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Strain based finite element for the analysis of heterogeneous hollow cylinders subjected to thermo-mechanical loading

  • Bouzeriba, Asma (Department of Science and Technology, Faculty of Science and Technology, Mechanical Engineering Materials and Structures Laboratory, Tissemsilt University) ;
  • Bouzrira, Cherif (Department of Civil Engineering, Faculty of Science and Technology, Mohammed Seddik Ben Yahia University)
  • Received : 2021.12.27
  • Accepted : 2022.08.10
  • Published : 2022.09.25

Abstract

The effectiveness and accuracy of the strain-based approach applied for analysis of two kinds of heterogeneous hollow cylinders subjected to thermal and mechanical loads are examined in this study. One is a multilayer cylinder in which the material in each layer is assumed to be linearly elastic, homogeneous and isotropic. Another is a hollow cylinder made of functionally graded materials with arbitrary gradient. The steady state condition without heat generation is considered. A sector in-plane finite element in the polar coordinate system based on strain approach is used. This element has only three degrees of freedom at each corner node. Analytical solutions available in the literature are presented to illustrate the accuracy of the sector element used. The obtained results for displacements and stresses are shown to be in good agreement with the analytical solutions.

Keywords

Acknowledgement

This research was supported by the Algerian Ministry of Higher Education and Scientific Research (MESRS).

References

  1. Abderrahmani, S., Maalem, T., Zatar, A. and Hamadi, D. (2017), "A new strain based sector finite element for plate bending problems", Int. J. Eng. Res. Africa, 33, 1-13. https://doi.org/10.4028/www.scientific.net/JERA.31.1.
  2. Assan, A.E. (2002), "Nonlinear analysis of reinforced concrete cylindrical shells", Comput. Struct., 80(27-30), 2177-2184. https://doi.org/10.1016/S0045-7949(02)00245-6.
  3. Belarbi, M.T. and Charif, A. (1998), "Nouvel element secteur base sur le modele de deformation avec rotation dans le plan", Revue Europeenne des Elements Finis, 7(4), 439-458. https://doi.org/10.1080/12506559.1998.10511312.
  4. Bouzriba, A. and Bouzrira, C. (2015), "Sector element for analysis of thick cylinders exposed to internal pressure and change of temperature", Gradevinar, 67(6), 547-555.
  5. Chareonsuk, J. and essakosol, P.V. (2011), "Numerical solutions for functionally graded solids under thermal and mechanical loads using a high-order control volume finite element method", Appl. Therm. Eng., 31(2-3), 213-227. https://doi.org/10.1016/j.appl thermaleng. 2010 .09.001.
  6. Djoudi, M.S. and Bahai, H. (2004), "Strain based finite element for the vibration of cylindrical panels with openings", Thin Wall. Struct., 42(4), 575-588. https://doi.org/10.1016/j.tws.2003.09.003.
  7. Ding, F., Wu, X., Xiang, P. and Yu, Z. (2021), "New damage ratio strength criterion for concrete and lightweight aggregate concrete", ACI Struct. J., 118(6), 165-178. https://doi.org/10.14359/51732989.
  8. Feng, S.Z., Cui, X.Y., Li, G.Y., Feng, H. and Xu, F.X. (2013), "Thermo-mechanical analysis of functionally graded cylindrical vessels using edge-based smoothed finite element method", Int. J. Press. Ves. Pip., 111, 302-309. https://doi.org/10.1016/j.ijpvp.2013.09.004.
  9. Himeur, M. and Guenfoud, M. (2011), "Bending triangular finite element with a fictitious fourth node based on the strain approach", Eur. J. Comput. Mech., 20(7-8), 455-485. https://doi.org/10.3166/ejcm.20.455-485.
  10. Himeur, M., Benmarce, A. and Guenfoud, M. (2014), "A new finite element based on the strain approach with transverse shear effect", Struct. Eng. Mech, 49(6), 793-810. https://doi.org/10.12989/sem.2014.49.6.793.
  11. Jabbari, M., Sohrabpour, S. and Eslami, M. (2002), "Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads", Int. J. Press. Ves. Pip., 79(7), 493-497. https://doi.org/10.1016/S0308-0161(02)00043-1.
  12. Jabbari, M., Bahtui, A. and Eslami, M.R. (2006), "Axisymmetric mechanical and thermal stresses in thick long FGM cylinders", J. Therm. Stress., 29(7), 643-663. https://doi.org/10.1080/01495730500499118.
  13. Li, X.F. and Peng, X.L. (2009), "A pressurized functionally graded hollow cylinder with arbitrarily varying material properties", J. Elast., 96(1), 81-95. https://doi.org/10.1007/s10659-009-9199-z.
  14. Nie, G.J. and Batra, R.C. (2010), "Exact solutions and material tailoring for functionally graded hollow circular cylinders", J. Elast., 99(2), 179-201. https://doi.org/10.1007/s10659-009-9239-8.
  15. Peng, X.L. and Li, X.F. (2009), "Thermoelastic analysis of functionally graded annulus with arbitrary gradient", Appl. Math. Mech., 30(10), 1211-1220. https://doi.org/10.1007/s10483-009-1001-7.
  16. Ozisik, M.N. (1980), Heat Conduction, John Wiley & Sons, New York.
  17. Rebiai, C. and Belounar, L. (2013), "A new strain based rectangular finite element with drilling rotation for linear and nonlinear analysis", Arch. Civil Mech. Eng., 13(1), 72-81. https://doi.org/10.1016/j.acme.2012.10.001.
  18. Ren, Y., Yu, Z., Huang, Q. and Ren, Z. (2018),"Constitutive model and failure criterions for lightweight aggregate concrete: A true triaxial experimental test", Constr. Build. Mater., 171, 759-769. https://doi.org/10.1016/j.conbuildmat.2018.03.219.
  19. Sabir, A.B. and Salhi, H.Y. (1986), "A strain based finite element for general plane elasticity problems in polar coordinates", Res Mechanica, 19(1), 1-16.
  20. Sburlati, R. (2012), "Analytical elastic solutions for pressurized hollow cylinders with internal functionally graded coatings", Compos. Struct., 94(12), 3592-3600. https://doi.org/10.1016/j.compstruct.2012.05.018.
  21. Shi, Z., Zhang, T. and Xiang, H. (2007), "Exact solutions of heterogeneous elastic hollow cylinders", Compos. Struct., 79(1), 140-147. https://doi.org/10.1016/j.compstruct.2005.11.058.
  22. Timoshenko, S. and Goodier, J.N. (1951), Theory of Elasticity, 3th Edition, McGraw Hill, New York.
  23. Tutuncu, N. and Ozturk, M. (2001), "Exact solutions for stresses in functionally graded pressure vessels", Compos. B. Eng., 32(8), 683-686. https://doi.org/10.1016/S1359-8368(01)00041-5.
  24. Tutuncu, N. (2007), "Stresses in thick-walled FGM cylinders with exponentially-varying properties", Eng. Struct., 29(9), 2032-2035. https://doi.org/10.1016/j.engstruct.2006.12.003.
  25. Vedeld, K. and Sollund, H.A. (2014), "Stresses in heated pressurized multi-layer cylinders in generalized plane strain conditions", Int. J. Press. Ves. Pip., 120, 27-35. https://doi.org/10.1016/j.ijpvp.2014.04.002.
  26. Wang, Z.W., Zhang, Q., Xia, L.Z., Wu, J.T. and Liu, P.Q. (2016), "Thermo-mechanical analysis of pressure vessels with functionally graded material coating", J. Press. Ves. Technol., 138(1), 011205. https://doi.org/10.1115/1.4031030.
  27. Yeo, W.H.J., Aliabadi, M.H., Ramesh, S. and Liew, H.L. (2017), "Exact solution for stresses/displacements in a multilayered hollow cylinder under thermo-mechanical loading", Int. J. Press. Ves. Pip., 151, 45-53. https://doi.org/10.1016/j.ijpvp.2017.01.003.
  28. Yu, Z., Tang, R., Cao, P., Huang, Q., Xie, X. and Shi, F. (2019), "Multi-axial test and failure criterion analysis on selfcompacting lightweight aggregate concrete", Constr. Build. Mater., 215, 786-798. https://doi.org/10.1016/j.conbuildmat.2019.04.236.
  29. Zhang, Q., Wang, Z.W., Tang, C.Y., Hu, D.P., Liu, P.Q. and Xia, L.Z. (2012), "Analytical solution of the thermo-mechanical stresses in a multilayered composite pressure vessel considering the influence of the closed ends", Int. J. Press. Ves. Pip., 98, 102-110. https://doi.org/10.1016/j.ijpvp.2012.07.009.
  30. Zhou, L., Parhizi, M. and Jain, A. (2021), "Temperature distribution in a multi-layer cylinder with circumferentiallyvarying convective heat transfer boundary conditions", Int. J. Therm. Sci., 160, 106673. https://doi.org/10.1016/j.ijthermalsci.20 20.106673.