×

Semi-exact solution for thermo-mechanical analysis of functionally graded elastic-strain hardening rotating disks. (English) Zbl 1351.74016

Summary: In this paper, distributions of stress and strain components of rotating disks with non-uniform thickness and material properties subjected to thermo-elasto-plastic loading are obtained by semi-exact method of Liao’s homotopy analysis method (HAM) and finite element method (FEM). The materials are assumed to be elastic-linear strain hardening and isotropic. The analysis of rotating disk is based on Von Mises’ yield criterion. A two dimensional plane stress analysis is used. The distribution of temperature is assumed to have power forms with the hotter point located at the outer surface of the disk. A mathematical technique of transformation has been proposed to solve the homotopy equations which are originally hard to be handled. The domain of the solution has been substituted by a new domain through which the unknown variable has been taken out from the argument of the function. This makes the solution much easier. A numerical solution of the governing differential equations is also presented based on the Runge-Kutta’s method. The results of three methods are presented and compared which shows good agreements. This verifies the implementation of the HAM and demonstrates its applicability to provide accurate solution for a very complicated case of strongly high nonlinear differential equations with no exact solution. It is important to notice that compared with other methods, HAM needs significant more computation time and computer hardware requirements which limit its application for those problems that other methods can easily handle them.

MSC:

74F05 Thermal effects in solid mechanics
74K20 Plates
74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74C99 Plastic materials, materials of stress-rate and internal-variable type
70E17 Motion of a rigid body with a fixed point

Software:

ANSYS
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ugural, S. C.; Fenster, S. K., Advanced strength and applied elasticity (1987), Elsevier: Elsevier New York · Zbl 0486.73002
[2] Eraslan, A. N.; Orcan, Y., Elastic-plastic deformation of a rotating solid disk of exponentially varying thickness, Mech Mater, 34, 423-432 (2002)
[3] Eraslan, A.; Argeso, H., Limit angular velocities of variable thickness rotating disks, Int J Solids Struct, 29, 3109-3130 (2002) · Zbl 1047.74020
[4] Gupta, V. K.; Singh, S. B.; Chandrawat, H. N.; Ray, S., Steady state creep and material parameters in a rotating disc of Al-SiCP composite, Eur J Mech A - Solids, 23, 335-344 (2004) · Zbl 1058.74529
[5] You, L. H.; Zhang, J. J., Elastic-plastic stresses in a rotating solid disk, Mech Sci, 41, 262-282 (1999) · Zbl 0953.74027
[6] You, L. H.; Tang, Y. Y.; Zhang, J. J.; Zheng, C. Y., Numerical analysis of elastic-plastic rotating disks with arbitrary variable thickness and density, Solid Struct, 37, 7809-7820 (2000) · Zbl 1001.74050
[7] 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) · Zbl 1048.74521
[8] Jahed, H.; Farshi, B.; Bidabadi, J., Minimum weight design of inhomogeneous rotating discs, Int J Press Vessels Piping, 82, 35-41 (2005)
[9] Kordkheili, S. A.H.; Naghdabadi, R., Thermoelastic analysis of a functionally graded rotating disk, Composite Structures, 79, 508-516 (2006)
[10] Asghari, M.; Ghafoori, E., A three-dimensional elasticity solution for functionally graded rotating disks, Compos Struct, 92, 1092-1099 (2010)
[11] Nie, G. J.; Batra, R. C., Stress analysis and material tailoring in isotropic linear thermoelastic incompressible functionally graded rotating disks of variable thickness, Compos Struct, 92, 720-729 (2010)
[12] Afsar, A. M.; Go, J., Finite element analysis of thermoelastic field in a rotating FGM circular disk, Appl Math Model, 34, 3309-3320 (2010) · Zbl 1201.74252
[13] Hojjati, M. H.; Jafari, S., Variational iteration solution of elastic non uniform thickness and density rotating disks, Far East J Appl Math, 29, 185-200 (2007) · Zbl 1145.74021
[14] Hojjati, M. H.; Hassani, A., Theoretical and numerical analyses of rotating discs of non-uniform thickness and density, Int J Press Vessel Piping, 85, 695-700 (2008)
[15] Hojjati, M. H.; Jafari, S., Semi-exact solution of elastic non-uniform thickness and density rotating disks by homotopy perturbation and Adomian’s decomposition methods Part I: elastic solution, Int J Press Vessels Piping, 85, 871-878 (2008)
[16] Hojjati, M. H.; Jafari, S., Semi-exact solution of non-uniform thickness and density rotating disks. Part II: Elastic strain hardening solution, Int J Press Vessels Piping, 86, 307-318 (2009)
[17] Hassani A, Hojjati MH, Farrahi G, Alashti RA, Mahdavi E. Thermo-mechanical analysis of rotating disks with non-uniform thickness and material properties, Int J Press Vessels Piping; submitted for publication.; Hassani A, Hojjati MH, Farrahi G, Alashti RA, Mahdavi E. Thermo-mechanical analysis of rotating disks with non-uniform thickness and material properties, Int J Press Vessels Piping; submitted for publication.
[18] Turkyilmazoglu, M., Analytic approximate solutions of rotating disk boundary layer flow subject to a uniform suction or injection, Int J Mech Sci, 52, 12, 1735-1744 (2010)
[19] Hassani, A.; Hojjati, M. H.; Farrahi, G.; Alashti, R. A., Semi-exact elastic solutions for thermo-mechanical analysis of functionally graded rotating disks, Compos Struct, 93, 12, 3239-3251 (2011)
[20] Liao, S. J., Beyond perturbation: introduction to the homotopy analysis method (2003), Chapman and Hall: Chapman and Hall Boca Raton
[21] Cheng, J.; Cang, J.; Shi-Jun Liao, S. J., On the interaction of deep water waves and exponential shear currents, Z Angew Math Phys, 60, 450-478 (2009) · Zbl 1173.76007
[22] Liao, S. J., An optimal homotopy-analysis approach for strongly nonlinear differential equations, Commun Nonlinear Sci Numer Simulat, 15, 2003-2016 (2010) · Zbl 1222.65088
[23] Liao, S. J.; Tan, Y., A general approach to obtain series solutions of nonlinear differential equations, Stud Appl Math, 119, 297-355 (2007)
[24] Turkyilmazoglu, M., A note on the homotopy analysis method, Appl Math Lett, 23, 1226-1230 (2010) · Zbl 1195.65104
[25] Liao, S. J., On the homotopy analysis method for nonlinear problems, Appl Math Comput, 147, 499-513 (2004) · Zbl 1086.35005
[26] Liao, S. J., Comparison between the homotopy analysis method and homotopy perturbation method, Appl Math Comput, 169, 1186-1194 (2005) · Zbl 1082.65534
[27] Gorder, R.; Vajravelu, K., On the selection of auxiliary functions, operators, and convergence control parameters in the application of the Homotopy Analysis Method to nonlinear differential equations: a general approach, Commun Nonlinear Sci Numer Simulat, 14, 4078-4089 (2009) · Zbl 1221.65208
[28] Molabahrami, A.; Khani, F., The homotopy analysis method to solve the Burgers-Huxley equation, Nonlinear Anal, B 10, 589-600 (2009) · Zbl 1167.35483
[29] Liao, S. J., On the relationship between the homotopy analysis method and Euler transform, Commun Nonlinear Sci Numer Simul, 15, 1421-1431 (2010) · Zbl 1221.65206
[30] Liao, S. J., An optimal homotopy-analysis approach for strongly nonlinear differential equations, Commun Nonlinear Sci Numer Simulat, 15, 2003-2016 (2010) · Zbl 1222.65088
[31] Li, Y.; Nohara, B. T.; Liao, S. J., Series solutions of coupled Van der Pol equation by means of homotopy analysis method, J Math Phys, 51, 063517 (2010) · Zbl 1311.70031
[32] Xu, H.; Lin, Z. L.; Liao, S. J.; Wu, J. Z.; Majdalani, J., Homotopy based solutions of the Navier-Stokes equations for a porous channel with orthogonally moving walls, Phys Fluids, 22, 053601 (2010) · Zbl 1190.76132
[33] Bayat, M.; Saleem, M.; Sahari, B. B.; Hamouda, A. M.S.; Mahdi, E., Mechanical and thermal stresses in a functionally graded rotating disk with variable thickness due to radially symmetry loads, Int J Press Vessels Piping, 86, 357-372 (2009)
[34] Timoshenko, S. P.; Goodier, J. N., Theory of elasticity (1970), Mc Graw-Hill: Mc Graw-Hill New York · Zbl 0266.73008
[35] Hencky, H., Zur theorie plastischer deformationen und der hierdurch im material hervorgerufenen nachspannungen, Z Angew Math Mech, 4, 323 (1924) · JFM 50.0546.03
[36] User’s manual of ANSYS 11.0, ANSYS Inc., 2007.; User’s manual of ANSYS 11.0, ANSYS Inc., 2007.
[37] Turkyilmazoglu, M., Purely analytic solutions of magnetohydrodynamic swirling boundary layer flow over a porous rotating disk, Comput Fluids, 39, 5, 793-799 (2010) · Zbl 1242.76368
[38] Turkyilmazoglu, M., Numerical and analytical solutions for the flow and heat transfer near the equator of an MHD boundary layer over a porous rotating sphere, Int J Thermal Sci, 50, 5, 831-842 (2011)
[39] Turkyilmazoglu, M., An optimal analytic approximate solution for the limit cycle of Duffing-van der Pol equation, J Appl Mech Trans ASME, 78, 2 (2011), [Art. no. 021005]
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.