2010
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3
3
106
Wave Propagation in Mixture of Generalized Thermoelastic Solids HalfSpace
2
2
This paper concentrates on the reflection of plane waves in the mixture of generalized thermo elastic solid halfspace. There exists quasi dilatational waves i.e. qP1, qP2, qT and two rotational waves S1, S2 in a two dimensional model of the solid. The boundary conditions are solved to obtain a system of five nonhomogeneous equations for amplitude ratios. These amplitude ratios are found to depend on the angle of incidence of incident wave, mixture and thermal parameters and have been computed numerically and presented graphically. The appreciable effects of mixtures and thermal on the amplitude ratios are obtained.
1

199
213


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


S
Devi
Department of Mathematics, D.N. College
Department of Mathematics, D.N. College
Iran
Dynamic theory of mixture
Amplitude ratios
Thermoelasticity
Wave propagation
Relaxation time
Reflection
[[1] Trusedell C., Tupin R.A., 1960, The Classical Field Theories, Volume III/1, SpringerVerlag, Berlin.##[2] Eringen A.C., Ingram J.D., 1965, A continuum theory of chemically reacting mediaI, International Journal of Engineering Science 3: 197212.##[3] Green A.E., Naghdi P.M., 1965, A dynamical theory of interacting continua, International Journal of Engineering Science 3: 231241.##[4] Bedford A., Stern M., 1972, A multicontinuum theory of elastic materials, Acta Mechanica 14: 85102.##[5] Bedford A., Stern M., 1972, Toward a diffusing continuum theory of composite elastic materials, ASME Journal of Applied Mechanics 38: 814.##[6] Bowen R.M., 1976, Theory of mixtures, in: Continuum Physics, Volume III, edited by A.C. Eringen, Academic Press, New York.##[7] Atkin R.J., Craine R.E., 1976, Continuum theories of mixtures: Applications, Journal of the Institute of Mathematical Applications 17: 153207.##[8] Atkin R.J., Craine R.E., 1976, Continuum theories of mixtures: Basic theory and Historical Development, Quarterly Journal of Mechanics and Applied Mathematics 29: 209245.##[9] Rajgopal K.R., Tao L., 1995, Mechanics of Mixtures, World Scientific, Singapore.##[10] Iesan D., 1991, On the theory of mixtures of thermoelastic solids, Journal of Thermal Stresses 14: 389408.##[11] Green A.E., Steel T.R., 1966, Constitutive equations for intereacting continua, International Journal of Engineering Science 4: 483500.##[12] Steel T.R., 1967, Applications of theory of interacting continua, Quarterly Journal of Mechanics and Applied Mathematics 20: 5772.##[13] Bowen R.M., Wiese J.C., 1969, Diffusion in mixtures of elastic materials, International Journal of Engineering Science 7: 689722.##[14] Martinez F., Quintanilla R., 1995, Some qualitative results for the linear theory of binary mixtures of thermoelastic solids, Collectanea Mathematica 46: 263277.##[15] Pompei A. Scalia A., 1999, On the theory of mixtures of thermoelastic solids, Journal of Thermal Stresses 22: 2334.##[16] Burchuladze T., Svanadze M., 2000, Potential method in the linear theory of binary mixtures of thermoelastic solids, Journal of Thermal Stresses 23: 601626.##[17] Pompei A., 2003, On the dynamical theory of mixtures of thermoelastic solids, Journal of Thermal Stresses 26: 873888.##[18] Passarella F., Vittorio Z., 2007, Some exponential decay estimates for the thermoelastic mixtures, Journal of Thermal Stresses 30: 2541.##[19] Sharma M. D., Gogna M. L., 1992, Reflection and refraction of plane harmonic waves at an interface between elastic solid and porous solid saturated by viscous liquid, Pageoph 138: 249266.##[20] Vashisth A. K., Sharma M. D., Gogna M. L., 1991, Reflection and transmission of elastic waves at a loosely bonded interface between an elastic solid and liquidsaturated porous solids, Geophysics International Journal 105: 601617.##[21] Apice C.D., Chirita S., Tibullo V., 2005, On the spatial behavior in dynamic theory of mixtures of thermoelastic solids, Journal of Thermal Stresses 28: 6382.##[22] Lord H., Shulman Y.A., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15: 299309.##[23] Schoenberg M., 1971, Transmission and reflection of plane waves at an elasticviscoelastic interface, Geophysical Journal Royal Astronomical Society 25:3547.##[24] Dhaliwal R. S., Singh A., 1980, Dynamic Coupled Thermoelasticity, Hindustan Publishers, Delhi.## ##]
An Exact Solution for LordShulman Generalized Coupled Thermoporoelasticity in Spherical Coordinates
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2
In this paper, the generalized coupled thermoporoelasticity model of hollow and solid spheres under radial symmetric loading condition (r, t) is considered. A full analytical method is used and an exact unique solution of the generalized coupled equations is presented. The thermal, mechanical and pressure boundary conditions, the body force, the heat source and the injected volume rate per unit volume of a distribute water source are considered in the most general forms and where no limiting assumption is used. This generality allows simulate varieties of applicable problems. At the end, numerical results are presented and compared with classic theory of thermoporoelasticity.
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214
230


M
Jabbari
Postgraduate School, South Tehran Branch, Islamic Azad University
Postgraduate School, South Tehran Branch,
Iran
mjabbari@oiecgroup.com


H
Dehbani
Sama Technical and Vocational Training School, Islamic Azad University, Varamin Branch
Sama Technical and Vocational Training School,
Iran
Coupled Thermoporoelasticity
Lordshulman
Hollow sphere
Exact solution
[[1] Hetnarski R.B., Eslami M.R., 2009, Thermal Stresses  Advanced Theory and Applications, Springer, New York.##[2] Lord H.W., Shulman Y., 1967, A Generalized Dynamical Theory of Themoelasticity, Journal of the Mechanics and Physics of Solids 15: 299309.##[3] Green A.E., Lindsay K.A., 1972, Thermoelasticity, Journal of Elasticity 2: 17.##[4] Green A.E., Naghdi P.M., 1972, Thermoelasticity Without Energy Disspation, Journal of Elasticity 2: 17.##[5] Youssef H.M., 2006, Theory of generalized porothermoelasticity, International Journal of Rock Mechanics and Mining Sciences 44: 222227.##[6] Bai B., 2006, Response of saturated porous media subjected to local thermal loading on the surface of semispace, Acta Mechanica Sinica 22: 5461.##[7] Bai B., 2006, Fluctuation responses of saturated porous media subjected to cyclic thermal loading, Computers and Geotechnics 33: 396403.##[8] Droujinine A., 2006, Generalized an elastic asymptotic ray theory, Wave Motion 43: 357367.##[9] Bai B., Li T., 2009, Solution for cylindrical cavity in saturated thermoporoelastic medium, Acta Mechanica Sinica 22(1): 8592.##[10] Hetnarski R.B., 1964, Solution of the coupled problem of thermoelasticity in the form of series of functions, Archives of Mechanics (Archiwum Mechaniki Stosowanej) 16: 919941.##[11] Hetnarski R.B., Ignaczak J., 1993, Generalized thermoelasticity: Closedform solutions, Journal of Thermal Stresses 16: 473498.##[12] Hetnarski R.B., Ignaczak J., 1994, Generalized thermoelasticity: Response of semispace to a shortlaser pulse, Journalof Thermal Stresses 17: 377396.##[13] Georgiadis H.G., Lykotrafitis G., 2005, Rayleigh waves generated by a thermal source: A threedimensional transiant thermoelasticity solution, Journal of Applied Mechanics 72: 129138.##[14] Wagner P., 1994, Fundamental matrix of the system of dynamic linear thermoelasticity, Journal of Thermal Stresses 17: 549565.##[15] Jabbari M., Dehbani H., Eslami M. R.,2009, An exact solution for classic coupled thermoporoelasticity in Spherical Coordinates, ASME Journal of Pressure Vessel 132 (2): 031201031211.##[16] Jabbari M., Dehbani H., 2009, An exact solution for classic coupled thermoporoelasticity in cylindrical coordinates, Journal of Solid Mechanics 1(4): 343357.##[17] Jabbari M., Dehbani H., Eslami M. R., 2010, An exact solution for classic coupled thermoporoelasticity in cylindrical coordinates, ASME Journal of Pressure Vessel, to appear.##[18] Jabbari M., Dehbani H., An exact solution for classic coupled thermoporoelasticity in Axisymmetric Cylinder, Journal of Solid Mechanics, to appear.## ##]
Finite Element Modeling of Crack Initiation Angle Under Mixed Mode (I/II) Fracture
2
2
Present study deals with the prediction of crack initiation angle for mixed mode (I/II) fracture using finite element techniques and JIntegral based approach. The FE code ANSYS is used to estimate the stress intensity factor numerically. The estimated values of SIF were incorporated into six different crack initiation angle criteria to predict the crack initiation angle. Single edge crack specimens of AralditeHardener were used for the present analysis. Load was applied up to critical limit of the specimens containing crack at different angles of inclination. The crack initiation angle obtained using stress intensity factor and Jintegral based approach were found close to each other and also found to be in good agreement with the available experimental results in literature. It is also investigated that as crack inclination angle increases material was found to behave in a brittle manner.
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231
247


S.S
Bhadauria
Department of Applied Mechanics, Maulana Azad National Institute of Technology Bhopal
Department of Applied Mechanics, Maulana
Iran
ssb.aero@gmail.com


K.K
Pathak
Advanced Materials Processes Research Institute (CSIR)
Advanced Materials Processes Research Institute
Iran


M.S
Hora
Department of Applied Mechanics, Maulana Azad National Institute of Technology Bhopal
Department of Applied Mechanics, Maulana
Iran
Finite Element Method
Mixed mode fracture
Stress intensity factor
Jintegral
Crack initiation angle
Fracture criteria
[[1] Abdalla J.E., Gerstle W.H., 1988, A finite element for arbitrarily precise determination of stress intensity factors, Bureau Of Engineering Report CE84(88), College of Engineering, University of New Mexico, Albuquerque.##[2] Ayhan A.O., 2004, Mixed mode stress intensity factors for deflected and inclined surface cracks in finitethickness plates, Engineering Fracture Mechanics 71: 10591079.##[3] Barsoum R.S., 1976, On the use of isoparametric finite elements in linear fracture mechanics, International Journal for Numerical Methods in Engineering 10: 2537.##[4] Barsoum R.S., 1977, Triangular quarterpoint elements as elastic and perfectly plastic crack tip elements, International Journal for Numerical Methods in Engineering 11: 8598.##[5] Cherepanov G.P., 1974, Mechanics of Brittle Fracture, Nauka, Moscow, (in Russian).##[6] Erdogan F., Shi G.C., 1963, On the crack extension in plates under plane loading and transverse shear, Journal of Basic Engineering 85: 519527.##[7] Griffith A.A., 1921, The phenomena of rupture and flow in solids, Philosophical Transactions of the Royal Society of London, Series A221, pp. 199.##[8] Henshell R.D., Shaw K.G., 1975, Crack tip finite element are unnecessary, International Journal for Numerical Methods in Engineering 9: 495507.##[9] Josh J., Ptaik S, 1989, On stress intensity factor computation by finite element method under mixed mode loading conditions, Engineering Fracture Mechanics 34(1): 169177.##[10] Knesl Z., 1988, Stress intensity factor computing under mixed mode loading conditions by the use of energy release rate (in Czech). Strojirenstvi 37: 163166##[11] Kong X.M., Schluter N., Dahl W., 1995, Effect of triaxial stress on mixed modefacture, Engineering Fracture Mechanics 52(2) :379388.##[12] Owen D.R.J., Fawkes A. J., 1983, Engineering Fracture MechanicsNumerical Methods and Applications, Pineridge Press, Swansea, UK.##[13] Pu S.L., Hussain M.A., Lorenson W.E., 1978, The collapse cubic isoparamteric elements as singular elements for crack problems, International Journal for Numerical Methods in Engineering 12: 17271742.##[14] Peter M., Haefele, Lee James D., 1995, Combination of finite element analyses and analytical crack tip solution for mixed mode fracture, Engineering Fracture Mechanics 50(5/6): 849868.##[15] Petit C., Vergne A., Zhang X., 1996, A comparative numerical review of cracked materials, Engineering Fracture Mechanics 54 (3): 423439.##[16] Rousseau C.E., Tippur H.V., 2000, compositionally graded materials with cracks normal to the elastic gradient, Acta Materialia 48: 4021 4033.##[17] Sih G.C., 1974, Strain energy density factor applied to mixed mode crack problems, International Journal of Fracture 10 (3): 305321.##[18] Sih G.C., 1973, Some basic problems in fracture mechanics and new concepts, Engineering Fracture Mechanics 5: 365377.##[19] Shafique M.A., Marwan K., 2000, Analyses of mixed mode crack initiation angles under various loading conditions, Engineering Fracture Mechanics 67: 397419.##[20] Shafique M.A., Marwan K., 2004, A new criterion for mixed mode fracture initiation based on crack tip plastic core region, International Journal of Plasticity 20: 5584.##[21] Theocaris P.S., Andrianopoulos N.P. 1982, The Tcriterion applied to ductile fracture, International Journal of Fracture 20: 125130.##[22] Theocaris P.S., Andrianopoulos N.P., 1982, The Mises elasticplastic boundary as the core region in fracture criteria, Engineering Fracture Mechanics 16: 425432.##[23] Theocaris P.S., Kardomateas G.A., Andrianopoulos N.P., 1982, Experimental study of the Tcriterion in ductile fracture, Engineering Fracture Mechanics 17: 439447.##[24] Tilbrook M.T., Reimanis I.E., Rozenburg K., Hoffman M., 2005, Effect of plastic yielding on crack propagation near ductile/brittle interfaces, Acta Materialia 53: 39353949.##[25] Ukadgaonker V.G., Awasare P.J., 1995, A new criterion for fracture initiation, Engineering Fracture Mechanics 51 (2): 265274.##[26] Zwing P.D., Swedlow J.L., Williams J.G., 1976, Further results on the angled crack problem, International Journal of Fracture 12(1):8593.##]
Investigation of Vacancy Defects on the Young’s Modulus of Carbon Nanotube Reinforced Composites in Axial Direction via a Multiscale Modeling Approach
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2
In this article, the influence of various vacancy defects on the Young’s modulus of carbon nanotube (CNT)  reinforcement polymer composite in the axial direction is investigated via a structural model in ANSYS software. Their high strength can be affected by the presence of defects in the nanotubes used as reinforcements in practical nanocomposites. Molecular structural mechanics (MSM)/finite element (FE) Multiscale modeling of carbon nanotube/polymer composites with linear elastic polymer matrix is used to study the effect of CNT vacancy defects on the mechanical properties. The nanotube is modeled at the atomistic scale using MSM, where as the interface we assumed to be bonded by Vander Waals interactions based on the LennarJonze potential at the interface and polymer matrix. A nonlinear spring is used for modeling of interactions. It is studied for zigzag and armchair Nanotubes with various aspect ratios (Length/Diameter). Finally, results of the present structural model show good agreement between our model and the experimental work.
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248
256


M.R
Davoudabadi
Department of Mechanical Engineering, Semnan University
Department of Mechanical Engineering, Semnan
Iran
davoudabadi.m@gmail.com


S.D
Farahani
Department of Mechanical Engineering, University of Tehran
Department of Mechanical Engineering, University
Iran
Polymer matrix
Carbon nanotubes
Nonlinear spring
Multiscale modeling
Defect
Interphase
Finite element model
[[1] Iijima S., 1991, Helical microtubules of graphitic carbon, Nature 354 568.##[2] Dresselhaus M.S., Dresselhaus G., Eklund P.C., 1996, Science of Fullerenes and Carbon Nanotubes, Academic Press, San Diego.##[3] Nardelli M.B., Fattebert J.L., Orlikowski D., Roland C., Zhao Q., Bernholc J., 2000, Mechanical properties, defects and electronic behavior of carbon nanotubes, Carbon 38: 1703–1711.##[4] Yakobson B.I., Avouris P., 2001, Mechanical properties of carbon nanotubes, Carbon Nanotubes, Topics in Applied Physics, edited by M.S. G. Dresselhaus, Dresselhaus, P. Avouris, Springer Verlag, Berlin/Heidelberg 80: 287329.##[5] Overney G., Zhong W., Tomanek D., 1993, Structural rigidity and lowfrequency vibrational modes of long carbon tubules, Zeitschrift Fur Physik D 27: 9396.##[6] Lu J.P., 1997, Elastic properties of carbon nanotubes and nanoropes, Physical Review Letters 79: 12971300.##[7] Chang T., Gao H., 2003, Sizedependent elastic properties of a singlewalled carbon nanotube via a molecular mechanics model nanotubes, Journal of the Mechanics and Physics of Solids 51: 10591074.##[8] Molina J.M., Savinsky S.S., Khokhriakov N.V., 1996, A tightbinding model for calculations of structures and properties of graphitic nanotubes, Journal of Chemical Physics 104: 46524656.##[9] Hernandez H., Goze C., Bernier P., Rubio A., 1998, Elastic properties of C and Bx Cy Nz composite nanotubes, Physical Review Letters 80: 45024505.##[10] Guzman de Villoria R.., Miravete A., 2007, Mechanical model to evaluate the effect of the dispersion in nanocomposites Acta Materialia 55 :30253031.##[11] Qian D., Wagner G.J., Liu W.K., Yu M.F., Rouff R.S., 2002, Mechanics of carbon nanotubes, Applied Mechanics Review 22: 495533.##[12] Tserpes K.I., Papanikos P., 2005, Finite element modeling of singlewalled carbon nanotubes, Composites Part B: Engineering 36: 468477.##[13] Sakhaeepour A., 2008, Vibrational analysis of single layered grapheme sheets, Nanothechnology 19: 085702.##[14] Chopra N. G., Zettl A., 1998, Measurement of the elastic modulus of a multiwall boron nitride nanotube, Solid State Communications 105: 297300.##[15] Krishnan A., Dujardin E., Ebbesen T.W., Yianilos P.N., Treacy M.M.J., 1998, Young’s modulus of singlewalled nanotubes, Physical Review B 58: 14 01314 019.##[16] Salvetat J.P., Bonard J.M., Thomson N.H., Kulik A.J., Forro L., Benoit W., Zuppiroli L.,1999, Mechanical properties of carbon nanotubes, Applied Physics A 69: 255260.##[17] Popov V.N., Van Doran V.E., Balkanski M., 2000, Elastic properties of singlewalled carbon nanotubes, Physical Review B 61: 30783084.##[18] Jin Y., Yuan F.G., 2002, Elastic properties of singlewalled carbon nanotubes, in: 43rd AIA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, April 2225, Denver, Colorado, USA.##[19] Frankland S.J.V., Caglar A., Brenner D.W., Griebel M., 2002, Molecular simulation of the influence of chemical crosslinks on the shear strength of carbon nanotubepolymer interfaces, Journal of Physical Chemistry B 106: 30463048.##[20] Montazeri A., Naghdabadi R., 2009, Study the effect of Viscoelastic matrix model on the stability of CNT/polymer composites by Multiscale modeling, polymer composites, Journal of the Brazilian Chemical Society 20(3): 466471.##[21] Yu M.F., Lourie O., Dyer M.J., Moloni K., Kelly T.F., Ruoff R.S., 2000, Strength and breaking mechanism of multi walled carbon nanotubes under tensile load, Science 287: 637640.##[22] Krasheninikov A.V., Nordlund K., 2004, Irradiation effects in carbon nanotubes, Nuclear Instruments and Methods in Physics Research Section B 216: 355366.##[23] Li C., Chou T.W., 2003, A structural mechanics approach for the analysis of carbon nanotubes, International Journal of Solids and Structures 40: 24872499.##[24] Sammalkorpi V.M., Krasheninnikov A.V., Kuronen A., Nordlund K., Kaski K., 2004, Mechanical properties of carbon nanotubes with vacancies and related defect, Physical Review B 1: 18.## ##]
Prediction of Crack Initiation Direction for Inclined Crack Under Biaxial Loading by Finite Element Method
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2
This paper presents a simple method based on strain energy density criterion to study the crack initiation angle by finite element method under biaxial loading condition. The crack surface relative displacement method is used to eliminate the calculation of the stress intensity factors which are normally required. The analysis is performed using higher order four node quadrilateral element. The results by finite element method are compared with DET (determinant of stress tensor criterion) and strain energy density criteria. Finite element results are in well agreement with the experimental and analytical results.
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257
266


P.C
Gope
Department of Mechanical Engineering, College of Technology, G. B. Pant University of Agriculture and Technology
Department of Mechanical Engineering, College
Iran
pcgope@rediffmail.com


S.P
Sharma
Mechanical Engineering Department, National Institute of Technology, Jamshedpur, Jharkhand
Mechanical Engineering Department, National
Iran


A.K
Srivastava
Deputy Manager (Design) Air Craft Upgrade Research and Design Centre, Hindustan Aeronautics Limited
Deputy Manager (Design) Air Craft Upgrade
Iran
Biaxial loading
mixed mode
Crack Initiation
Finite Element Method
Crack tip displacement
[[1] Erdogan F., Sih G.C., 1963, On the crack extension in plates under plane loading and transverse shear, Journal of Basic Engineering 85: 1927.##[2] Sih G.C., 1974, Strain energy density factor applied to mixed mode crack problems, International Journal of Fracture 11: 305321.##[3] Theocaris P.S., Andrianopoulos N.P., 1982, The TCriterion applied to ductile fracture, International Journal of Fracture 20: R125130.##[4] Hussain M.A., Pu S.L., Underwood J.H., 1974, Strain energy release rate for a crack under combined mode I and mode II, Fracture Analysis, ASTM STP 560: 228.##[5] Papadopoulos G.A., 1988, Crack initiation under biaxial loading, Engineering Fracture Mechanics 29: 585598.##[6] Shih C.F., 1974, Small scale yielding analysis of mixed mode plane strain crack problem, Fracture Analysis, ASTM, STP 560: 187210.##[7] Obta M., 1984, On stress field near a stationery crack tip, Mechanics of Materials 3: 35243.##[8] Saka M., Abe H., Tanaka S.,1986, Numerical analysis of blunting of crack tip in a ductile material under small scale yielding and mixed mode loading, Computational Mechanics 1: 1119.##[9] Dong P., Pan J., 1990, Plane strain mixed mode near tip fields in elastic perfectly plastic solids under small scale yielding condition, International Journal of Fracture 45: 243262.##[10] Dong P., Pan J., 1990, Plane stress mixed mode near tip fields in elastic perfectly solids, Engineering Fracture Mechanics 37: 4357.##[11] Sedmak A., 1984, Finite element evaluation of fracture mechanics parameter using rapid mesh refinement, Advance in Fracture Research, 10951106.##[12] Guydish Jacob J., Fleming J.F., 1978, Optimization of the finite element mesh for the solution of fracture problems, Engineering Fracture Mechanics 10:3142.##[13] Mahanty D.K., Maiti S.K., 1990, Experimental and finite element studies on mode I and mixed mode (I and II) stable crack growthI, Engineering Fracture Mechanics 37: 12371250.##[14] Mahanty D.K., Maiti S.K.,1990, Experimental and finite element studies on mode I and mixed mode (I and II) stable crack growthII, Engineering Fracture Mechanics 37: 12511275.##[15] Ju S.H., 2010, Finite element calculation of stress intensity factors for interface notches, Computer Methods in Applied Mechanics and Engineering 199 (3336): 22732280.##[16] Réthoré J., Roux S., Hild F., 2010, Mixedmode crack propagation using a Hybrid Analytical and extended Finite Element Method, Comptes Rendus Mécanique 338(3): 121126.##[17] Benrahou K.H., Benguediab M., Belhouari M., NaitAbdelaziz M., Imad A., 2007, Estimation of the plastic zone by finite element method under mixed mode (I and II) loading, Computational Materials Science 38(4): 595601.##[18] Ghorbanpoor A., Zhang J., 1990, Boundary element analysis of crack growth for mixed mode center slant crack problems, Engineering Fracture Mechanics 36(5): 661668.##[19] Wang J., Chow C.L., 1989, Mixed mode ductile fracture studies with non proportional loading based on continuum damage mechanics, Journal of Engineering material and Technology III, 204209.##[20] Sun Y.J., Xu L.M., 1985, Further studies on crack tip plasticity under mixed mode loading, in: Proceedings of 1985 Spring Conference, Experimental Mechanics Publication, Las Vegas, 2025.##[21] Lee K.Y., Lee J.D., Liebowitz H., 1997, Finite element analysis of slow crack growth process in mixed mode fracture, Engineering Fracture Mechanics 56: 551577.##[22] Seibi A.C., Zamrik S.Y., 2003, Prediction of crack initiation direction for surface flaws under biaxial loading, Journal of Pressure Vessel and Technology 125: 6575.##[23] Ling L. H., Woo C.W., 1984, On angle crack initiation under biaxial loading, Journal of Strain Analysis 19(1): 5159.##[24] Shlyannikov V.N., Kislovaa S.Y., Tumanova A.V., 2010, Inclined semielliptical crack for predicting crack growth direction based on apparent stress intensity factors, Theoretical and Applied Fracture Mechanics 53(3): 185193.##[25] Kibler J.J., Roberts R.., 1970, The effect of biaxial stresses on fatigue and fracture, Journal of Engineering for Industry 92: 727734.##[26] Hilton P.D., 1973, Plastic intensity factors for cracked plates subjected to biaxial loading, International Journal of Fracture 9: 149156.##[27] Liebowitz H., Lee J.D., Eftis J., 1978, Biaxial load effects in Fracture mechanics, Engineering Fracture Mechanics 10: 315335.##[28] Hafeele P. M., Lee J.D., 1995, The constant stress term, Engineering Fracture Mechanics 50: 869882.##[29] Yan X.., 2006, Multiple crack fatigue growth modeling by displacement discontinuity method with cracktip elements, Applied Mathematical Modeling 30: 489508.##[30] Kamaya M.., 2003, A crack growth evaluation method for interacting multiple cracks. JSME International Journal, Series A 46(1): 1523.##[31] Masayuki Kamaya, 2008, Growth evaluation of multiple interacting surface cracks. Part I: Experiments and simulation of coalesced crack, Engineering Fracture Mechanics 75:13361349.##[32] Masayuki Kamaya, 2008, Growth evaluation of multiple interacting surface cracks. Part II: Growth evaluation of parallel cracks, Engineering Fracture Mechanics 75: 13501366.##[33] Chow C.L., Lau K.J., 1976, Finite element analysis of cracked bodies to determine stress intensity factors, Journal of Strain Analysis 11, 1825.##[34] Woo C.W., Kuruppu M.D., 1982, Use of finite element method for determining stress intensity factors with a conicsection simulation model of crack surface, 20: 163178.##[35] Sneddon I.N., Lowengrub M., 1970, Crack Problems in Classical Theory of Elasticity, John Wiley, New York.##[36] Gope P.C., 2002, Investigation into the crack propagation under static and fatigue loading, PhD Thesis, Ranchi University, Ranchi.##[37] Bahuguna S., Kothari A., Awasthi P., 2001, Study on Mixed Mode Crack Propagation under Uniaxial Tensile Loading, B. Tech Project report, Govind Ballabh Pant University of Agriculture and Technology.##[38] Golos K., Wasiluk B., 2000, Role of plastic zone in crack growth direction under mixed mode loading, International Journal of Fatigue 102(4): 341353.##[39] Seibi A.C., Zamrik S.Y., 1997, Prediction of crack initiation direction for surface flaws under biaxial loading, in: 5th International Conference on Biaxial/Multiaxial Fatigue and Fracture Cracow ‘97 Poland 2, 611622.##[40] Ewing P.D., Williams J.G., 1974, The fracture of spherical shells under pressure and circular tubes with angled cracks in torsion, International Journal of Fracture 10 (4): 537544.## ##]
Free Vibration Analysis of Micropolar Thermoelastic Cylindrical Curved Plate in Circumferential Direction
2
2
The free vibration analysis ofhomogeneous isotropic micropolar thermoelastic cylindrical curved plate in circumferential direction has been investigated in the context of generalized themoelasticity III, recently developed by Green and Naghdi. The model has been simplified using Helmholtz decomposition technique and the resulting equations have been solved using separation of variable method. Mathematical modeling of the problem to obtain dispersion curves for curved isotropic plate leads to coupled differential equations and solutions are obtained by using Bessel functions. The frequency equations connecting the frequency with circumferential wave number and other physical parameters are derived for stress free cylindrical plate. In order to illustrate theoretical development, numerical solutions are obtained and presented graphically for a magnesium crystal.
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267
274


G
Partap
Department of Mathematics, Dr. B.R. Ambedkar National Institute of Technology, Jalandhar, Punjab
Department of Mathematics, Dr. B.R. Ambedkar
Iran
gp.recjal@gmail.com


R
Kumar
Department of Mathematics, Kurukshetra University
Department of Mathematics, Kurukshetra University
Iran
rajneesh_kuk@rediffmail.com
Micropolar
Phase velocity
Circumferential wave number
Thermoelasticity type III
Thermoelasticity without energy dissipation
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Review of Damage Tolerant Analysis of Laminated Composites
2
2
With advanced composites increasing replacing traditional metallic materials, the material inhomogeneity and inherent anisotropy of such materials lead to not only new attributes for aerospace structures, but also introduce new technology to damage tolerant design and analysis. The deleterious effects of changes in material properties and initiation and growth of structural damage must be addressed. The anisotropic and brittle properties make this requirement a challenging to composite structural designers. Accurate, reliable and userfriendly computational methods, design and analysis methods are vital for more damage tolerant composite structures. Both durability and damage tolerant methodologies must address the possible changes in mechanical properties and the evolving damage accumulations that may occur during the vehicle’s service lifetime. Delamination is a major failure mode in laminated composites and has received much research attention. It may arise out of manufacturing defects, free edge effects, structural discontinuities, low and high velocity impact damage, and even bird strikes. Early pioneering work established that the reduction in strength following delamination damages placed severe limits on the design allowable for highly loaded components such as aircraft wing and fuselage structure. In the present article, we provide a stateofart survey on damage tolerant design correlated failure behavior and analysis methodologies of laminated composites. Particular emphasis is placed on some advanced formulations and numerical approaches for efficient computational modeling and damage tolerant analysis of laminated composites.
1

275
289


X.L
Fan
State Key Laboratory for Mechanical Structural Strength and Vibration, School of Aerospace, Xi’an Jiao Tong University
State Key Laboratory for Mechanical Structural
Iran
fanxueling@mail.xjtu.edu.cn


Q
Sun
School of Aeronautics, Northwestern Polytechnical University
School of Aeronautics, Northwestern Polytechnical
Iran


M
Kikuchi
Faculty of Science and Engineering, Tokyo University of Science
Faculty of Science and Engineering, Tokyo
Iran
Damage tolerant analysis
Delamination
Virtual crack closureintegral technique
Cohesive zone model
Progressive failure analysis
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Flügge, Springer Verlag, Berlin, Germany, 558590.##[68] Krueger R., Minguet P.J., 2005, SkinStiffener Debond Prediction Based on Computational Fracture Analysis, NASA/CR2005213915.##[69] ABAQUS Analysis User’s Manual  Version 6.5, Volume I, 2005, ABAQUS Inc.##[70] Mabson G., Doper B., Deobald L., 2004, User Manual for Fracture and Traction Interface Elements  Version 1.3, The Boeing Company.##[71] Williams M.L., 1963, The Fracture of ViscoElastic Material, Wiley Interscience Publishers, Drucker.##[72] Schapery R.A., 1975, A theory of crack initiation and growth in viscoelastic media, International Journal of Fracture 11(1): 141159.##[73] Hillerborg A., Modeer M., Petersson P.E., 1976, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement Concrete Research 6: 773782.##[74] Unguwarungasri T., Knauss W.G., 1987, The role of damagesoftened material behavior in the fracture of composites and adhesive, International Journal of Fracture 35:221241.##[75] Needleman A., 1987, A continuum model for void nucleation by inclusion debonding, Journal of Applied Mechanics 54: 525531.##[76] Needleman A., 1990, An analysis of decohesion along an imperfect interface, International Journal of Fracture 42: 2140.##[77] Shahwan K.L., Wass A. M., 1997, Nonselfsimilar decohesion along a finite interface of unilaterally constrained delaminations, in: Proceeding of the Royal Society of London 453: 515550.##[78] Ortiz M., Pandolfi A., 1999, Finitedeformation irreversible cohesive elements for threedimensional crackpropagation analysis, International Journal for Numerical Methods in Engineering 44(9): 12671282.##[79] Yu C., 2001, Three Dimensional Cohesive Modeling of Impact Damage of Composites, PhD Thesis, Pasadena, CA.##[80] Corigliano A., Mariani S., Pandolfi A., 2006, Numerical analysis of ratedependent dynamic composite delamination, Composites Science and Technology 66: 766775.##[81] Reddy Jr.E.D., Mello F.J., Guess T.R.,1997, Modeling the initiation and growth of delaminations in composite structures, Journal of Composite Materials 31: 812831.##[82] Petrossian Z., Wisnom M.R., 1998, Prediction of delamination initiation and growth from discontinuous plies using interface elements, Composites: Part A 29: 503515.##[83] Mi Y., Crisfield M.A., Davies G.A.O., Hellweg H.B.,1998, Progressive delamination using interface elements, Journal of Composite Materials 32: 12461273.##[84] Turon A., Camanho P.P., Costa J., Davila C.G., 2006, A damage model for the simulation of delamination in advanced composites under variablemode loading, Mechanics of Materials 38(11): 10721089.##[85] Rice J.R., 1968, A path independent integral and the approximate analysis of strain concentration by notches and cracks, Journal of Applied Mechanics 31: 379386.##[86] Crisfield M.A., Hellweg H.B., Davies G.A.O., 1997, Failure analysis of composite structures using interface elements, in: Proceedings of the NAFEMS Conference on Application of Finite Elements to Composite Materials, London, U.K.##[87] Camanho P.P., Dávila C.G., Ambur D.R., 2001, Numerical Simulation of Delamination Growth in Composite Materials, NASA TP2001211041.##[88] Pandey A.K., Reddy J.N., 1987, A post firstply failure analysis of composite laminated composites, in: Proceedings of the AIAA/ASME/ASCE/AHS/ASC 28th Structures, Structural Dynamics, and Materials Conference, 788797.##[89] Ochoa O.O., Engblom J.J., 1987, Analysis of failure in composites, Composites Science and Technology 28: 87102.##[90] Chang F.K., Chang K.Y., 1987, A progressive damage model for laminated composites containing stress concentrations, Journal of Composite Materials 21: 834855.##[91] Chang F.K., Chang K.Y., 1987, Postfailure analysis of bolted composite joints in tension or shearout Mode failure, Journal of Composite Materials 21: 809833.##[92] Chang F.K., Lessard L.,1989, Modeling compression failure in laminated composite plates containing an open hole, in: Proceedings of the AIAA/ASME/ASCE/AHS/ASC 30th Structures, Structural Dynamics and Materials Conference, 979988.##[93] Reddy Y.S., Reddy J.N., 1992, Linear and nonlinear failure analysis of composite laminated composites with transverse shear, Composites Science and Technology 44: 227255.##[94] Reddy Y.S., Reddy J.N., 1993, Threedimensional finite element progressive failure analysis of composite laminated composites under axial extension, Journal of Composites Technology and Research 15(2): 7387.##[95] Engelstad S.P., Reddy J.N., Knight N.F., 1992, Postbuckling response and failure prediction of graphiteepoxy plates loaded in compression, AIAA Journal 30(8):21062113.##[96] Coats T.W., 1996, A Progressive Damage Methodology for Residual Strength Predictions of CenterCrack Tension Composite Panels, PhD Dissertation, Old Dominion University.##[97] Irvin F.B., Ginty C.A., 1986, Progressive fracture of fiber composites, Journal of Composite Materials 20: 166184.##[98] Huang D., Minnetyan L., 1998, Damage progression in carbonfiber reinforced Ibeams, ASCE Journal of Composites for Construction 2: 3845.##[99] Sleight D.W., 1999, Progressive Failure Analysis Methodology for Laminated Composite Structures, NASA/TP209107.##[100] Knight Jr.N.F., 2006, UserDefined Material Model for Progressive 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Static Analysis of Functionally Graded Annular Plate Resting on Elastic Foundation Subject to an Axisymmetric Transverse Load Based on the Three Dimensional Theory of Elasticity
2
2
In this paper, static analysis of functionally graded annular plate resting on elastic foundation with various boundary conditions is carried out by using a semianalytical approach (SSMDQM). The differential governing equations are presented based on the three dimensional theory of elasticity. The plate is assumed isotropic at any point, while material properties to vary exponentially through the thickness direction and the Poisson’s ratio remain constant. The system of governing partial differential equations can be writhen as state equations by expanding the state variables and using the state space method (SSM) about thickness direction and applying the one dimensional differential quadrature method (DQM) along the radial direction. Interactions between the plate and two parameter elastic foundations are treated as boundary conditions. The stresses and displacements distributions are obtained by solving these state equations. In this study, the influences of the material property graded index, the elastic foundation coefficients (WinklerPasternak), the thickness to radius ratio, and edge supports effect on the bending behavior of the FGM annular plate are investigated and discussed in details.
1

290
304


A
Behravan Rad
Department of Mechanical Engineering, Islamic Azad University, Karaj Branch
Department of Mechanical Engineering, Islamic
Iran
ahmadbehravan@yahoo.com


A
Alibeigloo
Department of Mechanical Engineering, Engineering Faculty, Tarbiat Modares University
Department of Mechanical Engineering, Engineering
Iran


S.S
Malihi
Department of Mechanical Engineering, Islamic Azad University, Karaj Branch
Department of Mechanical Engineering, Islamic
Iran
FGM annular Plate
Elastic foundation
SemiAnalytical Method
differential quadrature
state space
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