ORIGINAL_ARTICLE
Measurement of Variation in Fracture Strength and Calculation of Stress Concentration Factor in Composite Laminates with Circular Hole
In this research, residual strength and stress concentration factor of laminated composites with a circular open hole are studied analytically, numerically and experimentally. The numerical study was carried out using the finite element method. Moreover an analytical study was carried out with developing of point stress criterion. Mechanical testing was performed to determine the un-notched tensile properties and notched strength of composite laminates and characteristic length to reinforcement of the notched strength of composite laminates are determined. Results show that the influence of specimen dimension, notch size, lay ups and material properties are important on residual strength and stress concentration factor of laminated composite materials.
http://jsm.iau-arak.ac.ir/article_514479_509c3e00525d93de836d940c48099af8.pdf
2012-09-29T11:23:20
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226
236
Residual strength
Composite laminates
Characteristic length
Point stress
Stress concentration
A.R
Ghasemi
ghasemi@kashanu.ac.ir
true
1
Department of Mechanical Engineering, University of Kashan
Department of Mechanical Engineering, University of Kashan
Department of Mechanical Engineering, University of Kashan
LEAD_AUTHOR
I
Razavian
true
2
Department of Mechanical Engineering, University of Kashan
Department of Mechanical Engineering, University of Kashan
Department of Mechanical Engineering, University of Kashan
AUTHOR
[1] Rooijen R.V., Sinke J., De-Veris T. J., Zwaag S.V.D., 2004, Property optimization in fiber metal laminates, Journal of Applied Composite Materials 11(2): 63-76.
1
[2] Hagenbeek M., Hengel C., Bosker O.J., Vermeeren C.A.J.R., 2003, Static properties of fiber metal laminates, Journal Of Applied Composite Materials 10(4): 207-222.
2
[3] Nuismer R.J., Whitney J.M., 1976, Uniaxial fracture of composite laminates containing stress concentrations, Fracture Mechanics of Composites ASTM STP 593:117-142.
3
[4] Pipes R.B., Wetherhold R.C., Gillespie J.W., 1979, Notched strength of composite materials, Journal of Composite Materials 13: 148-160.
4
[5] Tan S.C., 1987, Laminated composites containing an elliptical opening. Approximate stress Analyses and fracture models, Journal of Composite Materials 21: 925-948.
5
[6] Chang F.K., Chang K.Y., 1987, A progressive damage model for laminated composites containing stress concentrations, Journal of Composite Materials 21: 834-855.
6
[7] Waddoups M.E., Eisenmann J.R., Kaminski B.E., 1971, Macroscopic fracture mechanics of advanced composite materials, Journal of Composite Materials 5: 446-454.
7
[8] Mar J.W., Lin K.Y., 1979, Characterization of splitting process in graphite/epoxy composites, Journal of Composite Materials 13: 278-287.
8
[9] Backlund J., 1981, Fracture analysis of notched composites, Computer and Structure 13: 145-154.
9
[10] Ericsson I., Aronsson C.G., 1990, Strength of tensile loaded graphite/ epoxy laminates containing cracks, open and filled holes, Journal of Composite Materials 24: 456-482.
10
[11] Shin C.S., Wang C.M., 2004, An improved cohesive zone model for residual notched strength prediction of composite laminates with different orthotropic lay-up, Journal of Composite Materials 38(9): 713-736.
11
[12] Khatibi A., Ye L., 1997, Residual strength simulation of fibre reinforced metal laminates containing a circular hole, Journal of Composite Materials 31(9): 142-163.
12
[13] Spotts M. F., 1998, Design of Machine Elements, Prentice Hall.
13
[14] Ansys Help System, Analysis Guide and Theory Reference, ver10.
14
[15] ASTM, 2003, Standard Test Method For Tensile Properties of Polymer Matrix Composite Materials, Designation D 3039.
15
[16] Wu G., Tan Y., Yang J.M., 2007, Evaluation of residual strength of notched fiber metal laminates, Journal of Materials Science and Engineering, Part A 457: 338-349.
16
17
ORIGINAL_ARTICLE
Displacements and Stresses in Pressurized Thick FGM Cylinders with Varying Properties of Power Function Based on HSDT
Using the inﬁnitesimal theory of elasticity and analytical formulation, displacements and stresses based on the high-order shear deformation theory (HSDT) is presented for axisymmetric thick-walled cylinders made of functionally graded materials under internal and/or external uniform pressure. The material is assumed to be isotropic heterogeneous with constant Poisson’s ratio and radially varying elastic modulus continuously along the thickness with a power function. At first, general governing equations of the FGM thick cylinders are derived by assumptions of the high-order shear deformation theory. Following that, the set of non-homogenous linear differential equations with constant coefficients, for the cylinder under the generalized clamped-clamped conditions have been solved analytically and the effect of loading and inhomogeneity on the stresses and displacements have been investigated. The results are compared with the findings of both first-order shear deformation theory (FSDT) and finite element method (FEM). Finally, the effects of higher order approximations on the stresses and displacements have been studied.
http://jsm.iau-arak.ac.ir/article_514480_4fb0d97c80580ad1756a604c446a3ec7.pdf
2012-09-30T11:23:20
2020-06-03T11:23:20
237
251
Thick cylinders
Shear deformation theory
FGM
HSDT
FEM
M
Ghannad
true
1
Department of Mechanical Engineering, Shahrood University of Technology
Department of Mechanical Engineering, Shahrood University of Technology
Department of Mechanical Engineering, Shahrood University of Technology
AUTHOR
H
Gharooni
gharooni.hamed@gmail.com
true
2
Department of Mechanical Engineering, Shahrood University of Technology
Department of Mechanical Engineering, Shahrood University of Technology
Department of Mechanical Engineering, Shahrood University of Technology
LEAD_AUTHOR
[1] Mirsky I., Hermann G., 1958, Axially motions of thick cylindrical shells, Journal of Applied Mechanics-Transactions of the ASME 25: 97-102.
1
[2] Reddy J.N., Liu C.F., 1985, A higher-order shear deformation theory of laminated elastic shells, International Journal of Engineering Science 23: 319–330.
2
[3] Greenspon J.E., 1960, Vibration of a thick-walled cylindrical shell, comparison of the exact theory with approximate theories, Journal of the Acoustical Society of America 32(5): 571-578.
3
[4] Fukui Y., Yamanaka N., 1992, Elastic analysis for thick-walled tubes of functionally graded materials subjected to internal pressure, The Japan Society of Mechanical Engineers Series I 35(4): 891-900.
4
[5] Simkins T.E., 1994, Amplifications of flexural waves in gun tubes, Journal of Sound and Vibration 172(2): 145-154.
5
[6] Eipakchi H.R., Rahimi G.H., Khadem S.E., 2003, Closed form solution for displacements of thick cylinders with varying thickness subjected to nonuniform internal pressure, Structural Engineering and Mechanics 16(6): 731-748.
6
[7] 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, Engineering Mechanics 134: 601-610.
7
[8] Hongjun X., Zhifei S., Taotao Z., 2006 , Elastic analyses of heterogeneous hollow cylinders, Journal of Mechanics, Research Communications 33(5): 681-691.
8
[9] Zhifei S., Taotao Z., Hongjun X., 2007, Exact solutions of heterogeneous elastic hollow cylinders, Composite Structures 79(1): 140-147.
9
[10] Tutuncu N., 2007, Stresses in thick-walled FGM cylinders with exponentially-varying properties, Engineering Structures 29: 2032-2035.
10
[11] Ghannad M., Rahimi G.H., Khadem S.E., 2010, General plane elasticity solution of axisymmetric functionally graded cylindrical shells, Journal of Modares Technology and Engineering 10(3): 31-43 (in Persian).
11
[12] Ghannad M., Rahimi G.H., Khadem S.E., 2010, General shear deformation solution of axisymmetric functionally graded cylindrical shells, Journal of Modares Technology and Engineering 10(4): 13-26 (in Persian).
12
[13] Zamaninejad M., Rahimi G.H., Ghannad M., 2009, Set of field equations for thick shell of revolution made of functionally graded materials in curvilinear coordinate system, Mechanika 3(77): 18-26.
13
[14] Ghannad M., Zamani Nejad M., Rahimi G.H., 2009, Elastic solution of axisymmetric thick truncated conical shells based on first-order shear deformation theory, Mechanika 5(79): 13-20.
14
[15] Ghannad M., Zamani Nejad M., 2010, Elastic analysis of pressurized thick hollow cylindrical shells with clamped-clamped ends, Mechanika 5(85): 11-18.
15
[16] Eipakchi H.R., 2010, Third-order shear deformation theory for stress analysis of a thick conical shell under pressure, Journal of Mechanics of materials and structures 5(1): 1-17.
16
[17] 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 1(18): 14-21.
17
18
ORIGINAL_ARTICLE
Effect of Magnetic Field on Torsional Waves in Non-Homogeneous Aeolotropic Tube
The effect of magnetic field on torsional waves propagating in non-homogeneous viscoelastic cylindrically aeolotropic material is discussed. The elastic constants and non-homogeneity in viscoelastic medium in terms of density and elastic constant is taken. The frequency equations have been derived in the form of a determinant involving Bessel functions. Dispersion equation in each case has been derived and the graphs have been plotted showing the effect of variation of elastic constants and the presence of magnetic field. The obtained dispersion equations are in agreement with the classical result. The numerical calculations have been presented graphically by using MATLAB.
http://jsm.iau-arak.ac.ir/article_514481_b50ef3e62210a309ec3c93d7707c2271.pdf
2012-09-30T11:23:20
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252
266
Aeolotropic Material
magnetic field
Viscoelastic Solids
Non-Homogeneous
Bessel Functions
R
Kakar
rkakar_163@rediffmail.com
true
1
Principal, DIPS Polytechnic College, Hoshiarpur
Principal, DIPS Polytechnic College, Hoshiarpur
Principal, DIPS Polytechnic College, Hoshiarpur
LEAD_AUTHOR
S
Kakar
true
2
Faculty of Electrical Engineering, SBBSIET Padhiana Jalandhar
Faculty of Electrical Engineering, SBBSIET Padhiana Jalandhar
Faculty of Electrical Engineering, SBBSIET Padhiana Jalandhar
AUTHOR
K.C
Gupta
true
3
Faculty of Science, DIPS Polytechnic College, Hoshiarpur
Faculty of Science, DIPS Polytechnic College, Hoshiarpur
Faculty of Science, DIPS Polytechnic College, Hoshiarpur
AUTHOR
K
Kaur
true
4
Faculty of Science, BMSCT, Muktsar
Faculty of Science, BMSCT, Muktsar
Faculty of Science, BMSCT, Muktsar
AUTHOR
[1] Kaliski S., Petykiewicz J., 1959, Dynamic equations of motion coupled with the field of temperatures and resolving functions for elastic and inelastic bodies in a magnetic field, Proceedings Vibration Problems 1(2):17-35.
1
[2] Narain S., 1978, Magneto-elastic torsional waves in a bar under initial stress, Proceedings Indian Academic Science 87 (5): 137-45.
2
[3] White J.E., Tongtaow C., 1981, Cylindrical waves in transversely isotropic media, Journal of Acoustic Society America 70(4):1147-1155.
3
[4] Das N.C., Bhattacharya S.K., 1978, Axisymmetric vibrations of orthotropic shells in a magnetic field, Indian Journal of Pure Applied Mathematics 45(1): 40-54.
4
[5] Andreou E., Dassios G., 1997, Dissipation of energy for magneto elastic waves in conductive medium, The Quarterly of Applied Mathematics 55: 23-39.
5
[6] Suhubi E.S., 1965, Small torsional oscillations of a circular cylinder with finite electrical conductivity in a constant axial magnetic field, International Journal of Engineering Science 2: 441.
6
[7] Abd-alla A.N., 1994, Torsional wave propagation in an orthotropic magneto elastic hollow circular cylinder, Applied Mathematics and Computation 63: 281-293.
7
[8] Datta B.K., 1985, On the stresses in the problem of magneto-elastic interaction on an infinite orthotropic medium with cylindrical hole, Indian Journal of Theoretical. Physics 33(4): 177-186.
8
[9] Acharya D.P., Roy I., Sengupta S., 2009, Effect of magnetic field and initial stress on the propagation of interface waves in transversely isotropic perfectly conducting media, Acta Mechanics 202: 35–45.
9
[10] Liu M.F., Chang T.P., 2005, Vibration analysis of a magneto-elastic beam with general boundary conditions subjected to axial load and external force, Journal of Sound and Vibration 288(1-2): 399-411.
10
[11] Dai H.L., Wang X., 2006, Magneto-elastodynamic stress and perturbation of magnetic field vector in an orthotropic laminated hollow cylinder, International Journal of Engineering Science 44: 365–378.
11
[12] Tang L., Xu X. M., 2010, Transient torsional vibration responses of finite, semi-infinite and infinite hollow cylinders, Journal of Sound and Vibration 329(8): 1089-1100.
12
[13] Selim M., 2007, Torsional waves propagation in an initially stressed dissipative cylinder, Applied Mathematical Sciences 1(29): 1419 – 1427.
13
[14] Chattopadhyay A., Gupta S., Sahu S., 2011, Dispersion equation of magnetoelastic shear waves in irregular monoclinic layer, Applied Mathematics and Mechanics 32(5): 571-586.
14
[15] Love A.E.H., 1911, Some Problems of Geodynamics, Cambridge University press.
15
[16] Thidé B., 1997, Electromagnetic Field Theory, Dover Publications.
16
[17] Chandrasekharaiahi D.S., 1972, On the propagation of torsional waves in magneto-viscoelastic solids, Tensor( N.S.) 23: 17-20.
17
[18] Watson G.N., 1944, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Second Edition.
18
[19] Green A.E., 1954, Theoretical Elasticity,Oxford University Press.
19
[20] Love A.E.H., 1944, Mathematical Theory of Elasticity, Dover Publications, Forth Edition.
20
[21] Timoshenko S., 1951, Theory of Elasticity, McGraw-Hill Book Company, Second Edition.
21
[22] Westergaard H.M., 1952, Theory of Elasticity and Plasticity, Dover Publications.
22
[23] Christensen R.M., 1971, Theory of Viscoelasticity, Academic Press.
23
24
ORIGINAL_ARTICLE
Nonlinear Vibration and Instability Analysis of a PVDF Cylindrical Shell Reinforced with BNNTs Conveying Viscose Fluid Using HDQ Method
Using harmonic differential quadrature (HDQ) method, nonlinear vibrations and instability of a smart composite cylindrical shell made from piezoelectric polymer of polyvinylidene fluoride (PVDF) reinforced with boron nitride nanotubes (BNNTs) are investigated while clamped at both ends and subjected to combined electro-thermo-mechanical loads and conveying a viscous-fluid. The mathematical modeling of the cylindrical shell and the resulting nonlinear coupling governing equations between mechanical and electrical fields are derived using Hamilton’s principle based on the first-order shear deformation theory (FSDT) in conjunction with the Donnell's non-linear shallow shell theory. The governing equations are discretized via HDQ method, and solved to obtain the resonant frequencies and critical flow velocities associated with divergence and flutter instabilities as well as re-stabilization of the system. Results indicate that the internal moving fluid plays an important role in the instability of the cylindrical shell. Application of a smart material such as PVDF improves significantly the stability and vibration of the system.
http://jsm.iau-arak.ac.ir/article_514482_3fee1f19c9e1a0a36bee2b3454a3b311.pdf
2012-09-30T11:23:20
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267
276
Nonlinear vibration
Instability
Electro-thermo-mechanical loadings
Viscous-fluid-conveying
HDQM
R
Kolahchi
true
1
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University of Kashan
AUTHOR
A
Ghorbanpour Arani
aghorban@kashanu.ac.ir
true
2
Faculty of Mechanical Engineering, University of Kashan---
Institute of Nanoscience & Nanotechnology, University of Kashan
Faculty of Mechanical Engineering, University of Kashan---
Institute of Nanoscience & Nanotechnology, University of Kashan
Faculty of Mechanical Engineering, University of Kashan---
Institute of Nanoscience & Nanotechnology, University of Kashan
LEAD_AUTHOR
[1] Païdoussis M.P., Denise J.P., 1972, Flutter of thin cylindrical shells conveying fluid, Journal of Sound and Vibration 20: 9-26.
1
[2] Amabili M., Garziera R., 2002, Vibrations of circular cylindrical shells with nonuniform constraints, elastic bed and added mass; Part II: shells containing or immersed in axial flow, Journal of Fluids and Structures 16: 31–51.
2
[3] Païdoussis M.P., 2004, Fluid–Structure Interactions: Slender Structures and Axial Flow, Elsevier Academic Press, London.
3
[4] Kotsilkova R., 2007, Thermoset Nanocomposites for Engineering Applications, Smithers, USA.
4
[5] Merharihybrid L., 2002, Nanocomposites for Nanotechnology, Springer Science, New York.
5
[6] Yu V., Christopher T., Bowen R., 2009, Electromechanical Properties in Composites Based on Ferroelectrics, Springer-Verlag, London.
6
[7] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A.A., Loghman, A., 2011, Electro-thermomechanical behaviors of FGPM spheres using analytical method and ANSYS software, Applied Mathematical Modelling 36: 139–157.
7
[8] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A.A., 2011, Effect of material inhomogeneity on electro-thermo-mechanical behaviors of functionally graded piezoelectric rotating cylinder, Applied Mathematical Modelling 35: 2771–2789.
8
[9] Bent A.A., Hagood N.W., Rodgers J.P., 1995, Anisotropic actuation with piezoelectric fiber composites, Journal of Material Sysistem and Structures 6: 338–349.
9
[10] Matsuna H., 2007, Vibration and buckling of cross-ply laminated composite circular cylindrical shells according to a global higher-order theory, International Journal of Mechanical Science 49: 1060-1075.
10
[11] Kadoli R., Ganesan N., 2003, Free vibration and buckling analysis of composite cylindrical shells conveying hot fluid, Composite Structures 60: 19–32.
11
[12] Messina A., Soldatos K.P., 1999, Vibration of completely free composite plates and cylindrical shell panels by a higher-order theory, International Journal of Mechanical Science 41: 891-918.
12
[13] Mosallaie Barzoki A.A., Ghorbanpour Arani A., Kolahchi R., Mozdianfard M.R., 2011, Electro-thermo-mechanical torsional buckling of a piezoelectric polymeric cylindrical shell reinforced by DWBNNTs with an elastic core, Applied Mathematical Modeling 36: 2983–2995.
13
[14] Bellman R.E., Casti J., 1971, Differential quadrature and long-term integration, Journal of Mathematics Analysis and Application 34: 235-238.
14
[15] Bellman R.E., Kashef B.G., Casti J., 1972, Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations, Journal of Computational and Physics 10: 40-52.
15
[16] Farsa J., Kukreti A.R., Bert C.W., 1993, Fundamental frequency analysis of laminated rectangular plates by differential quadrature method, International Journal of Numerical Methods and Engineering 36: 2341–56.
16
[17] Jang S.K., Bert C.W., Striz A.G., 1989, Application of differential quadrature to static analysis of structural components, International Journal of Numerical Methods Engineering 28: 561–77.
17
[18] Sherbourne A.N., Pandey M.D., 1991, Differential quadrature method in the buckling analysis of beams and composite plates, Computers and Structures 40: 903–913.
18
[19] Striz A.G., Wang X., Bert C.W., 1995, Harmonic differential quadrature method and applications to analysis of structural components, Acta Mechanica 111: 85–94.
19
[20] Liew K.M., Teo T.M., Han J.B., 1999, Comparative accuracy of DQ and HDQ methods for three-dimensional vibration analysis of rectangular plates, International Journal of Numerical Methods and Engineering 45: 1831–1848.
20
[21] Civalek Ö., 2004, Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns, Engineering Structures 26: 171–186.
21
[22] Amabili M., 2008, Nonlinear Vibrations and Stability of Shells and Plates, Cambridge University Press, USA.
22
[23] Wang L., Ni Q., 2009, A reappraisal of the computational modelling of carbon nanotubes conveying viscous fluid, Mechanics Research Communications 36: 833–837.
23
[24] Liew K.M., Han J.B., Xiao Z.M., 1996, Differential Quadrature Method for Thick Symmetric Cross-Ply Laminates with First-Order Shear Flexibility, International Journal of Solids and Structures 33: 2647-2658.
24
[25] Shu C., Richards B.E., 1992, Application of generalized differential quadrature to solve two-dimensional incompressible Navier– Stokes equations, International Journal of Numerical Methods in Fluids 15: 791–798.
25
[26] Malekzadeh P., 2008, Nonlinear free vibration of tapered Mindlin plates with edges elastically restrained against rotation using DQM, Thin-Walled Structures 46: 11–26.
26
[27] Chen W., Shu C., He W., Zhong, T., 2000, The applications of special matrix products to differential quadrature solution of geometrically nonlinear bending of orthotropic rectangular plates, Computers and Structures 74: 65–76.
27
[28] Zhou X., 2012, Vibration and stability of ring-stiffened thin-walled cylindrical shells conveying fluid, Acta Mechanica Solida Sinica 25:168–176.
28
29
ORIGINAL_ARTICLE
Effect of Temperature Changes on Dynamic Pull-in Phenomenon in a Functionally Graded Capacitive Micro-beam
In this paper, dynamic behavior of a functionally graded cantilever micro-beam and its pull-in instability, subjected to simultaneous effects of a thermal moment and nonlinear electrostatic pressure, has been studied. It has been assumed that the top surface is made of pure metal and the bottom surface from a metal–ceramic mixture. The ceramic constituent percent of the bottom surface ranges from 0% to 100%. Along with the Volume Fractional Rule of material, an exponential function has been applied to represent the continuous gradation of the material properties through the micro-beam thickness. Attentions being paid to the ceramic constituent percent of the bottom surface, five different types of FGM micro-beams have been studied. Nonlinear integro-differential thermo-electro-mechanical equation based on Euler–Bernoulli beam theory has been derived. The governing equation in the static case has been solved using Step-by-Step Linearization Method and Finite Difference Method. Fixed points or equilibrium positions and singular points of the FGM micro-beam have been determined and shown in the state control space. In order to study stability of the fixed points, beam motion trajectories have been drawn, with different initial conditions, in the phase plane. In order to find the response of the micro-beam to a step DC voltage, the nonlinear equation of motion has been solved using Galerkin-based reduced-order model and time histories and phase portrait for different applied voltages and various primal temperatures have been illustrated. The effects of temperature change and electrostatic pressure on the deflection and stability of FGM micro-beams having various amounts of the ceramic constituent have been studied .
http://jsm.iau-arak.ac.ir/article_514483_a2b474cdcab902c31e0dea12980a35e7.pdf
2012-09-30T11:23:20
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277
295
MEMS
FGM
Cantilever micro-beam
Thermal
Electrical
Dynamic pull-in voltage
Instability
B
Mohammadi-Alasti
behzad.alasti@gmail.com
true
1
Department of Agricultural Machinery Engineering, Bonab Branch, Islamic Azad University
Department of Agricultural Machinery Engineering, Bonab Branch, Islamic Azad University
Department of Agricultural Machinery Engineering, Bonab Branch, Islamic Azad University
LEAD_AUTHOR
G
Rezazadeh
true
2
Department of Mechanical Engineering, Urmia University
Department of Mechanical Engineering, Urmia University
Department of Mechanical Engineering, Urmia University
AUTHOR
M
Abbasgholipour
true
3
Department of Agricultural Machinery Engineering, Bonab Branch, Islamic Azad University
Department of Agricultural Machinery Engineering, Bonab Branch, Islamic Azad University
Department of Agricultural Machinery Engineering, Bonab Branch, Islamic Azad University
AUTHOR
[1] Simsek M., 2010, Vibration analysis of a functionally graded beam under a moving mass by using different beam theories, Composite Structures 92: 904–917.
1
[2] Sankar B.V., 2001, An elasticity solution for functionally graded beams, Composite Science and Technology 61(5): 689–696.
2
[3] Zhong Z., Yu T., 2007, Analytical solution of a cantilever functionally graded beam, Composites Science and Technology 67: 481-488.
3
[4] Chakraborty A., Gopalakrishnan S., Reddy J.N., 2003, A new beam finite element for the analysis of functionally graded materials, International Journal of Mechanic Science 45(3): 519–539.
4
[5] Chakraborty A., Gopalakrishnan S., 2003, A spectrally formulated finite element for wave propagation analysis in functionally graded beams, International Journal of Solids and Structures 40(10): 2421–2448.
5
[6] Kapuria S., Bhattacharyya M., Kumar A.N., 2008, Bending and free vibration response of layered functionally graded beams: A theoretical model and its experimental validation, Composite Structures 82(3): 390-402.
6
[7] Aydogdu M., Taskin V., 2007, Free vibration analysis of functionally graded beams with simply supported edges, Material Design 28(5): 1651–1656.
7
[8] Gharib A., Salehi M., Fazeli S., 2008, Deflection control of functionally graded material beams with bonded piezoelectric sensors and actuators, Materials Science and Engineering 498: 110-114.
8
[9] Piovan T., Sampaio R., 2008, Vibrations of axially moving flexible beams made of functionally graded materials, Thin-Walled Structures 46: 112-121.
9
[10] Xiang H.J., Shi Z.F., 2009, Static analysis for functionally graded piezoelectric actuators or sensors under a combined electro-thermal load, European Journal of Mechanics A/Solids 28: 338-346.
10
[11] Ying J., Lü C.F., Chen W.Q., 2008, Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations, Composite Structures 84(3): 209–219.
11
[12] Sina S.A., Navazi H.M., Haddadpour H., 2009, An analytical method for free vibration analysis of functionally graded beams, Materials and Design 30(3): 741–747.
12
[13] Simsek M., Kocatürk T., 2009, Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load, Composite Structures 90(4): 465-473.
13
[14] Simsek M., 2010, Non-linear vibration analysis of a functionally graded Timoshenko beam under action of a moving harmonic load, Composite Structures 92(10): 2532-2546.
14
[15] Simsek M., 2010, Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories, Nuclear Engineering and Design 240: 697-705.
15
[16] Khalili S.M.R., Jafari A.A., Eftekhari S.A., 2010, A mixed Ritz-DQ method for forced vibration of functionally graded beams carrying moving loads, Composite Structures 92(10): 2497-2511.
16
[17] Mahi A., Adda B.E.A., Tounsi A., Mechab I., 2010, An analytical method for temperature-dependent free vibration analysis of functionally graded beams with general boundary conditions, Composite Structures 92(8): 1877-1887.
17
[18] Craciunescu C.M., Wuttig M., 2003, New ferromagnetic and functionally grade shape memory alloys, Journal of Optoelectron Advance Material 5(1): 139–146.
18
[19] Fu Y.Q., Du H.J., Zhang S., 2003, Functionally graded TiN/TiNi shape memory alloy films, Journal of Materials Letters 57(20): 2995–2999.
19
[20] Fu Y.Q., Du H.J., Huang W.M., Zhang S., Hu M., 2004, TiNi-based thin films in MEMS applications: a review, Journal of Sensors and Actuators A 112(2–3): 395–408.
20
[21] Witvrouw A., Mehta A., 2005, The use of functionally graded poly-SiGe layers for MEMS applications, Journal of Functionally Graded Materials VIII 492–493: 255–260.
21
[22] Lee Z., Ophus C., Fischer L.M., Nelson-Fitzpatrick N., Westra K.L., Evoy S., et al., 2006, Metallic NEMS components fabricated from nanocomposite Al–Mo films, Journal of Nanotechnology 17(12): 3063–3070.
22
[23] Rahaeifard M., Kahrobaiyan M.H., Ahmadian M.T., 2009, Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials, Proceedings of the 3rd international conference on micro-and nanosystems (MNS3), San Diego, CA, USA.
23
[24] Senturia S., 2001, Microsystem Design, Norwell, MA: Kluwer.
24
[25] Sadeghian H., Rezazadeh G., Osterberg P., 2007, Application of the generalized differential quadrature method to the Study of Pull-In Phenomena of MEMS switches, Journal of Micro Electromechanical System IEEE/ASME 16(6): 1334-1340.
25
[26] Rezazadeh G., Khatami F., Tahmasebi A., 2007, Investigation of the torsion and bending effects on static stability of electrostatic torsional micromirrors, Journal of Microsystem Technologies 13(7): 715-722.
26
[27] Sazonova V., 2006, A Tunable Carbon Nanotube Resonator, Ph.D. Thesis, Cornell University.
27
[28] Rezazadeh G., Tahmasebi A., Zubtsov M., 2006, Application of piezoelectric layers in electrostatic MEM actuators: controlling of Pull-in Voltage, Journal of Microsystem Technologies 12(12): 1163-1170.
28
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[30] Mehdaoui A., Pisani M.B., Tsamados D., Casset F., Ancey P., Ionescu A.M., 2007, MEMS tunable capacitors with fragmented electrodes and rotational electro-thermal drive, Journal of Microsystem Technologies 13(11): 1589-1594.
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[31] Zhang Y., Zhao Y., 2006, Numerical and analytical study on the pull-in instability of micro- structure under electrostatic loading, Journal of Sensors and Actuators A: Physical 127: 366-367.
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[33] Hasanyan D.J., Batra R.C., Harutyunyan S., 2008, Pull-in instabilities in functionally graded micro-thermo electromechanical systems, Journal of Thermal Stresses 31: 1006–1021.
33
[34] Jia X.L., Yang J., Kitipornchai S., 2010, Characterization of FGM micro-switches under electrostatic and Casimir forces, Materials Science and Engineering 10: 012178.
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[35] Zhou L., Tang D., 2007, A functionally graded structural design of mirrors for reducing their thermal deformations in high-power laser systems by finite element method, Optics & Laser Technology 39: 980–986.
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[37] Erdogan F., Wu B.H., 1996, Crack problems in FGM layers under thermal stresses, Journal of Thermal Stresses 19: 237–265.
37
[38] Asghari M., Ahmadian M.T., Kahrobaiyan M.H., Rahaeifard M., 2010, On the size-dependent behavior of functionally graded micro-beams, Journal of Materials and Design 31: 2324–2329.
38
[39] Martin H., 2009, Sadd, Elasticity, Theory, Applications, and Numerics, Academic Press, second Edition.
39
[40] Mohammadi-Alasti B., Rezazadeh G., Borgheei A.M., Minaei S., Habibifar R., 2011, On the mechanical behavior of a functionally graded micro-beam subjected to a thermal moment and nonlinear electrostatic pressure, Composite Structures 93: 1516–1525.
40
[41] Sun Y., Fang D., Soh A.K., 2006, Thermoelastic damping in micro-beam resonators, International Journal of Solids and Structures 43: 3213-3229.
41
[42] Younis M., Nayfeh A.H., 2003, A study of the nonlinear response of a resonant micro-beam to an electric actuation, Journal of Nonlinear Dynamics 31: 91–117.
42
[43] Neubrand A., Chung T.J., Steffler E.D., Fett T., Rodel J., 2002, Residual stress in functionally graded plates, Journal of Material Research 17(11): 2912–2920.
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[44] Bin J., Wanji C., 2010, A new analytical solution of pure bending beam in couple stress elasto-plasticity, Theory and applications, International Journal of Solids and Structures 47: 779–785.
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[45] Abbasnejad B., Rezazadeh G., 2012, Mechanical behavior of a FGM micro-beam subjected to a nonlinear electrostatic pressure, International Journal of Mechanics and Materials in Design, 8:381–392 .
45
[46] Rezazadeh G., Pashapour M., Abdolkarimzadeh F., 2011, Mechanical behavior of a bilayer cantilever microbeam subjected to electrostatic force, mechanical shock and thermal moment, International Journal of Applied Mechanics, 3(3): 543–561.
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[47] Rezazadeh G., Fathalilou M., 2011, Pull-in Voltage of electrostatically-actuated microbeams in terms of lumped model Pull-in Voltage using novel design corrective coefficients, sensing and imaging, AnInternational Journal 12(3-4):117-131.
47
[48] Bhangale R.K., Ganesan N., Padmanabhan C., 2006, Linear thermoelastic buckling and free vibration behavior of functionally graded truncated conical shells, Journal of Sound and Vibration 292: 341–371.
48
[49] Yang J., Liew K.M., Wu Y.F., Kitipornchai S., 2006, Thermo-mechanical post-buckling of FGM cylindrical panels with temperature-dependent properties, International Journal of Solids Structures 43: 307–324.
49
[50] Ke L.L., Yang J., Kitipornchai S., 2010, Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams, Composite Structures 92: 676–683.
50
[51] Alibeigloo A., 2010, Thermoelasticity analysis of functionally graded beam with integrated surface piezoelectric layers, Composite Structures 92: 1535–1543.
51
[52] Anandakumar G., Kim J.H., 2010, On the modal behavior of a three-dimensional functionally graded cantilever beam: Poisson’s ratio and material sampling effects, Composite Structures 92: 1358–1371.
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[53] Azizi S., 2008, Design of micro accelerometer to use as airbag activator, MSc thesis, Mechanical Engineering Department, Tarbiat Modares University, Tehran, Iran, 53–54, (in Persian).
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[54] Seydel R., 2009, Practical Bifurcation and Stability Analysis, Springer-Verlag New York, LLC, Third Edition.
54
[55] Kuznetsov Y.A., 1998, Elements of Applied Bifurcation Theory, Springer-Verlag, New York, Second Edition.
55
56
ORIGINAL_ARTICLE
Buckling of Piezoelectric Composite Cylindrical Shell Under Electro-thermo-mechanical Loading
Using principle of minimum total potential energy approach in conjunction with Rayleigh-Ritz method, the electro-thermo-mechanical axial buckling behavior of piezoelectric polymeric cylindrical shell reinforced with double-walled boron-nitride nanotube (DWBNNT) is investigated. Coupling between electrical and mechanical fields are considered according to a representative volume element (RVE)-based micromechanical model. This study indicates how buckling resistance of composite cylindrical shell may vary by applying thermal and electrical loads. Applying the reverse voltage or decreasing the temperature, also, increases the critical axial buckling load. This work showed that the piezoelectric BNNT generally enhances the buckling resistance of the composite cylindrical shell.
http://jsm.iau-arak.ac.ir/article_514484_68a4ad3a78ee2c54fe0eab68f6acd32c.pdf
2012-09-30T11:23:20
2020-06-03T11:23:20
296
306
Axial buckling
DWBNNT
Cylindrical shell
Piezoelectric polymeric
Energy method
Electro-thermo-mechanical loadings
A
Ghorbanpour Arani
aghorban@kashanu.ac.ir
true
1
Faculty of Mechanical Engineering, University of Kashan---
Institute of Nanoscience & Nanotechnology, University of Kashan, Kashan
Faculty of Mechanical Engineering, University of Kashan---
Institute of Nanoscience & Nanotechnology, University of Kashan, Kashan
Faculty of Mechanical Engineering, University of Kashan---
Institute of Nanoscience & Nanotechnology, University of Kashan, Kashan
LEAD_AUTHOR
S
Shams
true
2
Department of Mechanical Engineering, Faculty of Engineering, Mobarakeh Branch, Islamic Azad University
Department of Mechanical Engineering, Faculty of Engineering, Mobarakeh Branch, Islamic Azad University
Department of Mechanical Engineering, Faculty of Engineering, Mobarakeh Branch, Islamic Azad University
AUTHOR
S
Amir
true
3
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University of Kashan
AUTHOR
M.J
Maboudi
true
4
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University of Kashan
AUTHOR
[1] Rubio A., Corkill J.L., Cohen M.L., 1994, Theory of graphitic boron nitride nanotubes, Physical Review B 49: 5081-5084.
1
[2] Blasé X., Rubio A., Louie S.G., Cohen M.L., 1994, Stability and Band Gap Constancy of Boron Nitride Nanotubes, Europhysics Letters 28:335-340.
2
[3] Chopra N.G., Luyken R.J., Cherrey K., Crespi V.H., Cohen M.L., Louie S.G., Zettl A., 1995, Boron nitride nanotubes, Science 269: 966-967.
3
[4] Chen Y., Zou J., Campbell S.J., Caer G.L., 2004, Boron nitride nanotubes: Pronounced resistance to oxidation, Applied Physics Letters 84: 2430-2432.
4
[5] Sai N., Mele E.J., 2003, Microscopic theory for nanotube piezoelectricity, Physical Review B 68: 241405-241408.
5
[6] Haque A., Ramasetty A., 2005, Theoretical study of stress transfer in carbon nanotube reinforced polymer matrix composites, Composite Structures 71: 68-77.
6
[7] Ghorbanpour Arani A., Maghamikia Sh., Mohammadimehr M., Arefmanesh A., 2011, Buckling analysis of laminated composite rectangular plates reinforced by SWCNTs using analytical and finite element methods, Journal of Mechanical Science and Technology 25: 809-820.
7
[8] Odegard G.M., Gates T.S., Wise K.E., Park C., Siochi E.J., 2003, Constitutive modeling of nanotube-reinforced polymer composites, Composites Science and Technology 63: 1671-1687.
8
[9] Vodenitcharova T., Zhang L.C., 2006, Bending and local buckling of a nanocomposite beam reinforced by a single-walled carbon nanotube, International Journal of Solids and Structures 43: 3006-3024.
9
[10] Gao X.L., Li K., 2005, A shear-lag model for carbon nanotube-reinforced polymer composites, International Journal of Solids and Structures 42: 1649-1667.
10
[11] Shen H.S., Zhang C.L., 2010, Thermal buckling and post buckling behavior of functionally graded carbon nanotube-reinforced composite plates, Materials and Design 31: 3403-3411.
11
[12] Salehi-Khojin A., Jalili N., 2008, Buckling of boron nitride nanotube reinforced piezoelectric polymeric composites subject to combined electro-thermo-mechanical loadings, Composites Science and Technology 68: 1489-1501.
12
[13] Salehi-Khojin A., Jalili N., 2008, A comprehensive model for load transfer in nanotube reinforced piezoelectric polymeric composites subjected to electro-thermo-mechanical loadings, Composites Part B Engineering 39: 986-998.
13
[14] Tan P., Tong L., 2001, Micro-electromechanics models for piezoelectric-fiber-reinforced composite materials, Composites Science and Technology 61: 759-69.
14
[15] Brockmann T.H., 2009, Theory of Adaptive Fiber Composites From Piezoelectric Material Behavior to Dynamics of Rotating Structures (Solid Mechanics and Its Applications), Springer, USA.
15
[16] Jone R.M., 1975, Mechanics of Composite Materials, Scripta Book Company, Washington.
16
[17] Whitney J.M., 1987, Structural Analysis of Laminated Anisotropic Plates, Technomic Publishing Company, Lancaster.
17
[18] Sanders J.L., 1959, An Improved First-Approximation Theory for Thin Shells, Technical Report NASA TR R-24, National Aeronautics and Space Administration, Langley Research Center.
18
[19] Koiter W.T., 1960, A Consistent First Approximation in the Ggeneral Theory of Thin Elastic Shells. In Proceedings of the Symposium on the Theory of Thin Elastic Shells, Internation Union of Theoretical and Applied Mechanics North-Holland, Amsterdam.
19
[20] Vinson J.R., 2005, Plate and Panel Structures of Isotropic: Composite and Piezoelectric Materials, Including Sandwich Construction, Springer, USA.
20
[21] Donnell L.H., 1933, Stability of thin-walled tubes under torsion, Technical Report NACA Report No. 479, National Advisory Committee for Aeronautics.
21
[22] Ye L., Lun G., Ong L.S., 2011, Buckling of a thin-walled cylindrical shell with foam core under axial compression, Thin Walled Structure 49: 106–111.
22
23
ORIGINAL_ARTICLE
Vibrations of Circular Plates with Guided Edge and Resting on Elastic Foundation
In this paper, transverse vibrations of thin circular plates with guided edge and resting on Winkler foundation have been studied on the basis of Classical Plate Theory. Parametric investigations on the vibration of circular plates resting on elastic foundation have been carried out with respect to various foundation stiffness parameters. Twelve vibration modes are presented. The location of the stepped region with respect to foundation stiffness parameter is presented.
http://jsm.iau-arak.ac.ir/article_514485_1353cc80bf2ea74ec12abca96ae3859f.pdf
2012-09-30T11:23:20
2020-06-03T11:23:20
307
312
Plate
frequency
Guided edge
Elastic foundation
L.B
Rao
bhaskarbabu_20@yahoo.com
true
1
School of Mechanical and Building Sciences, VIT University, Chennai Campus, Vandalur-Kelambakkam Road
School of Mechanical and Building Sciences, VIT University, Chennai Campus, Vandalur-Kelambakkam Road
School of Mechanical and Building Sciences, VIT University, Chennai Campus, Vandalur-Kelambakkam Road
LEAD_AUTHOR
C.K
Rao
true
2
Department of Mechanical Engineering, Gurnanak Institutions and Technical Campus, Ibrahimpatnam
Department of Mechanical Engineering, Gurnanak Institutions and Technical Campus, Ibrahimpatnam
Department of Mechanical Engineering, Gurnanak Institutions and Technical Campus, Ibrahimpatnam
AUTHOR
[1] Timoshenko S., Krieger S.W., 1959, Theory of Plates and Shells, McGraw-Hill Book Company Inc, Newyork, Chapter 8:265.
1
[2] Leissa A.W., 1969, Vibration of Plates (NASA SP-160), Office of Technology Utilization, Washington, DC.
2
[3] Szilard R., 2004, Theories and Applications of Plate Analysis, Classical Numerical and Engineering Methods, John Wiley & Sons Inc, Chapter 3.
3
[4] Chakraverty S., 2009, Vibration of Plates, CRC Press, Taylor & Francis Group , Chapter 4.
4
[5] Wang C.Y., Wang C.M., 2003, Fundamental frequencies of circular plates with internal elastic ring support, Journal of Sound and Vibration 263: 1071-1078.
5
[6] Leissa A. W., 1993, Vibration of Plates, Acoustical Society of America, Sewickley, PA.
6
[7] Salari M., Bert C. M., Striz A.G., 1987, Free Vibration of a Solid Circular Plate free at its edge and attached to a Winkler foundation, Journal of Sound and Vibration 118: 188-191.
7
[8] Ascione L., Grimaldi A., 1984, Unilateral contact between a plate and an elastic foundation, Mechanica 19: 23-233.
8
[9] Kang K.H., Kim K.J., 1996, Modal properties of beams and plates on resilient supports with rotational and translational complex stiffness, Journal of Sound and Vibration 190(2): 207-220.
9
[10] Zheng X. J., Zhou Y. H., 1988, Exact solution of nonlinear circular plate on elastic-foundation, Journal of Engineering Mechanics-ASCE 114: 1303-1316.
10
[11] Ghosh A. K., 1997, Axisymmetric dynamic response of a circular plate on an elastic foundation, Journal of Sound and Vibration 205: 112-120.
11
[12] Winkler E., 1867, Die Lehre von der Elasticitaet and Festigkeit, Prag, Dominicus.
12
[13] Soedel W., 1993, Vibrations of shells and plates, Mareel Dekker, Inc.
13
[14] Weisman Y., 1970, On foundations that react in compression only, Journal of Applied Mechanics 37: 1019-1030.
14
[15] Dempsey J. P., Keer L. M., Patel N. B., Glasser M. L.,1984, Contact between plates and unilateral supports, Journal of Applied Mechanics 51: 324-328.
15
[16] Celep Z., 1988, Circular plate on tensionless Winkler foundation, Journal of Engineering Mechanics 114(10): 1723-1739.
16
17
ORIGINAL_ARTICLE
Semi-analytical Solution for Time-dependent Creep Analysis of Rotating Cylinders Made of Anisotropic Exponentially Graded Material (EGM)
In the present paper, time dependent creep behavior of hollow circular rotating cylinders made of exponentially graded material (EGM) is investigated. Loading is composed of an internal pressure, a distributed temperature field due to steady state heat conduction with convective boundary condition and a centrifugal body force. All the material properties are assumed to be exponentially graded along radius. A semi analytical solution followed by the method of successive approximation has been developed to obtain history of stresses and deformations during creep evolution of the EGM rotating cylinder. The material creep constitutive model is defined by the Bailey-Norton time-dependent creep law. A comprehensive comparison has been made between creep response of homogenous and non-homogenous cylinder. It has been found that the material in-homogeneity exponent has a significant effect on creep response of the EGM cylinder. It has been concluded that using exponentially graded material significantly decreases creep strains, stresses and deformations of the EGM rotating cylinder.
http://jsm.iau-arak.ac.ir/article_514486_ff02335f3f52b2a4016bac1a60314bab.pdf
2012-09-30T11:23:20
2020-06-03T11:23:20
313
326
EGM Rotating cylinder
Bailey-Norton creep law
History of stresses
A
Loghman
aloghman@kashanu.ac.ir
true
1
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University of Kashan
LEAD_AUTHOR
V
Atabakhshian
true
2
Department of Mechanical Engineering, Faculity of Engineering, Bu-Ali Sina University
Department of Mechanical Engineering, Faculity of Engineering, Bu-Ali Sina University
Department of Mechanical Engineering, Faculity of Engineering, Bu-Ali Sina University
AUTHOR
[1] Nie G.J., Batra R.C., 2010, Material tailoring and analysis of functionally graded isotropic and incompressible linear elastic hollow cylinders, Composite Structures 92 : 265–274.
1
[2] Bayat M., Sahari B.B., Saleem M., Ali A., Wong S.V., 2009, Bending analysis of a functionally graded rotating disk based on the first order shear deformation theory, Applied Mathematical Modelling 33 : 4215–4230.
2
[3] Ghorbanpour Arani A., Loghman A., Abdollahitaher A., Atabakhshian V., 2011, Electrothermomechanical behaviour of a radially polarized functionally graded piezoelectric cylinder, Journal of Mechanics of Materials and Structures 6 (6): 869–882.
3
[4] You L.H., Zhang J.J., You X.Y., 2005, Elastic analysis of internally pressurized thick-walled spherical pressure vessel of functionally graded materials, International Journal ofPressure Vessels and Piping 82: 347–354.
4
[5] Fukui Y., Yamanaka N., 1992, Elastic analysis for thick-walled tubes of functionally graded material subjected to internal pressure, JSME International Journal Series I 35: 379-385.
5
[6] Loghman A., Wahab M.A., 1996, Creep damage simulation of thick-walled tubes using the theta projection concept, International Journal ofPressure Vessels and Piping 67: 105-111.
6
[7] Evans R.W., Parker J.D., Wilsher B., 1992, The theta projection concept a model based approach to design and life extention of engineering plant, International Journal ofPressure Vessels and Piping 50: 60-147.
7
[8] Loghman A., Shokouhi N., 2009, Creep damage evaluation of thick-walled spheres using a long-term creep constitutive model, JournalofMechanical ScienceandTechnology 23: 2577-2582.
8
[9] Aleayoub S.M.A., Loghman A., 2010, Creep stress redistribution Analysis of thick-walled FGM spheres, Journal of solid Mechanics 2 (2) :115-128.
9
[10] Chen J.J., Tu S.T., Xuan F.Z., Wang Z.D., 2007, Creep analysis for a functionally graded cylinder subjected to internal and external pressure, The Journal of Strain Analysis Engineering Design 42: 69-77.
10
[11] You L.H., Ou H., Zheng Z.Y., 2007, Creep deformations and stresses in thick-walled cylindrical vessels of functionally graded materials subject to internal pressure, Composite Structures 78:285-291.
11
[12] Singh T., Gupta V.K., 2011, Effect of anisotropy on steady state creep in functionally graded cylinder, Composite Structures 93:747-758.
12
[13] Yang Y.Y., 2000, Time-dependent stress analysis in functionally graded material, International Journal of Solids and Structures 37:7593-7608.
13
[14] Xuan F.Z., Chen J.J., Wang Z., Tu S.T., 2009, Time-dependent deformation and fracture of multi-material systems at high temperature, International Journal ofPressure Vessels and Piping 86: 604-615.
14
[15] Loghman A., Ghorbanpour Arani A., Amir S., Vajedi A., 2010, Magnetothermoelastic creep analysis of functionally graded cylinders, International Journal ofPressure Vessels and Piping 87:389-395.
15
[16] Loghman A., Aleayoub S.A.M., Hasani Sadi M., 2012, Time-dependent magnetothermoelastic creep Modeling of FGM spheres using method of successive elastic solution, Applied Mathematical Modelling 36: 836-845.
16
[17] Loghman A., Ghorbanpour Arani A., Aleayoub S.A.M., 2011, Time-dependent creep stress redistribution analysis of functionally graded spheres, Mechanics Time-Dependent Materials 15: 353-365.
17
[18] Loghman A., Ghorbanpour Arani A., Shajari A.R., Amir S., 2011, Time-dependent thermoelastic creep analysis of rotating disk made of Al–SiC composite, Archive of Applied Mechanics 81:1853-1864.
18
[19] Hosseini SM., Akhlaghi M., Shakeri M., 2007, Transient heat conduction in functionally graded thick hollow cylinders by analytical method, International Journal of Heat and Mass Transfer 43: 669-675.
19
[20] Abramowitz M., Stegun I., 1965, Handbook of Mathematical Functions, New York: Dover Publications Inc.
20
[21] Hosseini Kordkheili S.A., Naghdabadi R., 2007, Thermo-elastic analysis of a functionally graded rotating disk, Composite Structures 79: 508-516.
21
[22] Penny RK., Marriott DL., 1995, Design for creep, London, Chapman & Hall.
22
23