Effects of Inhomogeneity and Thickness Parameters on the Elastic Response of a Pressurized Hyperbolic Annulus/Disc Made of Functionally Graded Material

Abstract

A broad parametric study is carried out to investigate the effects of both the inhomogeneity parameter, and a profile index of Stodola’s hyperbolic function on the static response of such structures subjected to both the inner and outer pressures. The investigation is based on the analytical formulas lately published by the author. The effects of those parameters on the variation of the radial displacement, the radial and hoop stresses are all graphically illustrated for an annulus pressurized at its both surfaces. It is observed that, especially, the variation of the hoop stress in radial coordinate is closely sensible to variation of those parameters. For the chosen problems it was observed that one of two materials whose Young’s modulus is higher than the other is better to locate at the inner surface of the disc having divergent profile to get reasonable maximum hoop stresses. However much smaller radial displacements may be obtained by using positive inhomogeneity indexes for all discs whose surfaces host a material whose Young’s modulus is smaller than the other. To reach a final decision, analytical formulas such as those used in the present study together with a failure criteria such as Von Mises and Tresca become indispensable means in a design process.

Keywords

• functionally graded,Pressurized disc,hyperbolic annulus,variable thickness,exact solution,elasticity solution,thickness parameter,functionally graded

References

1. [1] Horgan, C., Chan, A., The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials. Journal of Elasticity, 55, 43-59, 1999.
2. [2] Horgan, C., Chan, A., The stress response of functionally graded isotropic linearly elastic rotating disks. Journal of Elasticity, 55, 219-230, 1999b.
3. [3] Bayat, M., Saleem, M., Sahari, B., Hamouda, A., Mahdi, E., Analysis of functionally graded rotating disks with variable thickness. Mechanics Research Communications, 35, 283-309, 2008.
4. [4] Yıldırım, V., Analytic solutions to power-law graded hyperbolic rotating discs subjected to different boundary conditions. International Journal of Engineering & Applied Sciences (IJEAS), 8/1, 138-52, 2016.
5. [5] Çallıoğlu, H., Bektaş, N.B., Sayer, M., Stress analysis of functionally graded rotating discs: analytical and numerical solutions. Acta Mechanica Sinica, 27, 950-955, 2011.
6. [6] Nejad, M.Z., Abedi, M., Lotfian, M.H., Ghannad, M., Elastic analysis of exponential FGM disks subjected to internal and external pressure. Central European Journal of Engineering, 3, 459-465, 2013.
7. [7] Nejad, M.Z., Rastgoo, A., Hadi, A., Exact elasto-plastic analysis of rotating disks made of functionally graded materials. International Journal of Engineering Science, 85, 47-57, 2014.
8. [8] You, L.H., Wang, J.X., Tang, B.P., Deformations and stresses in annular disks made of functionally graded materials subjected to internal and/or external pressure. Meccanica, 44, 283-292, 2009.

9. [9] Zenkour, A.M., Analytical solutions for rotating exponentially-graded annular disks with various boundary conditions. International Journal of Structural Stability and Dynamics, 5, 557-577, 2005.
10. [10] Zenkour, A.M., Elastic deformation of the rotating functionally graded annular disk with rigid casing. Journal of Materials Science, 42, 9717-9724, 2007.
11. [11] Zenkour, A.M., Stress distribution in rotating composite structures of functionally graded solid disks. Journal of Materials Processing Technology, 209, 3511-3517, 2009.
12. [12] Zenkour, A.M., Mashat, D.S., Stress function of a rotating variable-thickness annular disk using exact and numerical methods. Engineering, 3, 422-430, 2011.
13. [13] Eraslan, A.N., Akiş, T., On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems. Acta Mechanica, 181/(1–2), 43–63, 2006.
14. [14] Khorshidv, A.R., Khalili, S.M.R., A new analytical solution for deformation and stresses in functionally graded rotating cylinder subjected to thermal and mechanical loads. Continuum Mechanics, Fluids, Heat, 201-204, 2010.
15. [15] Saidi, A., Naderi, A., Jomehzadeh, E., A closed form solution for bending/stretching analysis of functionally graded circular plates under asymmetric loading using the Green function. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 224, 1153-1163, 2010.
16. [16] Peng, X.L., Li, X.F., Thermoelastic analysis of a functionally graded annulus with an arbitrary gradient. Applied Mathematics and Mechanics, 30, 1211–1220, 2009.
17. [17] Peng, X.L., Li, X.F., Effects of gradient on stress distribution in rotating functionally graded solid disks. Journal of Mechanical Science and Technology, 26, 1483-1492, 2012.
18. [18] Afsar, A.M., Go, J., Song, J.I., A mathematical analysis of thermoelastic characteristics of a rotating circular disk with an FGM coating at the outer surface. Advanced Composite Materials, 19, 269-288, 2010.
19. [19] Go, J., Afsar, A.M., Song, J.I., Analysis of thermoelastic characteristics of a rotating FGM circular disk by finite element method. Advanced Composite Materials, 19, 197-213, 2010.
20. [20] Amin, H., Saber, E., Khourshid, A.M., Performance of functionally graded rotating disk with variable thickness. International Journal of Engineering Research & Technology, 4/3, 556-564, 2015.
21. [21] Zheng, Y., Bahaloo, H., Mousanezhad, D., Mahdi, E., Vaziri, A. Nayeb-Hashemi, H., Stress analysis in functionally graded rotating disks with non-uniform thickness and variable angular velocity. International Journal of Mechanical Sciences, 119, 283–293, 2016.
22. [22] Gong, J.F., Ming, P.J., Xuan, L.K., Zhang, W.P., Thermoelastic analysis of three-dimensional functionally graded rotating disks based on finite volume method. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 228/4, 583-598, 2014.
23. [23] Tütüncü, N., Temel, B., An efficient unified method for thermoelastic analysis of functionally graded rotating disks of variable thickness. Mechanics of Advanced Materials and Structures, 20/1, 38-46, 2011.
24. [24] Boğa, C., Yıldırım, V., Direct application of the complementary functions method (CFM) to the static analysis of rotating disks with both parabolic-varying thickness profile and functionally graded (FG) material. Research on Engineering Structures and Materials, 3(1), 11-25, 2017.
25. [25] Yıldırım, V., Kacar, İ., Introducing a computer package program for elastic analysis of functionally graded rotating thick-walled annular structures. Digital Proceeding of ICOCEE – CAPPADOCIA2017, S. Sahinkaya and E. Kalıpcı (Editors), Nevsehir, Turkey, May 8-10, 1733-1742. 2017.
26. [26] Ghorbani, M.T., A semi-analytical solution for time-variant thermoelastic creep analysis of functionally graded rotating disks with variable thickness and properties. International Journal of Advanced Design and Manufacturing Technology, 5, 41-50, 2012.
27. [27] Kamdi, D.B., Lamba, N.K., Thermoelastic analysis of functionally graded hollow cylinder subjected to uniform temperature field. Journal of Applied and Computational Mechanics, 2/2, 118-127, 2016.
28. [28] Manthena, V.R., Lamba, N.K., Kedar, G.D., Springbackward phenomenon of a transversely isotropic functionally graded composite cylindrical shell. Journal of Applied and Computational Mechanics, 2/3, 134-143, 2016.
29. [29] Foudal, N., El-midany, T., Sadoun, A.M., Bending, buckling and vibration of a functionally graded porous beam using finite elements, Journal of Applied and Computational Mechanics DOI: 10.22055/JACM.2017.21924.1121, 2017.
30. [30] Akbaş, Ş.D., Vibration and static analysis of functionally graded porous plates. Journal of Applied and Computational Mechanics, 3/3, 199-207, 2017. DOI: 10.22055/jacm.2017.21540.1107
31. [31] Young W.C. and Budynas R.G., Roark’s Formulas for Stress and Strain, McGraw-Hill, Seventh Edition, New York, 2002.