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Effect of geometrical imperfection on the thermomechanical behavior of functionally graded material rotating disk

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Abstract

The thermoelastic analysis of axisymmetric bending of rotating functionally graded material (FGM) disks, with and without imperfection, is presented. Material properties are assumed to be temperature dependent and graded in the thickness direction following a grading index power-law distribution. Theories of von Karman and first-order shear deformation were implemented to calculate the stress and displacement fields. Numerical results are given for evaluating the effects of temperature, material properties and imperfection on displacement and stress fields in a disk with roller-supported boundary conditions. Small and large deflection theories are considered to obtain the stress field and displacement field for the perfect and imperfect in FG disks and also in full metal (or full ceramic) disks. A series-form solution is used to solve the large-deflection nonlinear equations. The results are compared and validated with the results from the finite element method. It is observed that applying the initial geometric imperfection to a rotating solid disk would increase the value of radial stress, circumferential stress and vertical displacement.

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References

  1. Koizumi M (1993) The concept of FGM ceramic transitional. Function Gradient Mater 34:3–10

    Google Scholar 

  2. Noda N, Tsuji T (1991) Steady thermal stresses in a plate of functionally gradient material. Trans Jpn Soc Mech Eng A 57:98–103

    Google Scholar 

  3. Obata Y, Noda N, Tsuji T (1992) Steady thermal stresses in a functionally gradient material plate. Nippon Kikai Gakkai Ronbunshu, A Hen 58(553):1689–1695

    Google Scholar 

  4. Tanaka K, Tanaka Y, Enomoto K, Poterasu VF, Sugano Y (1993) Design of thermoelastic materials using direct sensitivity and optimization methods. Reduction of thermal stresses in functionally gradient materials. Comput Methods Appl Mech Eng 106(1):271–284

    MATH  Google Scholar 

  5. Tanaka K, Tanaka Y, Watanabe H, Poterasu VF, Sugano Y (1993) An improved solution to thermoelastic material design in functionally gradient materials: scheme to reduce thermal stresses. Comput Methods Appl Mech Eng 109(3):377–389

    MATH  Google Scholar 

  6. Bayat M, Saleem M, Sahari BB, Hamouda AMS, Mahdi E (2009) Mechanical and thermal stresses in a functionally graded rotating disk with variable thickness due to radially symmetry loads. Int J Press Vessels Pip 86(6):357–372

    Google Scholar 

  7. Çallioğlu H, Bektaş NB, Sayer M (2011) Stress analysis of functionally graded rotating discs: analytical and numerical solutions. Acta Mech Sin 27(6):950–955

    MATH  Google Scholar 

  8. Bayat M, Saleem M, Sahari BB, Hamouda AMS, Mahdi E (2007) Thermo elastic analysis of a functionally graded rotating disk with small and large deflections. Thin Walled Struct 45(7):677–691

    Google Scholar 

  9. Asghari M, Ghafoori E (2010) A three-dimensional elasticity solution for functionally graded rotating disks. Compos Struct 92(5):1092–1099

    Google Scholar 

  10. Chen J, Ding H, Chen W (2007) Three-dimensional analytical solution for a rotating disc of functionally graded materials with transverse isotropy. Arch Appl Mech 77(4):241–251

    MATH  Google Scholar 

  11. Eraslan AN, Akis T (2006) On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems. Acta Mech 181(1–2):43–63

    MATH  Google Scholar 

  12. Peng XL, Li XF (2012) Effects of gradient on stress distribution in rotating functionally graded solid disks. J Mech Sci Technol 26(5):1483–1492

    Google Scholar 

  13. Zenkour AM (2009) Stress distribution in rotating composite structures of functionally graded solid disks. J Mater Process Technol 209(7):3511–3517

    Google Scholar 

  14. Zenkour AM (2005) Analytical solutions for rotating exponentially-graded annular disks with various boundary conditions. Int J Struct Stab Dyn 5(04):557–577

    MathSciNet  MATH  Google Scholar 

  15. Zenkour AM (2007) Elastic deformation of the rotating functionally graded annular disk with rigid casing. J. Mater Sci 42(23):9717–9724

    Google Scholar 

  16. Zenkour AM (2006) Thermoelastic solutions for annular disks with arbitrary variable thickness. Struct Eng Mech 24(5):515–528

    Google Scholar 

  17. Peng XL, Li XF (2012) Elastic analysis of rotating functionally graded polar orthotropic disks. Int J Mech Sci 60(1):84–91

    Google Scholar 

  18. Dai HL, Yan X, Yang L (2013) Nonlinear dynamic analysis for FGM circular plates. J Mech 29(02):287–296

    Google Scholar 

  19. Dai HL, Guo ZY, Yang L (2013) Nonlinear dynamic response of functionally graded materials circular plates subject to low-velocity impact. J Compos Mater 47(22):2797–2807

    Google Scholar 

  20. Damircheli M, Azadi M (2011) Temperature and thickness effects on thermal and mechanical stresses of rotating FG-disks. J Mech Sci Technol 25(3):827–836

    Google Scholar 

  21. Hassani A, Hojjati MH, Farrahi G, Alashti RA (2011) Semi-exact elastic solutions for thermo-mechanical analysis of functionally graded rotating disks. Compos Struct 93(12):3239–3251

    MATH  Google Scholar 

  22. Peng XL, Li XF (2010) Thermal stress in rotating functionally graded hollow circular disks. Compos Struct 92(8):1896–1904

    Google Scholar 

  23. Kordkheili SH, Naghdabadi R (2007) Thermoelastic analysis of a functionally graded rotating disk. Compos Struct 79(4):508–516

    MATH  Google Scholar 

  24. Afsar AM, Go J (2010) Finite element analysis of thermoelastic field in a rotating FGM circular disk. Appl Math Model 34(11):3309–3320

    MATH  Google Scholar 

  25. Brischetto S, Leetsch R, Carrera E, Wallmersperger T, Kröplin B (2008) Thermo-mechanical bending of functionally graded plates. J Therm Stresses 31(3):286–308

    Google Scholar 

  26. Kordkheili SH, Livani M (2013) Thermoelastic creep analysis of a functionally graded various thickness rotating disk with temperature-dependent material properties. Int J Press Vessels Pip 111:63–74

    Google Scholar 

  27. Dai T, Dai HL (2016) Thermo-elastic analysis of a functionally graded rotating hollow circular disk with variable thickness and angular speed. Appl Math Model 40(17):7689–7707

    MathSciNet  MATH  Google Scholar 

  28. Jahed H, Farshi B, Bidabadi J (2005) Minimum weight design of inhomogeneous rotating discs. Int J Press Vessels Pip 82(1):35–41

    Google Scholar 

  29. Zafarmand H, Hassani B (2014) Analysis of two-dimensional functionally graded rotating thick disks with variable thickness. Acta Mech 225(2):453–464

    MATH  Google Scholar 

  30. Arani AG, Loghman A, Shajari AR, Amir S (2010) Semi-analytical solution of magneto-thermo-elastic stresses for functionally graded variable thickness rotating disks. J Mech Sci Technol 24(10):2107–2118

    Google Scholar 

  31. Hojjati MH, Jafari S (2009) Semi-exact solution of non-uniform thickness and density rotating disks. Part II: elastic strain hardening solution. Int J Press Vessels Pip 86(5):307–318

    Google Scholar 

  32. Dai HL, Dai T, Yang L (2013) Free vibration of a FGPM circular plate placed in a uniform magnetic field. Meccanica 48(10):2339–2347

    MathSciNet  MATH  Google Scholar 

  33. Güven U, Çelik A (2001) On transverse vibrations of functionally graded isotropic linearly elastic rotating solid disks. Mech Res Commun 28(3):271–276

    MATH  Google Scholar 

  34. Brischetto S (2013) Exact elasticity solution for natural frequencies of functionally graded simply-supported structures. CMES 95(5):391–430

    MathSciNet  MATH  Google Scholar 

  35. Mashat DS, Carrera E, Zenkour AM, Al Khateeb SA, Filippi M (2014) Free vibration of FGM layered beams by various theories and finite elements. Compos B Eng 59:269–278

    Google Scholar 

  36. Hassani A, Hojjati MH, Mahdavi E, Alashti RA, Farrahi G (2012) Thermo-mechanical analysis of rotating disks with non-uniform thickness and material properties. Int J Press Vessels Pip 98:95–101

    Google Scholar 

  37. Li SR, Zhang JH, Zhao YG (2007) Nonlinear thermomechanical post-buckling of circular FGM plate with geometric imperfection. Thin Walled Struct 45(5):528–536

    Google Scholar 

  38. Librescu L, Souza MA (1993) Post-buckling of geometrically imperfect shear-deformable flat panels under combined thermal and compressive edge loadings. J Appl Mech 60(2):526–533

    MATH  Google Scholar 

  39. Librescu L, Souza MA (1998) Nonlinear response of geometrically imperfect stiffened flat panels under thermomechanical loading. J Therm Stresses 21(1):3–19

    Google Scholar 

  40. Shen HS (2000) Thermomechanical postbuckling of imperfect shear deformable laminated plates on elastic foundations. Comput Methods Appl Mech Eng 189(3):761–784

    MATH  Google Scholar 

  41. Shen HS (2001) Postbuckling of shear deformable laminated plates with piezoelectric actuators under complex loading conditions. Int J Solids Struct 38(44):7703–7721

    MATH  Google Scholar 

  42. Shen HS (2001) Thermal postbuckling behavior of imperfect shear deformable laminated plates with temperature-dependent properties. Comput Methods Appl Mech Eng 190(40):5377–5390

    MATH  Google Scholar 

  43. Zou G, Qiao P (2002) Higher-order finite strip method for postbuckling analysis of imperfect composite plates. J. Eng Mech 128(9):1008–1015

    Google Scholar 

  44. Ovesy HR, Ghannadpour SAM, Morada G (2005) Geometric non-linear analysis of composite laminated plates with initial imperfection under end shortening, using two versions of finite strip method. Compos Struct 71(3):307–314

    Google Scholar 

  45. Ovesy HR, GhannadPour SAM (2006) Geometric non-linear analysis of imperfect composite laminated plates, under end shortening and pressure loading, using finite strip method. Compos Struct 75(1):100–105

    Google Scholar 

  46. Girish J, Ramachandra LS (2005) Thermomechanical postbuckling analysis of symmetric and antisymmetric composite plates with imperfections. Compos Struct 67(4):453–460

    Google Scholar 

  47. Shahrjerdi A, Bahramibabamiri B (2015) The effect of different geometrical imperfection of buckling of composite cylindrical shells subjected to axial loading. Int J Mech Mater Eng 10(1):1–10

    Google Scholar 

  48. Shariat BS, Javaheri R, Eslami MR (2005) Buckling of imperfect functionally graded plates under in-plane compressive loading. Thin Walled Struct 43(7):1020–1036

    Google Scholar 

  49. Shen HS (2005) Postbuckling of FGM plates with piezoelectric actuators under thermo-electro-mechanical loadings. Int J Solids Struct 42(23):6101–6121

    MATH  Google Scholar 

  50. Yang J, Liew KM, Kitipornchai S (2006) Imperfection sensitivity of the post-buckling behavior of higher-order shear deformable functionally graded plates. Int J Solids Struct 43(17):5247–5266

    MATH  Google Scholar 

  51. Shariat BS, Eslami MR (2006) Thermal buckling of imperfect functionally graded plates. Int J Solids Struct 43(14):4082–4096

    MATH  Google Scholar 

  52. Touloukian YS (1967) Thermophysical properties of high temperature solid materials. Elements, vol I. Macmillan, New York

    Google Scholar 

  53. Reddy JN, Praveen GN (1998) Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates. Int J Solid Struct 35:4467–4476

    MATH  Google Scholar 

  54. Shen HS, Wang ZX (2010) Nonlinear bending of FGM plates subjected to combined loading and resting on elastic foundations. Compos Struct 92(10):2517–2524

    Google Scholar 

  55. Golmakani ME, Kadkhodayan M (2011) Large deflection analysis of circular and annular FGM plates under thermo-mechanical loadings with temperature-dependent properties. Compos B Eng 42(4):614–625

    Google Scholar 

  56. Xin L, Lu W, Ju C, Dui G (2016) Influence of linear work hardening on the elastic–plastic behavior of a functionally graded thick-walled tube. Acta Mech 227(8):2305–2321

    MathSciNet  MATH  Google Scholar 

  57. Xin L, Yang S, Zhou D, Dui G (2016) An approximate analytical solution based on the Mori-Tanaka method for functionally graded thick-walled tube subjected to internal pressure. Compos Struct 135:74–82

    Google Scholar 

  58. Reddy JN, Chin CD (1998) Thermoelastic analysis of functionally graded cylinders and plates. J Therm Stresses 21:593–626

    Google Scholar 

  59. Yang J, Shen H-S (2003) Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads under various boundary conditions. Compos B 34:103–115

    Google Scholar 

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Acknowledgements

The research in this paper was financially supported by Malayer University, Malayer, Iran.

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Correspondence to Ali Shahrjerdi.

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Technical Editor: Pedro Manuel Calas Lopes Pacheco, D.Sc.

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Bahrami Babamiri, B., Shahrjerdi, A. & Bayat, M. Effect of geometrical imperfection on the thermomechanical behavior of functionally graded material rotating disk. J Braz. Soc. Mech. Sci. Eng. 42, 271 (2020). https://doi.org/10.1007/s40430-020-02360-z

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  • DOI: https://doi.org/10.1007/s40430-020-02360-z

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