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http://dx.doi.org/10.12989/scs.2019.33.3.463

Creep analysis of a rotating functionally graded simple blade: steady state analysis  

Mirzaei, Manouchehr Mohammad Hosseini (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
Arefi, Mohammad (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
Loghman, Abbas (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
Publication Information
Steel and Composite Structures / v.33, no.3, 2019 , pp. 463-472 More about this Journal
Abstract
Initial thermo-elastic and steady state creep deformation of a rotating functionally graded simple blade is studied using first-order shear deformation theory. A variable thickness model for cantilever beam has been considered. The blade geometry and loading are defined as functions of length so that one can define his own blade profile and loading using any arbitrary function. The blade is subjected to a transverse distributed load, an inertia body force due to rotation and a distributed temperature field due to a thermal gradient between the tip and the root. All mechanical and thermal properties except Poisson's ratio are assumed to be longitudinally variable based on the volume fraction of reinforcement. The creep behaviour is modelled by Norton's law. Considering creep strains in stress strain relation, Prandtl-Reuss relations, Norton' law and effective stress relation differential equation in term of effective creep strain is established. This differential equation is solved numerically. By effective creep strain, steady state stresses and deflections are obtained. It is concluded that reinforcement particle size and form of distribution of reinforcement has significant effect on the steady state creep behavior of the blade.
Keywords
simple blade; functionally graded material; steady state creep; first-order shear deformation theory (FSDT);
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Times Cited By KSCI : 4  (Citation Analysis)
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1 Almasi, A. (2015), "Modern guidelines and latest case studies on condition monitoring of rotating equipment", Austral. J. Mech. Eng., 13(3), 172-186. https://doi.org/10.1080/14484846.2015.1093228   DOI
2 Anitescu, C., Atroshchenko, E., Alajlan, N. and Rabczuk, T. (2019), "Artificial neural network methods for the solution of second order boundary value problems", Comput. Mater. Continua, 59, 345-359.   DOI
3 Arefi, M. and Zenkour, A. (2017a), "Electro-magneto-elastic analysis of a three-layer curved beam", Smart. Struct. Syst., Int. J., 19(6), 695-703. https://doi.org/10.12989/sss.2017.19.6.695
4 Arefi, M. and Zenkour, A.M. (2017b), "Size-dependent free vibration and dynamic analyses of piezo-electro-magnetic sandwich nanoplates resting on viscoelastic foundation", Phys. B: Cond. Matt., 521, 188-197. https://doi.org/10.1016/j.physb.2017.06.066   DOI
5 Arefi, M. and Zenkour, A.M. (2017c), "Transient sinusoidal shear deformation formulation of a size-dependent three-layer piezo-magnetic curved nanobeam", Acta. Mech., 228(10), 3657-3674. https://doi.org/10.1007/s00707-017-1892-6   DOI
6 Arefi, M. and Zenkour, A.M. (2018a), "Employing the coupled stress components and surface elasticity for nonlocal solution of wave propagation of a functionally graded piezoelectric Love nanorod model", J. Intell. Mater. Syst. Struct., 28(17), 2403-2413. https://doi.org/10.1177/1045389X17689930   DOI
7 Arefi, M. and Zenkour, A.M. (2018b), "Size-dependent electro-elastic analysis of a sandwich microbeam based on higher-order sinusoidal shear deformation theory and strain gradient theory", J. Intell. Mater. Syst. Struct., 29(7), 1394-1406. https://doi.org/10.1177/1045389X17733333   DOI
8 Arefi, M., Rahimi, G.H. and Khoshgoftar, M.J. (2012), "Exact solution of a thick walled functionally graded piezoelectric cylinder under mechanical, thermal and electrical loads in the magnetic field", Smart. Struct. Syst., Int. J., 9(5), 427-439. https://doi.org/10.12989/sss.2012.9.5.427   DOI
9 Arefi, M., Faegh, R.K. and Loghman, A. (2016), "The effect of axially variable thermal and mechanical loads on the 2D thermoelastic response of FG cylindrical shell", J. Thermal Stresses, 39(12), 1539-1559. https://doi.org/10.1080/01495739.2016.1217178   DOI
10 Arefi, M., Zamani, M.H. and Kiani, M. (2018), "Size-dependent free vibration analysis of three-layered exponentially graded nanoplate with piezomagnetic face-sheets resting on Pasternak's foundation", J. Intell. Mater. Syst. Struct., 29(5), 774-786. https://doi.org/10.1177/1045389X17721039   DOI
11 Chakraborty, A., Gopalakrishnan, S. and Reddy, J.N. (2003), "A new beam finite element for the analysis of functionally graded materials", Int. J. Mech. Sci., 45(3), 519-539. https://doi.org/10.1016/S0020-7403(03)00058-4   DOI
12 Chau-Dinh, T., Zi, G., Lee, P.-S., Rabczuk, T. and Song, J.-H. (2012), "Phantom-node method for shell models with arbitrary cracks", Comput. Struct., 92-93, 242-256. https://doi.org/10.1016/j.compstruc.2011.10.021   DOI
13 Davoudi Kashkoli, M. and Nejad, M. (2018), "Time-dependent creep analysis and life assessment of 304 L austenitic stainless steel thick pressurized truncated conical shells", Steel Compos. Struct., Int. J., 28(3), 349-362. https://doi.org/10.12989/scs.2018.28.3.349
14 Duy, H., Van, T. and Noh, H.-C. (2014), Eigen analysis of functionally graded beams with variable cross-section resting on elastic supports and elastic foundation", Struct. Eng. Mech., Int. J., 52, 1033-1049. https://doi.org/10.12989/sem.2014.52.5.1033   DOI
15 Filippi, M., Carrera, E. and Zenkour, A.M. (2015), "Static analyses of FGM beams by various theories and finite elements", Compos. Part B: Eng., 72, 1-9. https://doi.org/10.1016/j.compositesb.2014.12.004   DOI
16 Giunta, G., Belouettar, S. and Carrera, E. (2010), "Analysis of FGM Beams by Means of Classical and Advanced Theories", Mech. Adv. Mater. Struct.res, 17(8), 622-635. https://doi.org/10.1080/15376494.2010.518930   DOI
17 Gupta, V.K., Singh, S.B., Chandrawat, H.N. and Ray, S. (2004), "Steady state creep and material parameters in a rotating disc of Al-SiCP composite", Eur. J. Mech. - A/Solids, 23(2), 335-344. https://doi.org/10.1016/j.euromechsol.2003.11.005   DOI
18 Giunta, G., Crisafulli, D., Belouettar, S. and Carrera, E. (2013), "A thermo-mechanical analysis of functionally graded beams via hierarchical modelling", Compos. Struct., 95, 676-690. https://doi.org/10.1016/j.compstruct.2012.08.013   DOI
19 Golmakaniyoon, S. and Akhlaghi, F. (2016), "Time-dependent creep behavior of Al-SiC functionally graded beams under in-plane thermal loading", Computat. Mater. Sci., 121(Supplement C), 182-190. https://doi.org/10.1016/j.commatsci.2016.04.038   DOI
20 Guo, H., Zhuang, X. and Rabczuk, T. (2019), "A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate", Comput. Mater. Continua, 59(2), 433-456.   DOI
21 Hamdia, K.M., Ghasemi, H., Zhuang, X., Alajlan, N. and Rabczuk, T. (2018), "Sensitivity and uncertainty analysis for flexoelectric nanostructures", Comput. Methods Appl. Mech. Eng., 337, 95-109. https://doi.org/10.1016/j.cma.2018.03.016   DOI
22 Hamdia, K.M., Silani, M., Zhuang, X., He, P. and Rabczuk, T. (2017), "Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions", Int. J. Fracture, 206(2), 215-227. https://doi.org/10.1007/s10704-017-0210-6   DOI
23 Jafari Fesharaki, J., Loghman, A., Yazdipoor, M. and Golabi, S. (2014), "Semi-analytical solution of time-dependent thermomechanical creep behavior of FGM hollow spheres", Mech. Time-Depend. Mater., 18(1), 41-53. https://doi.org/10.1007/s11043-013-9212-6   DOI
24 Kadoli, R., Akhtar, K. and Ganesan, N. (2008), "Static analysis of functionally graded beams using higher order shear deformation theory", Appl. Math. Model., 32(12), 2509-2525. https://doi.org/10.1016/j.apm.2007.09.015   DOI
25 Li, X.F. (2008), "A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams", J. Sound Vib., 318(4), 1210-1229. https://doi.org/10.1016/j.jsv.2008.04.056   DOI
26 Kapania, R.K. and Raciti, S. (1989), "Recent advances in analysis of laminated beams and plates. Part I - Sheareffects and buckling", AIAA Journal, 27(7), 923-935. https://doi.org/10.2514/3.10202   DOI
27 Kiani, Y. and Eslami, M.R. (2010), "Thermal buckling analysis of functionally graded material beams", Int. J. Mech. Mater. Des., 6(3), 229-238. https://doi.org/10.1007/s10999-010-9132-4   DOI
28 Kordkheili, S.A.H. and Naghdabadi, R. (2007), "Thermoelastic analysis of a functionally graded rotating disk", Compos. Struct., 79(4), 508-516. https://doi.org/10.1016/j.compstruct.2006.02.010   DOI
29 Loghman, A. and Wahab, M.A. (1996), "Creep damage simulation of thick-walled tubes using the ${\Theta}$ projection concept", Int. J. Press. Vessels Pip., 67(1), 105-111. https://doi.org/10.1016/0308-0161(94)00175-8   DOI
30 Loghman, A., Ghorbanpour Arani, A. and Aleayoub, S.M.A. (2011), "Time-dependent creep stress redistribution analysis of thick-walled functionally graded spheres", Mech. Time-Depend. Mater., 15(4), 353-365. https://doi.org/10.1007/s11043-011-9147-8   DOI
31 Loghman, A., Faegh, R. and Arefi, M. (2017a), "Two dimensional time-dependent creep analysis of a thick-walled FG cylinder based on first order shear deformation theory", Steel Compos. Struct., Int. J., 26(5), 533-547. https://doi.org/10.12989/scs.2018.26.5.533
32 Loghman, A., Hammami, M. and Loghman, E. (2017b), "Effect of the silicon-carbide micro- and nanoparticle size on the thermo-elastic and time-dependent creep response of a rotating Al-SiC composite cylinder", J. Appl. Mech. Tech. Phys., 58(3), 443-453. https://doi.org/10.1134/S0021894417030099   DOI
33 Niknam, H., Fallah, A. and Aghdam, M.M. (2014), "Nonlinear bending of functionally graded tapered beams subjected to thermal and mechanical loading", Int. J. Non-Linear Mech., 65(Supplement C), 141-147. https://doi.org/10.1016/j.ijnonlinmec.2014.05.011   DOI
34 Mendelson, A. (1968), Plasticity Theory and Applications, The Macmillan Company.
35 Mirsky, I. (1959), "Axially symmetric motions of thick cylindrical shells", 25, 97-102.   DOI
36 Nguyen, T.-K., Vo, T.P. and Thai, H.-T. (2013), "Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory", Compos. Part B: Eng., 55, 147-157. https://doi.org/10.1016/j.compositesb.2013.06.011   DOI
37 Oh, Y. and Yoo, H.H. (2016), "Vibration analysis of rotating pretwisted tapered blades made of functionally graded materials", Int. J. Mech. Sci., 119(Supplement C), 68-79. https://doi.org/10.1016/j.ijmecsci.2016.10.002   DOI
38 Pandey, A.B., Mishra, R.S. and Mahajan, Y.R. (1993), "Creep fracture in Al-SiC metal-matrix composites", J. Mater. Sci., 28(11), 2943-2949. https://doi.org/10.1007/BF00354697   DOI
39 Rao, J.S. and Vyas, N.S. (1996), "Determination of blade stresses under constant speed and transient conditions with nonlinear damping", J. Eng. Gas Turbines Power, 118(2), 424-433. https://doi.org/10.1115/1.2816607   DOI
40 Roy, P.A. and Meguid, S.A. (2018), "Analytical modeling of the coupled nonlinear free vibration response of a rotating blade in a gas turbine engine", Acta Mechanica, 229(8), 3355-3373. https://doi.org/10.1007/s00707-018-2165-8   DOI
41 Sankar, B.V. (2001), "An elasticity solution for functionally graded beams", Compos. Sci. Technol., 61(5), 689-696. https://doi.org/10.1016/S0266-3538(01)00007-0   DOI
42 Vu-Bac, N., Lahmer, T., Zhuang, X., Nguyen-Thoi, T. and Rabczuk, T. (2016), "A software framework for probabilistic sensitivity analysis for computationally expensive models", Adv. Eng. Software, 100, 19-31. https://doi.org/10.1016/j.advengsoft.2016.06.005   DOI
43 Sankar, B.V. and Tzeng, J.T. (2002), "Thermal stresses in functionally graded beams", AIAA Journal, 40(6), 1228-1232. https://doi.org/10.2514/2.1775   DOI
44 Sapountzakis, E.J. and Panagos, D.G. (2008), "Shear deformation effect in non-linear analysis of composite beams of variable cross section", Int. J. Non-Linear Mech., 43(7), 660-682. https://doi.org/10.1016/j.ijnonlinmec.2008.03.005   DOI
45 Shi, G., Lam, K.Y. and Tay, T.E. (1998), "On efficient finite element modeling of composite beams and plates using higher-order theories and an accurate composite beam element", Compos. Struct., 41(2), 159-165. https://doi.org/10.1016/S0263-8223(98)00050-6   DOI
46 Xu, Y. and Zhou, D. (2012), "Two-dimensional thermoelastic analysis of beams with variable thickness subjected to thermo-mechanical loads", Appl. Math. Model., 36(12), 5818-5829. https://doi.org/10.1016/j.apm.2012.01.048   DOI
47 Zappino, E., Viglietti, A. and Carrera, E. (2018), "Analysis of tapered composite structures using a refined beam theory", Compos. Struct., 183, 42-52. https://doi.org/10.1016/j.compstruct.2017.01.009   DOI