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Theoretical analysis of rotary hyperelastic variable thickness disk made of functionally graded materials

  • Received : 2021.09.27
  • Accepted : 2022.08.03
  • Published : 2022.10.10
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Abstract

This research investigates a rotary disk with variable cross-section and incompressible hyperelastic material with functionally graded properties in large hyperelastic deformations. For this purpose, a power relation has been used to express the changes in cross-section and properties of hyperelastic material. So that (m) represents the changes in cross-section and (n) represents the manner of changes in material properties. The constants used for hyperelastic material have been obtained from experimental data. The obtained equations have been solved for different m, n, and (angular velocity) values, and the values of radial stresses, tangential stresses, and elongation have been compared. The results show that m and n have a significant impact on disk behavior, so the expected behavior of the disk can be obtained by an optimal selection of these two parameters.

Keywords

References

  1. Arruda, E.M. and Boyce, M.C. (1993), "A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials", J. Mech. Phys. Solids. 41(2), 389-412. https://doi.org/10.1016/0022-5096(93)90013-6.
  2. Attard, M.M. (2003), "Finite strain-isotropic hyperelasticity", Int. J. Solids Struct., 40(17), 4353-4378. https://doi.org/10.1016/S0020-7683(03)00217-8.
  3. Batra, R. (2006), "Torsion of a functionally graded cylinder", AIAA journal. 44(6), 1363-1365. https://doi.org/10.2514/1.19555.
  4. Batra, R. (2008), "Optimal design of functionally graded incompressible linear elastic cylinders and spheres", AIAA J., 46(8), 2050-2057. https://doi.org/10.2514/1.34937.
  5. Batra, R. (2011), "Material tailoring and universal relations for axisymmetric deformations of functionally graded rubberlike cylinders and spheres", Mathem. Mech. Solids. 16(7), 729-738. https://doi.org/10.1177/1081286510387404.
  6. Batra, R. and Bahrami, A. (2009), "Inflation and eversion of functionally graded non-linear elastic incompressible circular cylinders", Int. J. Non-Linear Mech., 44(3), 311-323. https://doi.org/10.1016/j.ijnonlinmec.2008.12.005.
  7. Batra, R., Mueller, I., Strehlow, P.J.M. and solids, M.O. (2005), "Treloar's biaxial tests and Kearsley's bifurcation in rubber sheets", 10(6), 705-713. https://doi.org/10.1177/1081286505043032.
  8. Beatty, M.F. (1987), "Topics in finite elasticity: Hyperelasticity of rubber, elastomers, and biological tissues-with examples", Appl. Mech. Rev., 40(12), 1699-1734. https://doi.org/10.1115/1.3149545.
  9. Benatta, M., Mechab, I., Tounsi, A. and Bedia, E.A. (2008), "Static analysis of functionally graded short beams including warping and shear deformation effects", Comput. Mater. Sci., 44(2), 765-773. https://doi.org/10.1016/j.commatsci.2008.05.020.
  10. Bilgili, E. (2004), "Functional grading of rubber tubes within the context of a molecularly inspired finite thermoelastic model", Acta Mech., 169(1-4), 79-85. https://doi.org/10.1007/s00707-004-0094-1.
  11. Bilgili, E., Bernstein, B. and Arastoopour, H. (2002), "Influence of material non homogeneity on the shearing response of a neo hookean slab", Rubber Chemistry Technol., 75(2), 347-363. https://doi.org/10.5254/1.3544983.
  12. Bilgili, E., Bernstein, B. and Arastoopour, H. (2003), "Effect of material non-homogeneity on the inhomogeneous shearing deformation of a Gent slab subjected to a temperature gradient", Int. J. Non-Linear Mech., 38(9), 1351-1368. https://doi.org/10.1016/S0020-7462(02)00075-6.
  13. Blatz, P.J. and Ko, W.L. (1962), "Application of finite elastic theory to the deformation of rubbery materials", Transact. Soc. Rheology. 6(1), 223-252. https://doi.org/10.1122/1.548937.
  14. Dehshahri, K., Nejad, M.Z., Ziaee, S., Niknejad, A. and Hadi, A. (2020), "Free vibrations analysis of arbitrary threedimensionally FGM nanoplates", Ad. Nano Res., 8(2), 115-134. https://doi.org/10.12989/anr.2020.8.2.115.
  15. Ding, H.X. and She, G.L. (2021), "A higher-order beam model for the snap-buckling analysis of FG pipes conveying fluid", Struct. Eng. Mech., 80(1), 63-72. https://doi.org/10.12989/sem.2021.80.1.063.
  16. Ebrahimi, T., Nejad, M.Z., Jahankohan, H. and Hadi, A. (2021), "Thermoelastoplastic response of FGM linearly hardening rotating thick cylindrical pressure vessels", Steel Compos. Struct., 38(2), 189-211. https://doi.org/10.12989/scs.2021.38.2.189.
  17. Emadi, M., Nejad, M.Z., Ziaee, S. and Hadi, A. (2021), "Buckling analysis of arbitrary two-directional functionally graded nanoplate based on nonlocal elasticity theory using generalized differential quadrature method", Steel Compos. Struct., 39(5), 565-581. https://doi.org/10.12989/scs.2021.39.5.565.
  18. Gharibi, M., Zamani Nejad, M. and Hadi, A. (2017), "Elastic analysis of functionally graded rotating thick cylindrical pressure vessels with exponentially-varying properties using power series method of Frobenius", J. Comput. Appl. Mech., 48(1), 89-98.
  19. Holzapfel, G.A.J.M. (2002), "Nonlinear solid mechanics: a continuum approach for engineering science", 37(4), 489-490
  20. Horgan, C. and Polignone, D. (1995), "Cavitation in nonlinearly elastic solids: A review", Appl. Mech. Rev., 48(8), 471-485. https://doi.org/10.1115/1.3005108.
  21. Iaccarino, G. and Batra, R. (2012), "Analytical solution for radial deformations of functionally graded isotropic and incompressible second-order elastic hollow spheres", J. Elasticity. 107(2), 179-197. https://doi.org/10.1007/s10659-011-9350-5.
  22. Ikeda, Y. (2003), "Graded styrene-butadiene rubber vulcanizates", J. Appl. Polymer Sci., 87(1), 61-67. https://doi.org/10.1002/app.11670.
  23. Khoram, M.M., Hosseini, M., Hadi, A. and Shishehsaz, M. (2020), "Bending analysis of bidirectional FGM timoshenko nanobeam subjected to mechanical and magnetic forces and resting on winkler-pasternak foundation", Int. J. Appl. Mech., 12(08), 2050093. https://doi.org/10.1142/S1758825120500933.
  24. Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B: Eng., 28(1-2), 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9.
  25. Lu, L., She, G.L. and Guo, X. (2021), "Size-dependent postbuckling analysis of graphene reinforced composite microtubes with geometrical imperfection", Int. J. Mech. Sci., 199, 106428.https://doi.org/10.1016/j.ijmecsci.2021.106428.
  26. Lu, L., Wang, S., Li, M. and Guo, X. (2021), "Free vibration and dynamic stability of functionally graded composite microtubes reinforced with graphene platelets", Compos. Struct., 272, 114231. https://doi.org/10.1016/j.compstruct.2021.114231.
  27. Mark, J.E., Erman, B. and Roland, M. (2013), The Science and Technology of Rubber, Academic Press
  28. Mooney, M. (1940), "A theory of large elastic deformation", J. Appl. Phys., 11(9), 582-592. https://doi.org/10.1063/1.1712836.
  29. Nejad, M.Z., Rastgoo, A. and Hadi, A. (2014), "Exact elastoplastic analysis of rotating disks made of functionally graded materials", Int. J. Eng. Sci., 85 47-57. https://doi.org/10.1016/j.ijengsci.2014.07.009.
  30. Ogden, R.W. (1972). "Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubberlike solids", Proc. R. Soc. Lond. A. https://doi.org/10.1098/rspa.1972.0026.
  31. Reddy, J.N. (2006), Theory and Analysis of Elastic Plates and Shells, CRC Press.
  32. Rivlin, R. (1948), "Large elastic deformations of isotropic materials IV. Further developments of the general theory", Phil. Trans. R. Soc. Lond. A. 241(835), 379-397. https://doi.org/10.1098/rsta.1948.0024.
  33. Sankar, B.V. (2001), "An elasticity solution for functionally graded beams", Compos. Sci. Technol., 61(5), 689-696. https://doi.org/10.1016/S0266-3538(01)00007-0.
  34. Saravanan, U. and Rajagopal, K. (2003), "On the role of inhomogeneities in the deformation of elastic bodies", Mathem. Mech. Solids, 8(4), 349-376. https://doi.org/10.1177/10812865030084002.
  35. Saravanan, U. and Rajagopal, K. (2004), A Comparison of the Response of Isotropic Inhomogeneous Elastic Cylindrical and Spherical Shells and Their Homogenized Counterparts, Springer
  36. Saravanan, U. and Rajagopal, K. (2005), "Inflation, extension, torsion and shearing of an inhomogeneous compressible elastic right circular annular cylinder", Mathem. Mech. Solids, 10(6), 603-650. https://doi.org/10.1177/1081286505036422.
  37. She, G.L. (2021), "Guided wave propagation of porous functionally graded plates: The effect of thermal loadings", J. Thermal Stresses. 44(10), 1289-1305. https://doi.org/10.1080/01495739.2021.1974323.
  38. She, G.L., Liu, H.B. and Karami, B. (2021), "Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets", Thin-Wall. Struct., 160, 107407. https://doi.org/10.1016/j.tws.2020.107407.
  39. Suresh, S. and Mortensen, A. (1998), Fundamentals of Functionally Graded Materials, The Institut of Materials
  40. Timoshenko, S. and Goodier, J.J.F.-C.C.R.R.B.D.F.T.D.O.E.E., (1971), Theory of Elasticity, McGraw-Hill, New York.
  41. Rabin, B.H. and Shiota, I. (1995), Functionally Gradient Materials, MRS bulletin, 20(1), 14-18. https://doi.org/10.1557/S0883769400048855
  42. Yeoh, O. (1990), "Characterization of elastic properties of carbonblack-filled rubber vulcanizates", Rubber Chemistry technology. 63(5), 792-805. https://doi.org/10.5254/1.3538289.
  43. Zamani Nejad, M., Jabbari, M. and Hadi, A. (2017), "A review of functionally graded thick cylindrical and conical shells", J. Comput. Appl. Mech., 48(2), 357-370. https://doi.org/10.22059/jcamech.2017.247963.220.
  44. Zamani Nejad, M., Rastgoo, A. and Hadi, A. (2014), "Effect of exponentially-varying properties on displacements and stresses in pressurized functionally graded thick spherical shells with using iterative technique", J. Solid Mech., 6(4), 366-377. https://dorl.net/dor/20.1001.1.20083505.2014.6.4.3.3. 1001.1.20083505.2014.6.4.3.3
  45. Zarezadeh, E., Hosseini, V. and Hadi, A. (2020), "Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory", Mech. Based Des. Struct. Machines. 48(4), 480-495. https://doi.org/10.1080/15397734.2019.1642766.
  46. Zhang, Y.Y., Wang, Y.X., Zhang, X., Shen, H.M. and She, G.-L. (2021), "On snap-buckling of FG-CNTR curved nanobeams considering surface effects", Steel Compos. Struct. 38(3), 293-304.