechanical Engineering, Isfahan University of Technology
Department of Mechanical Engineering, Isfahan
Iran


M
Esfahanian
Department of Mechanical Engineering, Isfahan University of Technology
Department of Mechanical Engineering, Isfahan
Iran
mesf1964@cc.iut.ac.ir


S
Ziaei Rad
Department of Mechanical Engineering, Isfahan University of Technology
Department of Mechanical Engineering, Isfahan
Iran
Hydraulic engine
Mr fluid
Dynamic stiffness
Vibration isolation
[[1] Yunhe Y., Nagi G.N., Rao V.D., 2001, A literature review of automotive vehicle engine mounting systems, Mechanism and Machine Theory 36: 123142.##[2] Christopherson J., Jazar G.N., 2006, Dynamic behavior comparison of passive hydraulic engine mounts. Part 1: Mathematical analysis, Journal of Sound and Vibration 290: 10401070.##[3] Ushijima T., Takano K., Kojima H., 1988, High performance hydraulic mounts for improving vehicle noise and vibration, SAE Paper no 880073.##[4] Nguyen M., 2009, A Novel semiactive magnetorheological mount for vibration isolation, Mechanical Engineering Thesis, The University of Toledo.##[5] Vahdati N., Ahmadian M., 2003, Single pumper semiactive fluid mount, ASME International Mechanical Engineering Congress & Exposition (IMECE2003), November 1621, Washington, D.C.##[6] Foumani M.S., Khajepour A., Durali M., 2002, Application of SMA to a new adaptive hydraulic mount, in: Proceedings of the SAE International Body Engineering Conference & Exhibition and Automotive & Transportation Technology Congress.##[7] Carlson J.D., Jolly R.M., 2001, MR fluid, foam and elastomer devices, Mechatronics 10: 555569.##[8] Hong S.R., Choi S.B., Jung W.J., Ham I.B., Kim D.K., 2001, Vibration control of an ER mount subjected to high static loads, Journal of Sound and Vibration 242(2): 740748.##[9] Baudendistel T.A., Tewani S.G., Shores J.M., Long M.W., Longhouse R.E., Namuduri C.S., Alexandridis A.A., 2003, Hydraulic mount with magnetorheological fluid, US Patent No. 6,622,995 B2.##[10] Stelzer G.J., Schulz M.J., Kim J., Allemang R.J., 2003, A magnetorheological semiactive isolator to reduce noise and vibration transmissibility in automobiles, Journal of Intelligent Material Systems and Structures 14: 743765.##[11] Choi S.B., Song H.J., Lee H.H., Lim S.C., Kim J.H., Choi H.J., 2003, Vibration control of a passenger vehicle featuring magnetorheological engine mounts, International Journal of Vehicle Design 33: 216.##[12] Barber D. E., Carlson J. D., 2009, Performance characteristics of prototype MR engine mounts containing Lord Glycol MR fluids, Journal of Physics: Conference Series 149: 012035##[13] Srinivasan A.V., McFarland M.D., 2001, Smart Structures: Analysis and Design, Cambridge University Press, New York.##[14] Lord Corporation, Cary, NC, MRF 132LD, 1999.##[15] Choi Y.T., Wereley N. M., 2002, Comparative Analysis of the Time Response of Electrorheological and Magnetorheological Dampers Using Nondimensional Parameters, Journal of Intelligent Material Systems and Structures 13: 443451.##[16] Singh R., Kim G., Ravindra P.V., 1992, Linear analysis of automotive hydraulicmechanical mounts emphasis on decoupler characteristics, Journal of Sound and Vibration 158: 219243.## ##]
Thermal Stress Analysis of a Composite Cylinder Reinforced with FG SWCNTs
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2
Thermal stress analysis of a thickwalled cylinder reinforced with functionally graded (FG) singlewalled carbon nanotubes (SWCNTs) is considered in radial direction. Thickwalled cylinder is subjected to a thermal field. Two layouts of variations in the volume fraction of SWCNTs were considered in the composite cylinder along the radius from inner to outer surface, where their names are incrementally decreasing (Inc Dec) and incrementally increasing (Inc Inc). Micromechanical models based on the MoriTanaka is used to define effective macroscopic properties of the nano composite shell. Using equations of motion, stressstrain and their corresponding constitutive correlations of a polystyrene vessel, a second order ordinary differential equation was proposed based on the radial displacement. The higher order governing equation was solved in order to obtain the distribution of displacement and thermal stresses in radial, circumferential and axial directions. The results indicate that FG distributions of SWCNTs have significant effect on thermal stresses and displacements in axial, radial and circumferential directions, so that in Inc Inc layout, the radial and circumferential stresses are lower than of other FG structures.
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132
141


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


S
Amir
Department of Mechanical Engineering, Faculty of Engineering, University of Kashan
Department of Mechanical Engineering, Faculty
Iran


V
Sadooghi
Department of Mechanical Engineering, Faculty of Engineering, University of Kashan
Department of Mechanical Engineering, Faculty
Iran


M
Mohammadimehr
Department of Mechanical Engineering, Faculty of Engineering, University of Kashan
Department of Mechanical Engineering, Faculty
Iran
Thermal Stress analysis
Nano Composite
MoriTanaka
FG SWCNTs reinforcement
Thickwalled cylinder
[[1] Saito R., Dresselhaus G., Dresselhaus M.S., 1998, Physical Properties of Carbon Nanotubes, Imperial College Press, London.##[2] Qian D., Wagner G.J., Liu W.K., Yu M.F., Ruoff R.S., 2002, Mechanics of Carbon Nanotubes, Applied Mechanics Reviews 55(6): 495533.##[3] Ajayan P.M., Stephan O., Colliex C., Trauth D., 1994, Aligned carbon nanotube arrays formed by cutting a polymer resin—nanotube composite, Science 256: 12121214.##[4] Lourie O., Cox D.M., Wagner H.D., 1998, Buckling and Collapse of Embedded Carbon Nanotube, Physical Review Letters 81(8): 16381641.##[5] Haggenmueller R., Gommans H.H., Rinzler A.G., Fischer J.E., Winey K.I., 2000, Aligned SingleWall Carbon Nanotubes In Composites by Melt Processing Methods, Chemical Physics Letters 330: 219225.##[6] Fidelus J.D., Wiesel E., Gojny F.H., Schulte K.,Wagner H.D., 2005, Thermomechanical properties of randomly oriented Carbon/epoxy nanocomposites, Composites Part A: Applied Science and Manufacturing 36: 15551361.##[7] Bonnet P., Sireude D., Garnier B., Chauvet O., 2007, Thermal properties and percolation in carbon nanotube–polymer composites, Journal of Applied Physics 91: 201910.##[8] Qian D., Dickey E.C., Andrews R., Rantell T., 2000, Load Transferand and Deformation Mechanisms in Carbon NanotubePolystyrene Composites, Applied Physics Letters 76: 28682870.##[9] Odegard G.M., Gates T.S., Wise K.E., Park C., Siochi E.J., 2002, Constitutive Modeling of NanotubeReinforced Polymer Composites, Composites Science and Technology 63(11): 16711687.##[10] Wuite J., Adali S., 2005, Deflection and stress behaviour of nanocomposite reinforced beams using a multiscale analysis, Composite Structures 71: 388396.##[11] Vodenitcharova T., Zhang L.C., 2006, Bending and local buckling of a nanocomposite beam reinforced by a singlewalled carbon nanotube, International Journal of Solids and Structures 43: 30063024.##[12] Han Y., Elliott J., 2007, Molecular dynamics simulations of the elastic properties of polymer/ carbon nanotube composites, Computation Materials Science 39: 315323.##[13] Zhu R., Pan E., Roy A.K., 2007, Molecular dynamics study of the stressstrain behavior of carbonnanotube reinforced Epon 862 composites, Materials Science and Engineering A 447: 5157.##[14] Shen H.S., 2009, Nonlinear bending of functionally graded carbon nanotubereinforced composite plates in thermal environments, Composite Structures 91: 919.##[15] Ke L.L., Yang J., Kitipornchai S., 2010, Nonlinear free vibration of functionally graded carbon nanotubereinforced composite beams, Composite Structures 92(3): 676683.##[16] Wang X., 1995, Thermal shock in a hollow cylinder caused by rapid arbitrary heating, Journal of Sound and Vibration 183: 899906.##[17] Cho H., Kardomateas G.A., Valle C.S.,1998, Elastodynamic solution for the thermal shock stresses in an orthotropic thick cylindrical shell, Journal of Applied Mechanics 65: 184192.##[18] Ding H.J., Wang H.M., Chen W.Q., 2001, A theoretical solution of cylindrically isotropic cylindrical tube for axisymmetric plane strain dynamic thermoelastic problem, Acta Mechanica Solida Sinica 14: 357363.##[19] Pelletier J.L., Vel S.S., 2006, An exact solution for the steadystate thermoelastic response of functionally graded orthotropic cylindrical shells, International Journal of Solidsand Structures 43: 11311158.##[20] Horgan C.O., Chan A.M., 1999, the pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials,Journal of Elasticity55: 4359.##[21] Tarn J.Q., 2001, Exact solutions for functionally graded anisotropic cylinders subjected to thermal and mechanical loads. International Journal of Solids and Structures 38: 81898206.##[22] AbdAlla A.M., Farhan A.M., 2008, Effect of the nonhomogenity on the composite infinite cylinder of orthotropic material, Physics Letters A 372: 756260.##[23] 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, JournalofEngineeringMaterials andTechnology 126: 250257.##[24] Hill R., 1965, A Self Consistent Mechanics of Composite Materials, Journalof the Mechanics andPhysicsofSolids13: 213222.##[25] Popov V.N., Van Doren V.E., Balkanski M., 2000, Elastic Properties of Crystals of SingleWalled Carbon Nanotubes, Solid State Communications 114: 395–399.##[26] Mark J.E., 1999, Polymer Data Handbook, Oxford University Press, New York. Oxford.##[27] Hetnarski R.B., Eslami M.R., 2008, Thermal Stresses Advanced Theory and Application, Springer.## ##]
TimeDependent ThermoElectroMechanical Creep Behavior of Radially Polarized FGPM Rotating Cylinder
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2
Timedependent creep analysis is crucial for the performance and reliability of piezoactuators used for highprecision positioning and loadbearing applications. In this study history of stresses, deformations and electric potential of hollow rotating cylinders made of functionally graded piezoelectric material (FGPM), e.g., PZT_7A have been investigated using Mendelson’s method of successive elastic solution. Loading is composed of an internal pressure, a distributed temperature field, an inertia body force and a constant electric potential difference between the inner and outer surfaces of the FGPM cylinder. All the mechanical, thermal and piezoelectric properties are assumed to be the same power functions of the radial graded direction. Using equations of equilibrium, strain displacement, stressstrain relation and the electric potential equation a differential equation containing creep strains for displacement is derived. A semianalytical method in conjunction with the method of successive approximation has therefore been proposed for this analysis. It has been found that a major redistribution for electric potential take place throughout the thickness. Electric potentials are increasing with time in the same direction as the compressive radial stress histories. That is the electric potential histories are induced by the compressive radial stress histories during creep deformation of the FGPM cylinder.
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142
157


A
Ghorbanpour Arani
Department of Mechanical Engineering, Faculty of Engineering, University of Kashan
Thermoelasticity Center of Excellence, Department of Mechanical Engineering, Amirkabir University of Technology
Department of Mechanical Engineering, Faculty
Iran
aghorban@kashanu.ac.ir


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


A.A
Mosallaie Barzoki
Department of Mechanical Engineering, Faculty of Engineering, University of Kashan
Department of Mechanical Engineering, Faculty
Iran


A
Loghman
Department of Mechanical Engineering, Faculty of Engineering, University of Kashan
Department of Mechanical Engineering, Faculty
Iran
aloghman@kashanu.ac.ir
Timedependent
Thermoelectromechanical creep
Stress histories
Electric potential histories
FGPM Rotating cylinder
[[1] Jabbari M., Sohrabpour 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.##[2] Liew K.M., Kitipornchai S., Zhang X.Z., Lim C.W., 2003, Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders, International Journal of Solids and Structures 40: 23552380.##[3] You L.H., Zhang J.J., You X.Y., 2005, Elastic analysis of internally pressurized thickwalled spherical pressure vessels of functionally graded materials, International Journal of Pressure Vessel and Piping 82: 347354.##[4] 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.##[5] Bahtui A., Eslami M.R., 2007, Coupled thermoelasticity of functionally graded cylindrical shells, Mechanics Research Communications 34: 118.##[6] 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 Modeling 35: 27712789.##[7] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A.A., Loghman A., 2011, Electrothermomechanical behaviors of FGPM spheres using analytical method and ANSYS software, Applied Mathematical Modeling 36: 139157.##[8] Pai D.H., 1967, steadystate creep analysis of thickwalled orthotropic cylinders, International Journal of Mechanics Science 9: 335482.##[9] Sim R.G., Penny R.K., 1971, Plane strain creep behaviour of thickwalled cylinders, International Journal of Mechanics Science 13: 9871009.##[10] Bhatnagar N.S., Arya V.K., 1974, Large strain creep analysis of thickwalled cylinders, International Journal of NonLinear Mechanics 9: 12740.##[11] Simonian A.M., 1979, Calculation of thermal stresses in thickwalled cylinders taking account of nonlinear creep, International Journal of Engineering Science 17: 513522.##[12] Yang Y.Y., 2000, Timedependent stress analysis in functionally graded materials, International Journal of Solids and Structures 37: 75937608.##[13] Altenbach H., Gorash Y., Naumenko K., 2008, Steadystate creep of a pressurized thick cylinder in both the linear and the power law ranges, Acta Mechanica 195: 263274.##[14] Loghman A., Ghorbanpour Arani A., Amir S., Vajedi A., 2010, Magneto thermoelastic creep analysis of functionally graded cylinders, International Journal of Pressure Vessel and Piping 87: 389395.##[15] Ghorbanpour Arani A., Mosallaie Barzoki A.A., Kolahchi R., Mozdianfard M.R., Loghman A., 2011, Semianalytical solution of timedependent electrothermomechanical creep for radially polarized piezoelectric cylinder, Computer and Structures 89: 14941502.##[16] Zhou D., Kamlah M., 2006, Roomtemperature creep of soft PZT under static electrical and compressive stress loading, Acta Materialia 54: 13891396.##[17] Tiersten H.F., 1969, Linear piezoelectric plate vibrations, Plenum Press, New York.##[18] Fungn Y.C., 1965, Foundations of solid mechanics, PrenticeHall, New York.##[19] Mendelson A., 1968, Plasticity Theory and Applications, Macmillan, New York.##[20] Kordkheili S.A.H., Naghdabadi R., 2007, Thermoelastic analysis of a functionally graded rotating disk, Computer and Structures 79: 508516.##[21] Bayat M., Saleem M., Sahari B.B., Hamouda A.M.S., Mahdi E., 2009, Mechanical and thermal stresses in a functionally graded rotating disk with variable thickness due to radially symmetry loads, International Journal of Pressure Vessel and Piping 86: 357372.##[22] Penny R.K., Marriott D.L., 1995, Design for Creep, Chapman and Hall, London.##[23] Norton F.H., 1929, The Creep of Steel at High Temperatures, McGrawHill, London.##[24] Jaffe H., Berlincourt D.A., 1965, Piezoelectric transducer materials, Proceedings of IEEE 53: 13721386.## ##]
Mechanical Behavior of a FGM Capacitive MicroBeam Subjected to a Heat Source
2
2
This paper presents mechanical behavior of a functionally graded (FG) cantilever microbeam subjected to a nonlinear electrostatic pressure and thermal moment considering effects of material length scale parameters. Material properties through the beam thickness direction are graded. The top surface of the microbeam is made of pure metal and the bottom surface from a mixture of metal and ceramic. The material properties through the thickness direction follow the volume fraction of the constitutive materials in exponential function form. The governing nonlinear thermoelectromechanical differential equation based on EulerBernoulli beam theory assumptions is derived using modified couple stress theory (MCST) and is solved using the Galerkin based weighted residual method. The effects of the electrostatic pressure and temperature changes on the deflection and stability of the FGM microbeam, having various ceramic constituent percents, are studied. The obtained results are compared with the results predicted by classic theory (CT) and for some cases are verified with those reported in the literature.
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158
171


I
JafarSadeghiPournaki
Mechanical Engineering Department, Urmia University
Mechanical Engineering Department, Urmia
Iran


M.R
Zamanzadeh
Mechanical Engineering Department, Urmia University
Mechanical Engineering Department, Urmia
Iran


R
Shabani
Mechanical Engineering Department, Urmia University
Mechanical Engineering Department, Urmia
Iran


G
Rezazadeh
Mechanical Engineering Department, Urmia University
Mechanical Engineering Department, Urmia
Iran
g.rezazadeh@urmia.ac.ir
FGM Cantilever microbeam
Euler–Bernoulli
Pullin voltage
Sizedependent
Exponential volume fraction law
[[1] Suresh S., Mortensen A., 1998, Fundamentals of Functionally Graded Materials, IQM communications, London.##[2] Kapuria S., Bhattacharyya M., Kumar A.N., 2008, Bending and free vibration response of layered functionally graded beam: A theorical model and its experimental validation, Composite Structures 82: 390402.##[3] Khalili S.M.R., Jafari A., Eftekhari S.A., 2010, A mixture RitzDQ method for vibration of functionally graded beams carrying moving loads, Composite Structures 92: 24972511.##[4] Sadeghian H., RezaZadeh G., M.Osterberg P., 2007, Application of the generalized differential quadrature method of the study of pullin phenomenon of MEMS switches, Journal of Micromechanics 16(6): 13341340.##[5] Sankar B.V., 2001, An elasticity solution for functionally graded beams, Composite Science Technology 61: 689696.##[6] Sankar B.V., Taeng J.T., 2002, Thermal stresses in functionally graded beams, AIAA Journal 40:12281232.##[7] Venkataraman S., Sankar B.V., 2003, Elasticity solution for stresses in a sandwich beam with functionally graded core, AIAA Journal 41: 25012505.##[8] Massalas C. V., Kalpakidis V. K., 1983, Coupled thermoelastic vibration of a simply supported beam, Journal of Sound Vibration 88: 425429.##[9] Chakraborty A., Gopalakrishnan S., Reddy J.N., 2003, A new beam finite element for the analysis of functionally graded materials, International Journal of Mechanical Science 45: 519539 .##[10] Alibeigloo A. 2010, Thermoelasticity analysis of functionally graded beam with integrated surface piezoelectric layers, Journal of Composite Structures 92: 15351543.##[11] Babaei M.H., Abbasi M., Eslami M.R., 2008, Coupled thermoelasticity of functionally graded beams, Journal of Thermal Stresses 31: 680–697.##[12] Pamidighantam S., Puers R., Baert K., A C Tilmans H., 2002, Pullin voltage analysis of electrostatically actuated beam structures with fixed–fixed and fixed–free end conditions, Journal of Micromechanics and Microengineering 12: 458464.##[13] Ramezani A., Alasty A., Akbari A., 2007, Closedform solutions of the pullin instability in nanocantilevers under electrostatic and intermolecular surface forces, Journal of Solids and Structures 44: 49254941.##[14] Hasanyan D.J., Batra R.C., Harutyunyan S., 2008, Pullin instabilities in functionally graded microthermoelectromechanical systems, Journal of Thermal Stress 31: 10061021.##[15] Rezazadeh M. Pashapour F. Abdolkarimzadeh 2011, Mechanical behavior of bilayer cantilever microbeam subjected to electrostatical force, mechanical shock and thermal moment, International Journal of Applied Mechanics 3(3): 543561.##[16] Rezazadeh G., Keyvani A., Jafarmadar S., 2012, On a MEMS based dynamic remote temperature sensor using transverse vibration of bilayer microcantilever, Journal of Measurement 45 (3): 580589.##[17] Mohammadialasti B., Rezazadeh G., Borghei A., Minaei S., Habibifar R., 2011, On the mechanical behavior of functionally graded microbeam subjected to a thermal moment and nonlinear electrostatic pressure, Composite and Structures 93: 15161525.##[18] Kong S., Zhou S., Nie Z., Wang K., 2008, The sizedependent natural frequency of BernoulliEuler microbeams, International Journal of Engineering Science 46(5): 427437.##[19] Nix W.D., 1989. Mechanical properties of thin ﬁlms. Metallurgical and Materials Transactions 20A(11): 22172245.##[20] Fleck N.A., Muller G.M., Ashby, M.F., Hutchinson, J.W., 1994, Strain gradient plasticity: theory and experiment, Acta Metallurgica et Materialia 42(2): 475–487.##[21] Poole W.J., Ashby M.F., Fleck N.A., 1996, Microhardness of annealed and workhardened copper polycrystals, Scripta Materialia 34 (4): 559564.##[22] 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 (10): 27312743.##[23] Abbasnejad B., Rezazadeh G., Shabani R., Stability analysis of a capacitive FGM microbeam using modified couple stress theory, Acta Mechanica Solid and Sinica, Accepted paper.##[24] Asghari M., Ahmadian M.T., Kahrobaiyan M.H., Rahaeifard M., 2010, On the sizedependant behavior of functionally graded microbeams, Materials and Design 31: 23242329.##[25] Martin H. Sadd, 2009, Elasticity, Theory, Applications, and Numerics, Second edition, Academic Press.##[26] Saeedi Vahdat A., Rezazadeh G., 2011, Effects of axial and residual stresses on thermoelastic damping in capacitive microbeam resonators, Journal of the the Franklin Institute 348 :622639.##[27] Toupin R.A., 1962, Elastic materials with couple stresses, Archive for Rational Mechanics and Analysis 11: 385414.##[28] Mindlin R.D., Tiersten H.F., 1962, Effects of couplestresses in linear elasticity, Archive for Rational Mechanics and Analysis 11: 415448.##[29] Koiter W.T., 1964, Couple stresses in the theory of elasticity, I and II, Philosophical Transactions of the Royal Society of London B 67: 1744.##[30] Mindlin R.D., 1964, Microstructure in linear elasticity, Archive for Rational Mechanics and Analysis 16: 5178.##[31] Mindlin R. D., 1965, Stress functions for a Cosserat continuum, International Journal of Solids and Structures 1: 265271.##[32] Eringen A.C., 1968, Theory of micropolar elasticity, in: Fracture 1, edited by H. Leibowitz, Academic Press:621729.##[33] Sadeghian H., Goosen H., Bossche A., Thijsse B., van Keulen F., 2011, On the sizedependent elasticity of silicon nanocantilevers: Impact of defects, Journal of Physics D: Applied Physics 44(7): 20012007.## ##]
Free Vibration of Thick Isotropic Plates Using Trigonometric Shear Deformation Theory
2
2
In this paper a variationally consistent trigonometric shear deformation theory is presented for the free vibration of thick isotropic square and rectangular plate. In this displacement based theory, the inplane displacement field uses sinusoidal function in terms of thickness coordinate to include the shear deformation effect. The cosine function in terms of thickness coordinate is used in transverse displacement to include the effect of transverse normal strain. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Results of frequency of bending mode, thicknessshear mode and thicknessstretch mode are obtained from free vibration of simply supported isotropic square and rectangular plates and compared with those of other refined theories and frequencies from exact theory. Present theory yields exact dynamic shear correction factor π2/12 from thickness shear motion of the plate.
1

172
182


Y.M
Ghugal
Department of Applied Mechanics, Government Engineering College, Aurangabad431005 (Maharashtra State)
Department of Applied Mechanics, Government
Iran
ghugal@rediffmail.com


A.S
Sayyad
Department of Applied Mechanics, Government Engineering College, Aurangabad431005 (Maharashtra State)
Department of Applied Mechanics, Government
Iran
Shear deformation
Thick isotropic plate
Shear correction factor
Transverse normal strain
Free vibration
Thickness shear frequencies
[[1] Kirchhoff G.R., 1850, Uber das gleichgewicht und die bewegung einer elastischen scheibe, Journal of Reine Angew. Math.(Crelle) 40: 5188.##[2] Kirchhoff G.R., 1850, Uber die schwingungen einer kriesformigen elastischen scheibe, Poggendorffs Annalen 81: 258264.##[3] Reissner E., 1944, On the theory of bending of elastic plates, Journal of Mathematics and Physics 23: 184191.##[4] Reissner E., 1945, The effect of transverse shear deformation on the bending of elastic plates, ASME Journal of Applied Mechanics 12: 6977.##[5] Mindlin R.D., 1951, Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, ASME Journal of Applied Mechanics 18: 3138.##[6] Wang C.M., Lim G.T., Reddy J.N., Lee K.H., 2001, Relationships between bending solutions of Reissner and Mindlin plate theories, Engineering Structures 23 (7): 838849.##[7] Librescu L., 1975, Elastostatic and Kinetics of Anisotropic and Heterogeneous ShellType Structures, Nooedhoff International, Leyden, The Netherlands.##[8] Donnell L.H., 1976, Beams, Plates and Shells, McGrawHill, New York.##[9] Lo K.H., Christensen R.M., Wu E.M., 1977, A highorder theory of plate deformation, Part1: Homogeneous plates, ASME Journal of Applied Mechanics 44: 663668.##[10] Lo K.H., Christensen R.M., Wu E.M., 1977, A highorder theory of plate deformation, Part2: Laminated plates, ASME Journal of Applied Mechanics 44: 669676.##[11] Levinson M., 1980, An accurate, simple theory of the statics and dynamics of elastic plates, Mechanics Research Communications 7: 343350.##[12] Murty A.V.K., Vellaichamy S., 1988, Higherorder theory of homogeneous plate flexure, AIAA Journal 26: 719725.##[13] Reddy J.N., 1984, A refined nonlinear theory of plates with transverse shear deformation, International Journal of Solids and Structures 20(9/10): 881896.##[14] Reddy J.N., 1984, A simple higher order theory for laminated composite plates, ASME Journal of Applied Mechanics 51: 745752.##[15] Reddy J.N., Phan N.D., 1985, Stability and vibration of isotropic, orthotropic and laminated plates according to higher order deformation theory, Journal of Sound and Vibration 98: 157170.##[16] Srinivas S., Rao A.K., Joga Rao C.V., 1969, Flexure of simply supported thick homogenous and laminated rectangular plates, ZAMM: Zeitschrift fur Angewandte Mathematic und Mchanik 49(8): 449458.##[17] Srinivas S., Joga Rao C.V., Rao A. K., 1970, An exact analysis for vibration of simply supported homogeneous and laminated thick rectangular plates, Journal of sound and vibration 12(2): 187199.##[18] Noor A.K., Burton W.S., 1989, Assessment of shear deformation theories for multilayered composite plates, Applied Mechanics Reviews 42: 113.##[19] Reddy J.N., 1989, On the generalization of displacementbased laminate theories, Applied Mechanics Reviews 42:S213S222.##[20] Reddy J.N., Robbins D.H.Jr., 1994, Theories and computational models for composite laminates, Applied Mechanics Reviews 47: 147169.##[21] Liu D., Li X., 1996, An overall view of laminate theories based on displacement hypothesis, Journal of Composite Materials 30:1539561.##[22] Liew K.M., Xiang Y., Kitipornchai S., 1995, Research on thick plate vibration, Journal of Sound and Vibration 180:163176.##[23] Ghugal Y.M., Shimpi R.P., 2002, A review of refined shear deformation theories for isotropic and anisotropic laminated plates, Journal of Reinforced Plastics and Composites 21: 775813.##[24] Kreja I., 2011, A literature review on computational models for laminated composite and sandwich panels, Central European Journal of Engineering 1(1): 5980.##[25] Levy M., 1877, Memoire sur la theorie des plaques elastique planes, Journal des Mathematiques Pures et Appliquees 30: 219306.##[26] Stein M., Jegly D.C., 1987, Effect of transverse shearing on cylindrical bending, vibration and buckling of laminated plates, AIAA Journal 25: 123129.##[27] Shimpi R.P., Arya H., Naik N.K., 2003, A higher order displacement model for the plate analysis, Journal of Reinforced Plastics and Composites 22: 16671688.##[28] Shimpi R.P., Patel H.G., 2006, Free vibration of plate using two variable refined plate theory, Journal of Sound and Vibration 296:979999.##[29] Ghugal Y.M., Pawar M.D., 2011, Buckling and vibration of plates by hyperbolic shear deformation theory, Journal of Aerospace Engineering and Technology 1(1):112.##[30] Ghugal Y.M., Pawar M.D., 2011, Flexural analysis of thick plates by hyperbolic shear deformation theory, Journal of Experimental and Applied Mechanics 2(1):121.##[31] Ghugal Y.M., Sayyad A.S., 2010, Free vibration of thick orthotropic plates using trigonometric shear deformation theory, Latin American Journal of Solids and Structures 8: 229243.##[32] Ghugal Y.M., Sayyad A.S., 2010, A flexure of thick isotropic plate using trigonometric shear deformation theory, Journal of Solid Mechanics 2(1): 7990.##[33] Ghugal Y.M., Kulkarni S.K., 2011, Thermal stress analysis of crossply laminated plates using refined shear deformation theory,Journal of Experimental and Applied Mechanics: An International Journal 2(1): 4766.##[34] Timoshenko S.P., Goodier J.N., 1970, Theory of Elasticity, Third edition, McGraw Hill, New York.##[35] Manjunatha B.S., Kant T., 1993, Different numerical techniques for the estimation of multiaxial stresses in symmetric/unsymmetric composite and sandwich beams with refined theories, Journal of Reinforced Plastics and Composites 12: 237.##[36] Vinayak R.U., Prathap G., Naganarayana B.P., 1996, Beam elements based on a higher order theory — I: Formulation and analysis of performance, Computers and Structures 58: 775789.##[37] Lamb Horace, 1917, On waves in an elastic plate, Proceedings of Royal Society London, Series A 93: 114128.## ##]
A Power Series Solution for Free Vibration of Variable Thickness Mindlin Circular Plates with TwoDirectional Material Heterogeneity and Elastic Foundations
2
2
In the present paper, a semianalytical solution is presented for free vibration analysis of circular plates with complex combinations of the geometric parameters, edgeconditions, material heterogeneity, and elastic foundation coefficients. The presented solution covers many engineering applications. The plate is assumed to have a variable thickness and made of a heterogeneous material whose properties vary in both radial and transverse directions. While the edge is simplysupported, clamped, or free; the bottom surface of the plate is resting on a twoparameter (WinklerPasternak) elastic foundation. A comprehensive sensitivity analysis including evaluating effects of various parameters is carries out. Mindlin theory is employed for derivation of the governing equations whereas the differential transform method is used to solve the resulted equations. In this regard, both the inplane and rotary inertia are considered. Results show that degradations caused by a group of the factors (e.g., the geometric parameters) in the global behavior of the structure may be compensated by another group of factors of different nature (e.g, the material heterogeneity parameters). Moreover, employing the elastic foundation leads to higher natural frequencies and postponing the resonances.
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183
197


M.M
Alipour
Faculty of Mechanical Engineering, K.N. Toosi University of Technology
Faculty of Mechanical Engineering, K.N. Toosi
Iran


M
Shariyat
Faculty of Mechanical Engineering, K.N. Toosi University of Technology
Faculty of Mechanical Engineering, K.N. Toosi
Iran
m_shariyat@yahoo.com
Free vibration
Circular plate
Elastic foundation
Twodirectional functionally graded material
Variable thickness
Differential transform
[[1] Zhou D., Lo S.H., Au F.T.K., Cheung Y.K., 2006, Three dimensional free vibration of thick circular plates on Pasternak foundation, Journal of Sound and Vibration 292: 726741.##[2] HosseiniHashemi Sh., Rokni Damavandi Taher H., Omidi M., 2008, 3D free vibration analysis of annular plates on Pasternak elastic foundation via pRitz method, Journal of Sound and Vibration 311: 11141140.##[3] Ramaiah G.K., Vijayakumar K., 1973, Natural frequencies of polar orthotropic annular plates, Journal of Sound and Vibration 26: 517531.##[4] Narita Y., 1984, Natural frequencies of completely free annular and circular plates having polar orthotropy, Journal of Sound and Vibration 92: 3338.##[5] Lin C.C., Tseng C.S., 1998, Free vibration of polar orthotropic laminated circular and annular plates, Journal of Sound and Vibration 209: 797810.##[6] Prakash T., Ganapathi M., 2006, Asymmetric flexural vibration and thermoelastic stability of FGM circular plates using finite element method, Composites Part B 37: 642–649.##[7] Efraim E., Eisenberger M., 2007, Exact vibration analysis of variable thickness thick annular isotropic and FGM plates, Journal of Sound and Vibration 299: 720738.##[8] Nie G.J., Zhong Z., 2007, Semianalytical solution for threedimensional vibration of functionally graded circular plates, Computer Methods in Applied Mechanics and Engineering 196: 49014910.##[9] Dong C.Y., 2008, Threedimensional free vibration analysis of functionally graded annular plates using the ChebyshevRitz method, Materials and Design 29: 15181525.##[10] Malekzadeh P., 2009, Threedimensional free vibration analysis of thick functionally graded plates on elastic foundations, Composite Structures 89: 367373.##[11] Wang Y., Xu R.Q., Ding H.J., 2009, Free axisymmetric vibration of FGM circular plates, Applied Mathematics and Mechanics 30: 10771082.##[12] Nie G.J., Zhong Z., 2010, Dynamic analysis of multidirectional functionally graded annular plates, Applied Mathematical Modelling 34: 608616.##[13] Arikoglu A., Ozkol I., 2005, Solution of boundary value problems for integrodifferential equations by using differential transform method, Applied Mathematicsand Computation 168: 11451158.##[14] Chen C.K., Ho S.H., 1998, Application of differential transformation to eigenvalue problems, Applied Mathematicsand Computation 79: 173188.##[15] Malik M., Dang H.H., 1998, Vibration analysis of continuous systems by differential transformation, Applied Mathematicsand Computation 96: 1726.##[16] Yeh Y.L., Jang M.J., Wang C.C., 2006, Analyzing the free vibrations of a plate using finite difference and differential transformation method, Applied Mathematicsand Computation 178: 493501.##[17] Yeh Y.L., Wang C.C., Jang M.J., 2007, Using finite difference and differential transformation method to analyze of large deflections of orthotropic rectangular plate problem, Applied Mathematicsand Computation 190: 11461156.##[18] Yalcin H.S., Arikoglu A., Ozkol I., 2009, Free vibration analysis of circular plates by differential transformation method, Applied Mathematicsand Computation 212: 377386.##[19] Shariyat M., Alipour MM., 2011, Differential transform vibration and modal stress analyses of circular plates made of twodirectional functionally graded materials, resting on elastic foundations, Archives of Applied Mechanics 81: 12891306.##[20] Alipour M.M., Shariyat M., Shaban M., 2010, A semianalytical solution for free vibration of variable thickness twodirectionalfunctionally graded plates on elastic foundations, International Journal of Mechanics and Materials in Design 6: 293304.##[21] Reddy J.N., 2007, Theory and Analysis of Elastic Plates and Shells, CRC/Taylor & Francis, Second edition.##[22] Reddy J.N., 2004, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Second edition.##[23] HosseiniHashemi Sh., Fadaee M., Es’haghi M., 2010, A novel approach for inplane, outofplane frequency analysis of functionally graded circular/annular plates, International Journal of Mechanical Sciences 52: 10251035.##[24] Irie T., Yamada G., Takagi K., 1980, Natural Frequencies of Circular Plates, Journal of Applied Mechanics 47: 652655.##[25] Gupta U.S., Lal R., Sharma S., 2007, Vibration of nonhomogeneous circular Mindlin plates with variable thickness, Journal of Sound and Vibration 302: 117.## ##]
Effect of Boundary Condition on PreExisting Crack Under Fatigue Loading
2
2
In this paper, the present investigation has been conducted keeping in mind some of the problems concerning the crack propagation direction and growth under constant loading in an inclined crack geometry. The present studies mainly focused on the development and modifications in the crack growth criterion to account the biaxial, shear loading and number of stress terms. Existing criteria for the prediction of crack initiation direction have been modified taking higher order stress terms. The effective methods of experimentally determining the stress intensity factor for a body containing a crack is to analyze the isochromatic pattern obtained from a photoelastic model. The effect of biaxial load factor, crack angle, Crack length/width of specimen and length of specimen/width of specimen were studied and a regression model was developed for geometry correction to predict stress intensity factor for tearing mode and intensity factor for shearing mode. This approach is being used to predict crack growth trajectory under biaxial cyclic loading by assuming that the crack may grow in a number of discrete steps using the vectorial method. MTS criterion (Maximum Tangential Stress criterion) is used for prediction of crack initiating angle. The crack growth trajectory has been determined by cycle simulation procedure.
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198
207


V.K
Singh
Department of Mechanical Engineering, College of Technology, Govind Ballabh Pant University of Agriculture & Technology
Department of Mechanical Engineering, College
Iran
vks2319@yahoo.co.in


P.C
Gope
Department of Mechanical Engineering, College of Technology, Govind Ballabh Pant University of Agriculture & Technology
Department of Mechanical Engineering, College
Iran
pcgope@rediffmail.com


R.K
Bhagat
Department of Mechanical Engineering, College of Technology, Govind Ballabh Pant University of Agriculture & Technology
Department of Mechanical Engineering, College
Iran
Stress intensity factor
crack growth
Photo elasticity
[[1] Irwin G.R., 1957, Analysis of stress strains near the end of a crack traversing plate, ASME Journal of Applied Mechanics 24(3): 361364.##[2] Singh S., 1983, Applied Stress Analysis, Khanna Publishers, Second edition, Delhi, India: 346347.##[3] Nash W., 2007, Strength of Materials, McGrawHill, Fourth edition, 7.17.44, New York.##[4] Ramesh K., Gupta S., Kelkar A.A., 1997, Evaluation of stress field parameter in fracture mechanics by photoelasticity, Engineering Fracture Mechanics 56(1): 2545.##[5] Kelley L.G., 1991, Handbook of Numerical Method and Applications, AddisonWerly, p. 99.##[6] Erdogan F., Sih G.C., 1963, On crack extension in plates under plane loading transverse shear, ASME Journal of basic Engineering D 85: 519527.##[7] Paris P.C., Erdogan F., 1963, A critical analysis of crack propagation laws, ASME Journal of basic Engineering D 85: 528533.##[8] Khan Shafique M.A., Khraisheh M.K., 2000, Analysis of Mixed Mode Crack Initiation Angle under Various Loading Conditions, Elsevier science Ltd.: 110.##[9] Liebowitz H.., Lee J.D., Eftis J., 1978, Biaxial load effects in fracture mechanics, Engineering Fracture Mechanics 10: 315335.##[10] Stephens R.I., Fatemi A., Stephens R. R., Fuchs H.O., 2001, Fatigue in Engineering, Second edition, John Wiley & Sons, Inc., New York.## ##]