Abstract
A thermo elastic analysis is presented for axisymmetric rotating disks made of functionally graded material (FGM) with variable thickness. Material properties are assumed to be temperature-dependent and graded in the radial direction according to a grading index power law distribution. The temperature field considered is assumed to be uniformly distributed over the disk surface and varied in the radial direction. Semi-analytical solutions for the displacement field are given for solid disk and annular disk under free-free and fixed-free boundary conditions. The effects of the thermal field, the material grading index and the geometry of the disk on the displacement and stress fields are investigated. Results of this study emphasize on the crucial role of the temperature-dependent properties in a high temperature environment. A comparison of these results with the reported ones in the literature that is temperature-dependent versus temperature-independent suggests that a functionally graded rotating disk with concave thickness profile can work more efficiently than the one with uniform thickness irrespective of whether the material properties are assumed to be temperature-dependent or temperature-independent.
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Bayat, M., Sahari, B.B., Hamouda, A.M.S., Saleem, M., Mahdi, E.: On the stress analysis of functionally graded gear wheels with variable thickness. Int. J. Comput. Eng. 9, 121–137 (2008). doi:10.1080/15502280701815416
Bayat, M., Saleem, M., Sahari, B.B., Hamouda, A.M.S., Mahdi, E.: Thermo analysis of functionally graded rotating disks with variable thickness. Int. J. Press Vessel. Pip. 1–16 (2009). doi:10.1016/S1359-8368(99)00069-4
Cheng, Z.Q., Batra, R.C.: Three-dimensional thermoelastic deformations of a functionally graded elliptic plate. Compos. Part B Eng. 31, 97–106 (2000). doi:10.1016/S1359-8368(99)00069-4
Eraslan, A.N.: Elastic–plastic deformation of rotating variable thickness annular disks with free, pressurized and radially constrained boundary conditions. Int. J. Mech. Sci. 45, 643–667 (2003). doi:10.1016/S0020-7403(03)00112-7
Eraslan, A.N., Argeso, H.: Limit angular velocities of variable thickness rotating disks. Int. J. Solids Struct 39, 3109–3130 (2002). doi:10.1016/S0020-7683(02)00249-4
Eraslan, A.N., Orcan, Y.: Elastic–plastic deformation of a rotating disk of exponentially varying thickness. Mech. Mater. 34, 423–432 (2002). doi:10.1016/S0167-6636(02)00117-5
Goupee, A.J., Vel, S.S.: Multi-objective optimization of functionally graded materials with temperature-dependent material properties. Mater. Des. 28, 1861–1879 (2007)
Guven, U.: Elastic–plastic stresses in a rotating annular disk of variable thickness and variable density. Int. J. Mech. Sci. 34(2), 133–138 (1992). doi:10.1016/0020-7403(92)90078-U
Jianping, P., Harik, I.E.: Axisymmetric pressure and thermal gradients in conical missile tips. J. Aerosp. Eng. 4, 237–255 (1991). doi:10.1061/(ASCE)0893-1321(1991)4:3(237)
Kitipornchai, S., Yang, J., Liew, K.M.: Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections. Int. J. Solids Struct. 41, 305–315 (2004). doi:10.1016/j.ijsolstr.2003.12.019
Kordkheili, S.A.H., Naghdabadi, R.: Thermoelastic analysis of a functionally graded rotating disk. Compos. Struct. 79(4), 508–516 (2007). doi:10.1016/j.compstruct.2006.02.010
Na, K.S., Kim, J.H.: Three-dimensional thermomechanical buckling analysis for functionally graded composite plates. Compos. Struct. 73, 413–422 (2006). doi:10.1016/j.compstruct.2005.02.012
Noda, N., Tsuji, T.: Steady thermal stresses in a plate of functionally gradient material with temperature-dependent properties. Trans. Jpn. Soc. Mech. Eng. Ser. A 57, 625–631 (1991)
Obata, Y., Noda, N., Tsuji, T.: Steady thermal stresses in a functionally gradient material plate: influence of Mechanical Boundary Conditions. Trans. Jpn. Soc. Mech. Eng. 58, 1689–1695 (1992)
Orcan, Y., Eraslan, A.N.: Elastic–plastic stresses in linearly hardening rotating solid disks of variable thickness. Mech. Res. Commun. 29, 269–281 (2002). doi:10.1016/S0093-6413(02)00261-6
Prakash, T., Ganapathi, M.: Supersonic flutter characteristics of functionally graded flat panels including thermal effects. Compos. Struct. 72, 10–18 (2006). doi:10.1016/j.compstruct.2004.10.007
Praveen, G.N., Chin, C.D., Reddy, J.N.: Thermo elastic analysis of functionally graded ceramic-metal cylinder. J. Eng. Mech. 125, 1259–1267 (1999). doi:10.1061/(ASCE)0733-9399(1999)125:11(1259)
Qian, L.F., Batra, R.C., Chen, L.M.: Analysis of cylindrical bending thermo elastic deformations of functionally graded plates by a meshless local Petrov–Galerkin method. Comput. Mech. 33, 263–273 (2004). doi:10.1007/s00466-003-0527-z
Reddy, J.N.: Analysis of functionally graded plates. Int. J. Numer. Mech. Eng. 47, 663–684 (2000). doi:10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
Reddy, J.N., Chin, C.D.: Thermomechanical analysis of functionally graded cylinders and plates. J. Therm. Stresses 21, 593–626 (1998). doi:10.1080/01495739808956165
Reddy, T.Y., Srinath, H.: Elastic stresses in a rotating anisotropic annular disk of variable thickness and variable density. Int. J. Mech. Sci. 16, 85–89 (1974). doi:10.1016/0020-7403(74)90078-2
Reddy, J.N., Wang, C.M., Kitipornchai, S.: Axisymmetric bending of functionally graded circular and annular plates. Eur. J. Mech. A/Solids 18, 185–199 (1999)
Ruhi, M., Angoshtari, A., Naghdabadi, R.: Thermoelastic analysis of thick-walled finite-length cylinders of functionally graded materials. J. Therm. Stresses 28, 391–408 (2005). doi:10.1080/01495730590916623
Sankar, B.V., Tzeng, J.T.: Thermal stresses in functionally graded beams. AIAA J. 40, 1228–1232 (2002). doi:10.2514/2.1775
Shen, H.S.: Postbuckling analysis of pressure-loaded functionally graded cylindrical shells in thermal environments. Eng. Struct. 25, 487–497 (2003). doi:10.1016/S0141-0296(02)00191-8
Suresh, S., Mortensen, A.: Fundamentals of Functionally Graded Material. Processing and Thermomechanical Behavior of Graded Metals and Metal-Ceramic Composites. IOM Communications LTD, London, UK (1998)
Tanaka, K., Tanaka, Y., Watanabe, H., Poterasu, V.F., Sugano, Y.: An improved solution to thermoelastic material design in functionally gradient materials: scheme to reduce thermal stresses. Comput. Methods Appl. Mech. Eng. 109, 377–389 (1993). doi:10.1016/0045-7825(93)90088-F
Tanigawa, Y.: Some basic thermoplastic problems for no homogeneous structural material. Appl. Mech. 48, 377–389 (1995)
Teymur, M., Chitkara, N.R., Yohngjo, K., Aboudi, J., Pindera, M.J., Arnold, S.M.: Thermoelastic theory for the response of materials functionally graded in two directions. Int. J. Solids Struct. 33(7), 931–966 (1996). doi:10.1016/0020-7683(95)00084-4
Tutuncu, N.: Effect of anisotropy on stresses in rotating discs. Int. J. Mech. Sci. 37(8), 873–881 (1995). doi:10.1016/0020-7403(94)00097-4
Vel, S.S., Batra, R.C.: Exact solution for thermoelastic deformations of functionally graded thick rectangular plates. AIAA J. 40, 1421–1433 (2002). doi:10.2514/2.1805
Yang, J., Shen, H.S.: Vibration characteristics and transient response of shear-deformable functionally graded plates in thermal environments. J. Sound Vib. 225, 579–602 (2002). doi:10.1006/jsvi.2001.4161
Yang, J., Liew, K.M., Wu, Y.F., Kitipornchai, S.: Thermo-mechanical post buckling of FGM cylindrical panels with temperature-dependent properties. Int. J. Solids Struct. 43, 307–324 (2006). doi:10.1016/j.ijsolstr.2005.04.001
Zimmerman, R.W., Lutz, M.P.: Thermal stresses and thermal expansion in a uniformly heated functionally graded cylinder. J. Therm. Stresses 22, 177–188 (1999). doi:10.1080/014957399280959
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Bayat, M., Sahari, B.B., Saleem, M. et al. Thermo elastic analysis of functionally graded rotating disks with temperature-dependent material properties: uniform and variable thickness. Int J Mech Mater Des 5, 263–279 (2009). https://doi.org/10.1007/s10999-009-9100-z
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DOI: https://doi.org/10.1007/s10999-009-9100-z