×

zbMATH — the first resource for mathematics

Elastic analysis of variable profile and polar orthotropic FGM rotating disks for a variation function with three parameters. (English) Zbl 1433.74015
Summary: Analytical solutions are developed for the analysis of elastic polar orthotropic functionally graded annular disks rotating with constant angular velocity. The formulations are carried out by presuming a state of plane stress and small deformations. The elasticity moduli and thickness are varied radially by a nonlinear function controlled by three parameters, while the radial variation of density may be defined by any form of continuous function. Poisson’s ratios are taken to be constant. Annular disks having traction-free inner and outer surfaces, and annular disks mounted on a circular rigid shaft having traction-free outer surface are studied separately. The analytical solutions are verified numerically by the use of a computational model based on the nonlinear shooting method. An analysis that inspects the effects of the degree of orthotropy is presented. Elastic limit angular velocities are determined according to Hosford’s yield criteria. Stress, displacement and strain profiles are compared within the elastic range.

MSC:
74A35 Polar materials
Software:
LSODE; ODEPACK; PROMAL
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abramowitz, M., Stegun, A.I.: Handbook of Mathematical Functions. US Goverment Printing Office, Washington (1970) · Zbl 0171.38503
[2] Alexandrova, N; Alexandrov, S, Elastic-plastic stress distribution in a plastically anisotropic rotating disk, J. Appl. Mech., 71, 427-429, (2004) · Zbl 1111.74306
[3] Alexandrova, N; Vila Real, PMM, Deformation and stress analysis of an anisotropic rotating annular disk, Int. J. Comput. Methods Eng. Sci. Mech., 9, 43-50, (2008) · Zbl 1136.74024
[4] Argeso, H, Analytical solutions to variable thickness and variable material property rotating disks for a new three-parameter variation function, Mech. Based Des. Struct., 40, 133-152, (2012)
[5] Banabic, D.: Sheet Metal Forming Processes: Constitutive Modelling and Numerical Simulation. Springer, Berlin (2010)
[6] Bayat, M; Sahari, BB; Saleem, M; Hamouda, AMS; Mahdi, E; Reddy, JN, 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)
[7] Bayat, M; Saleem, M; Sahari, BB; Hamouda, AMS; Mahdi, E, Analysis of functionally graded rotating disks with variable thickness, Mech. Res. Commun., 35, 283-309, (2008) · Zbl 1258.74131
[8] Çallıoğlu, H, Thermal stress analysis of curvilinearly orthotropic rotating discs, J. Thermoplast. Compos., 20, 357-369, (2007)
[9] Çallıoğlu, H; Topcu, M; Altan, G, Stress analysis of curvilinearly orthotropic rotating discs under mechanical and thermal loading, J. Reinf. Plast. Compos., 24, 831-838, (2005)
[10] Çallıoğlu, H; Topcu, M; Tarakcılar, AR, Elastic-plastic stress analysis of an orthotropic rotating disc, Int. J. Mech. Sci., 48, 985-990, (2006) · Zbl 1192.74223
[11] Eraslan, AN, Elastoplastic deformations of rotating parabolic solid disks using tresca’s yield criterion, Eur. J. Mech. A Solid, 22, 861-874, (2003) · Zbl 1032.74578
[12] Eraslan, AN, Tresca’s yield criterion and linearly hardening rotating solid disks having hyperbolic profiles, Forsch. Ing., 69, 17-28, (2004)
[13] Eraslan, AN, Von mises’ yield criterion and nonlinearly hardening rotating shafts, Acta Mech., 168, 129-144, (2004) · Zbl 1063.74016
[14] Eraslan, AN, A class of nonisothermal variable thickness rotating disk problems solved by hypergeometric functions, Turk. J. Eng. Environ. Sci., 29, 241-269, (2005)
[15] Eraslan, AN, Stress distributions in elastic-plastic rotating disks with elliptical thickness profiles using Tresca and von Mises criteria, ZAMM Z. Angew. Math. Mech., 85, 252-266, (2005) · Zbl 1155.74310
[16] Eraslan, AN; Akis, T, On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems, Acta Mech., 181, 43-63, (2006) · Zbl 1103.74032
[17] Eraslan, AN; Argeso, H, Limit angular velocities of variable thickness rotating disks, Int. J. Solids Struct., 39, 3109-3130, (2002) · Zbl 1047.74020
[18] Eraslan, AN; Argeso, H, A nonlinear shooting method applied to solid mechanics: part 2. numerical solution of a plane strain model, Int. J. Nonlinear Anal. Phenom., 2, 31-42, (2005)
[19] Eraslan, AN; Kartal, EM, A nonlinear shooting method applied to solid mechanics: part 1. numerical solution of a plane stress model, Int. J. Nonlinear Anal. Phenom., 1, 27-40, (2004) · Zbl 1129.74351
[20] Eraslan, AN; Kaya, Y; Varlı, E, Analytical solutions to orthotropic variable thickness disk problems, Pamukkale Univ. J. Eng. Sci., 22, 24-30, (2016)
[21] Eraslan, AN; Orcan, Y, Elastic-plastic deformation of a rotating disk of exponentially varying thickness, Mech. Mater., 34, 423-432, (2002)
[22] Eraslan, AN; Orcan, Y, On the rotating elastic-plastic solid disks of variable thickness having concave profiles, Int. J. Mech. Sci., 44, 1445-1466, (2002) · Zbl 1026.74044
[23] Gurushankar, GV, Thermal stresses in a rotating, nonhomogeneous, anisotropic disk of varying thickness and density, J. Strain Anal. Eng., 10, 137-142, (1975)
[24] Güven, U, Elastic-plastic stresses in a rotating annular disk of variable thickness and variable density, Int. J. Mech. Sci., 34, 133-138, (1992) · Zbl 0825.73340
[25] Güven, U, Elastic-plastic stress distribution in a rotating hyperbolic disk with rigid inclusion, Int. J. Mech. Sci., 40, 97-109, (1998) · Zbl 0899.73269
[26] Hill, R.: The Mathematical Theory of Plasticity. Clarendon Press, Oxford (1950) · Zbl 0041.10802
[27] Hill, R, Theoretical plasticity of textured aggregates, Math. Proc. Camb. Philos. Soc., 85, 179-191, (1979) · Zbl 0388.73029
[28] Hindmarsh, AC, LSODE and lsodi, two new initial value ordinary differential equation solvers, SIGNUM Newsl., 15, 10-11, (1980)
[29] Hindmarsh, AC; Stepleman, RS (ed.), ODEPACK: a systematized collection of ODE solvers, 55-64, (1983), Amsterdam
[30] Hoffman, J.D.: Numerical Methods for Engineers and Scientists, 2nd edn. Marcel Dekker, New York (2001) · Zbl 1068.65001
[31] Horgan, CO; Chan, AM, The stress response of functionally graded isotropic linearly elastic rotating disks, J. Elast., 55, 219-230, (1999) · Zbl 0970.74017
[32] Hosford, W.F.: On yield loci of anisotropic cubic metals. In: Proceedings of the 7th North American Metalworking Conference (NMRC), Dearborn (1979)
[33] Hosford, W.F.: Fundamentals of Engineering Plasticity. Cambridge University Press, New York (2013)
[34] Ichikawa, K. (ed.): Functionally Graded Materials in the 21 Century: A Workshop on Trends and Forecasts. Springer, Berlin (2001)
[35] Jain, R; Ramachandra, K; Simha, KRY, Singularity in rotating orthotropic discs and shells, Int. J. Mech. Sci., 41, 639-648, (1999) · Zbl 0987.74033
[36] Johnson, W., Mellor, P.B.: Engineering Plasticity. Von Nostrand Reinhold, London (1978)
[37] Jones, R.M.: Mechanics of Composite Materials. Taylor and Francis, Philadelphia (1999)
[38] Kaw, A.K.: Mechanics of Composite Materials. CRC Press, Boca Raton (2006) · Zbl 0918.73001
[39] Kaya, Y.: Analytical and Numerical Solutions to Rotating Orthotropic Disk Problems. Master’s thesis, Middle East Technical University (2007)
[40] Logan, R; Hosford, WF, Upper-bound anisotropic yield locus calculations assuming (111)—pencil glide, Int. J. Mech. Sci., 22, 419-430, (1980)
[41] Ma, G; Hao, H; Miyamoto, Y, Limit angular velocity of rotating disc with unified yield criterion, Int. J. Mech. Sci., 43, 1137-1153, (2001) · Zbl 0998.74046
[42] Nie, GJ; Zhong, Z; Batra, RC, Material tailoring for orthotropic elastic rotating disks, Compos. Sci. Technol., 71, 406-414, (2011)
[43] Peng, XL; Li, XF, Elastic analysis of rotating functionally graded polar orthotropic disks, Int. J. Mech. Sci., 60, 84-91, (2012)
[44] Radhakrishnan, K., Hindmarsh, A.C.: Description and Use of LSODE, the Livermore Solver for Ordinary Differential Equations, Technical Report. UCRL-ID-113855. Lawrence Livermore National Laboratory (1993) · Zbl 1063.74016
[45] Reddy, TY; Srinath, H, Elastic stresses in a rotating anisotropic annular disk of variable thickness and variable density, Int. J. Mech. Sci., 16, 85-89, (1974)
[46] Rees, D.W.A.: Mechanics of Solids and Structures. Imperial College Press, London (2000) · Zbl 0953.74001
[47] Ross, S.L.: Differential Equations. Wiley, New York (1984) · Zbl 0644.34001
[48] Timoshenko, S., Goodier, J.N.: Theory of Elasticity. McGraw-Hill, New York (1970) · Zbl 0266.73008
[49] Ugural, A.C., Fenster, S.K.: Advanced Mechanics of Materials and Applied Elasticity. Prentice-Hall, Englewood Cliffs (2011) · Zbl 0486.73002
[50] Vullo, V; Vivio, F, Elastic stress analysis of non-linear variable thickness rotating disks subjected to thermal load and having variable density along the radius, Int. J. Solids Struct., 45, 5337-5355, (2008) · Zbl 1255.74020
[51] Vullo, V., Vivio, F.: Rotors: Stress Analysis and Design. Springer, Milan (2013) · Zbl 1255.74020
[52] You, LH; Tang, YY; Zhang, JJ; Zhang, CY, Numerical analysis of elastic-plastic rotating disks with arbitrary variable thickness and density, Int. J. Solids Struct., 37, 7809-7820, (2000) · Zbl 1001.74050
[53] You, LH; You, XY; Zhang, JJ; Li, J, On rotating circular disks with varying material properties, Z. Angew. Math. Phys., 58, 1068-1084, (2007) · Zbl 1125.74029
[54] Zenkour, AM, Analytical solutions for rotating exponentially-graded annular disks with various boundary conditions, Int. J. Struct. Stab. Dyn., 5, 557-577, (2005) · Zbl 1205.74080
[55] Zenkour, AM, Elastic deformation of the rotating functionally graded annular disk with rigid casing, J. Mater. Sci., 42, 9717-9724, (2007)
[56] Zenkour, AM, Stress distribution in rotating composite structures of functionally graded solid disks, J. Mater. Process. Technol., 209, 3511-3517, (2009)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.