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Abstrakty
Analytical and numerical nonlinear solutions for rotating variable-thickness functionally graded solid and annular disks with viscoelastic orthotropic material properties are presented by using the method of successive approximations.Variable material properties such as Young’s moduli, density and thickness of the disk, are first introduced to obtain the governing equation. As a second step, the method of successive approximations is proposed to get the nonlinear solution of the problem. In the third step, the method of effective moduli is deduced to reduce the problem to the corresponding one of a homogeneous but anisotropic material. The results of viscoelastic stresses and radial displacement are obtained for annular and solid disks of different profiles and graphically illustrated. The calculated results are compared and the effects due to many parameters are discussed.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
423--440
Opis fizyczny
Bibliogr. 32 poz., rys.
Twórcy
autor
- Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
autor
- Department of Mathematics, Faculty of Science, Damietta University, Damietta 34517, Egypt
autor
- Department of Mathematics, Faculty of Science, Damietta University, Damietta 34517, Egypt
autor
- Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
- Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt
Bibliografia
- [1] S. Tang. Elastic stresses in rotating anisotropic disks. International Journal of Mechanical Sciences, 11(6):509–517, 1969. doi: 10.1016/0020-7403(69)90052-6.
- [2] A.C. Ugural and S.K. Fenster. Advanced Strength and Applied Elasticity. Elsevier, 1987.
- [3] A.N. Eraslan and Y. Orcan. Elastic–plastic deformation of a rotating solid disk of exponentially varying thickness. Mechanics of Materials, 34(7):423–432, 2002. doi: 10.1016/S0167-6636(02)00117-5.
- [4] A.N. Eraslan and H. Argeso. Limit angular velocities of variable thickness rotating disks. International Journal of Solids and Structures, 39(12):3109–3130, 2002. doi: 10.1016/S0020-7683(02)00249-4.
- [5] S.P. Timoshenko and J.N. Goodier. Theory of Elasticity. McGraw Hill, New York, 1970.
- [6] C.O. Horgan and A.M. Chan. The stress response of functionally graded isotropic linearly elastic rotating disks. Journal of Elasticity, 55(3):219–230, 1999. doi: 10.1023/A:1007644331856.
- [7] H. Jahed, B. Farshi, and J. Bidabadi. Minimum weight design of inhomogeneous rotating discs. International Journal of Pressure Vessels and Piping, 82(1):35–41, 2005. doi: 10.1016/j.ijpvp.2004.06.006.
- [8] M.H. Hojjati and A. Hassani. Theoretical and numerical analyses of rotating discs of non-uniform thickness and density. International Journal of Pressure Vessels and Piping, 85(10):694–700, 2008. doi: 10.1016/j.ijpvp.2008.02.010.
- [9] A.N. Eraslan and T. Akis. On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems. Acta Mechanica, 181(1):43–63, 2006. doi: 10.1007/s00707-005-0276-5.
- [10] S.A.H. Kordkheili and R. Naghdabadi. Thermoelastic analysis of a functionally graded rotating disk. Composite Structures, 79(4):508–516, 2007. doi: 10.1016/j.compstruct.2006.02.010.
- [11] L.H. You, X.Y. You, J.J. Zhang, and J. Li. On rotating circular disks with varying material properties. Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 58(6):1068–1084, 2007. doi: 10.1007/s00033-007-5094-2.
- [12] M.H. Hojjati and S. Jafari. Semi-exact solution of elastic non-uniform thickness and density rotating disks by homotopy perturbation and Adomian’s decomposition methods. Part I: Elastic solution. International Journal of Pressure Vessels and Piping, 85(12):871–878, 2008. doi: 10.1016/j.ijpvp.2008.06.001.
- [13] V. Vullo and F. Vivio. Elastic stress analysis of non-linear variable thickness rotating disks subjected to thermal load and having variable density along the radius. International Journal of Solids and Structures, 45(20):5337–5355, 2008. doi: 10.1016/j.ijsolstr.2008.05.018.
- [14] F. Vivio and V. Vullo. Elastic stress analysis of rotating converging conical disks subjected to thermal load and having variable density along the radius. International Journal of Solids and Structures, 44(24):7767–7784, 2007. doi: 10.1016/j.ijsolstr.2007.05.013.
- [15] M. Bayat, M. Saleem, B.B. Sahari, A.M.S. Hamouda, and E. Mahdi. Analysis of functionally graded rotating disks with variable thickness. Mechanics Research Communications, 35(5):283–309, 2008. doi: 10.1016/j.mechrescom.2008.02.007.
- [16] M. Bayat, M. Saleem, B.B. Sahari, A.M.S. Hamouda, and E. Mahdi. Mechanical and thermal stresses in a functionally graded rotating disk with variable thickness due to radially symmetry loads. International Journal of Pressure Vessels and Piping, 86(6):357–372, 2009. doi: 10.1016/j.ijpvp.2008.12.006.
- [17] M. Bayat, B.B. Sahari, M. Saleem, A. Ali, and S.V.Wong. Thermoelastic solution of a functionally graded variable thickness rotating disk with bending based on the first-order shear deformation theory. Thin-Walled Structures, 47(5):568–582, 2009. doi: 10.1016/j.tws.2008.10.002.
- [18] M. Bayat, B.B. Sahari, A. Saleem, M. and Ali, and S.V. Wong. Bending analysis of a functionally graded rotating disk based on the first order shear deformation theory. Applied Mathematical Modelling, 33(11):4215–4230, 2009. doi: 10.1016/j.apm.2009.03.001.
- [19] A.M. Zenkour. Elastic deformation of the rotating functionally graded annular disk with rigid casing. Journal of Materials Science, 42(23):9717–9724, 2007. doi: 10.1007/s10853-007-1946-6.
- [20] A.M. Zenkour. Stress distribution in rotating composite structures of functionally graded solid disks. Journal of Materials Processing Technology, 209(7):3511–3517, 2009. doi: 10.1016/j.jmatprotec.2008.08.008.
- [21] G.J. Nie and R.C. Batra. Stress analysis and material tailoring in isotropic linear thermoelastic incompressible functionally graded rotating disks of variable thickness. Composite Structures, 92(3):720–729, 2010. doi: 10.1016/j.compstruct.2009.08.052.
- [22] W.W. Feng. On finite deformation of viscoelastic rotating disks. International Journal of Non-Linear Mechanics, 20(1):21–26, 1985. doi: 10.1016/0020-7462(85)90044-7.
- [23] A.M. Zenkour and M.N.M. Allam. On the rotating fiber-reinforced viscoelastic composite solid and annular disks of variable thickness. International Journal for Computational Methods in Engineering Science and Mechanics, 7(1):21–31, 2006. doi: 10.1080/155022891009639.
- [24] M.N.M. Allam, A.M. Zenkour, and T.M.A. El-Azab. Viscoelastic deformation of the rotating inhomogeneous variable thickness solid and annular disks. International Journal for Computational Methods in Engineering Science and Mechanics, 8(5):313–322, 2007. doi: 10.1080/15502280701471657.
- [25] A.M. Zenkour. Thermoelastic analysis of an annular sandwich disk with metal/ceramic faces and functionally graded core. Journal of Thermoplastic Composite Materials, 22(2):163–181, 2009. doi: 10.1177/0892705708091770.
- [26] A.M. Zenkour. Analytical solutions for rotating exponentially-graded annular disks with various boundary conditions. International Journal of Structural Stability and Dynamics, 5(04):557–577, 2005. doi: 10.1142/S0219455405001726.
- [27] A.M. Zenkour. Thermoelastic solutions for annular disks with arbitrary variable thickness. Structural Engineering and Mechanics, 24(5):515–528, 2006. doi: 10.12989/sem.2006.24.5.515.
- [28] A.M. Zenkour. Steady-state thermoelastic analysis of a functionally graded rotating annular disk. International Journal of Structural Stability and Dynamics, 6(04):559–574, 2006. doi: 10.1142/S0219455406002064.
- [29] A.M. Zenkour. Rotating moderately thick annular disks via an extension to classical theory. Journal of Mechanics, 28(2):355–360, 2012. doi: 10.1017/jmech.2012.39.
- [30] B.E. Pobedrya. Structural anisotropy in viscoelasticity. Polymer Mechanics, 12(4):557–561, 1976. doi: 10.1007/BF00857005.
- [31] M.N.M. Allam and B.E. Pobedrya. On the solution of quasi-statical problems of anisotropic viscoelasticity. Mekhanica, 31:19–27, 1978. (in Russian).
- [32] A.A. Illyushin and B.E. Pobedrya. Foundations of Mathematical Theory of Thermo-Visco-Elasticity. Nauka, Moscow, 1970. (in Russian).
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-6b17eb2a-29bd-4196-b872-ae9ad3aa7deb