Elastic Analysis Of Functionally Graded Rotating Spherical Pressure Vessels

Year 2023, Volume: 9 Issue: 3, 467 - 476, 01.01.2024

Durmuş Yarımpabuç , Mehmet Eker , Aybegüm Çalışkan

Abstract

In this study, elastic analysis of functionally graded rotating hollow spherical pressure vessels is investigated. It is assumed that the material properties of these structures, thought to be formed gradually from a mixture of metal and aluminum in the radial direction, are graded using the Halpin-Tsai homogenization scheme. These conditions result in a variable coefficient boundary value problem that may difficult to be solved by conventional analytical methods. The solution to this problem is handled by the Pseudospectral Chebyshev Method. Based on the differential matrix approach, this method transforms the differential equation into a linear equation system, making it easily solvable by any decomposition method. The solutions available in the literature are used to validate the results. The effects of internal pressure and rotation with a mixture of randomly selected metal and aluminum on the stress and displacement distributions are demonstrated.

Keywords

Thick-walled sphere, rotating sphere, Functionally graded materials, Halpin-Tsai method

Kalın Cidarlı Fonksiyonel Dereceli Dönen Küresel Basınçlı Kapların Elastik Analizi

Abstract

Bu çalışmada fonksiyonel derecelendirilmiş, dönen, kalın cidarlı küresel basınçlı kaplar elastik olarak incelenmiştir. Radyal doğrultuda metal ve alüminyum karışımından oluşan kürenin malzeme özelliklerinin Halpin-Tsai homojenleştirme şeması kullanılarak derecelendirildiği varsayılmıştır. Bu koşullar, geleneksel analitik yöntemlerle çözülmesi zor, değişken katsayılı sınır değer problemi ile sonuçlanır. Problemin çözümü pseudospektral Chebyshev yöntemi ile ele alınmıştır. Diferansiyel matris yaklaşımına dayanan bu yöntem, diferansiyel denklemi doğrusal bir denklem sistemine dönüştürerek herhangi bir ayrıştırma yöntemiyle kolayca çözülebilir hale getirir. Elde edilen sonuçları doğrulamak için literatürde mevcut analitik çözümler kullanılmıştır. Rastgele seçilen metal ve alüminyum karışımı ile iç basınç ve döndürmenin gerilme ve yer değiştirme dağılımları üzerindeki etkileri gösterilmiştir.

Keywords

Kalın cidarlı küre, Dönen küre, Fonksiyonel dereceli malzemeler, Halpin-Tsai yöntemi

References

• [1] F. Erdogan, “Fracture mechanics of functionally graded materials,” Composites Engineering, vol. 5, no. 7, 1995, doi:10.1016/0961-9526(95)00029-M
• [2] M. Koizumi, “FGM activities in Japan,” Composite Part:B Engineering, vol. 28, no. 1–2, pp. 1–4, Jan. 1997, doi:10.1016/S1359-8368(96)00016-9
• [3] Y. Miyamoto, W.A. Kaysser, B.H. Rabin, A. Kawasaki, and R.G. Ford, Functionally graded materials design, process, and applications, USA: Springer, 1999. doi:10.1007/978-1-4615-5301-4
• [4] A. S. Kaddour and M. J. Hinton, “Maturity of 3D failure criteria for fibre-reinforced composites: Comparison between theories and experiments: Part B of WWFE-II,” Journal of Composite materials, vol. 47, no. 6–7, pp. 925–966, Mar. 2013, doi:10.1177/0021998313478710 [5] L. L. Vignoli, M. A. Savi, P. M. C. L. Pacheco, and A. L. Kalamkarov, “Comparative analysis of micromechanical models for the elastic composite laminae,” Composite Part:B Engineering, vol. 174, Oct. 2019, doi:10.1016/j.compositesb.2019.106961
• [6] R. Madan and S. Bhowmick, “Modeling of functionally graded materials to estimate effective thermo-mechanical properties,” World Journal of Engineering, vol. 19, no. 3, pp. 291–301, 2022. doi:10.1108/WJE-09-2020-0445
• [7] E. Arslan, “Analysis on multi-layered and functionally graded spherical pressure vessels,” Pamukkale University Journal of Engineering Sciences, vol. 23, no. 1, pp. 24–35, 2017, doi:10.5505/pajes.2016.56688
• [8] A. N. Eraslan and T. Akis, “Analytical Solutions To Elastic Functionally Graded Cylindrical And Spherical Pressure Vessels,” Journal of Multidisciplinary Engineering Science and Technology, vol. 2, no. 10, pp. 2687–2693, 2015.
• [9] M. R. Eslami, M. H. Babaei, and R. Poultangari, “Thermal and mechanical stresses in a functionally graded thick sphere,” International Journal of Pressure Vessels and Piping, vol. 82, no. 7, pp. 522–527, Jul. 2005, doi:10.1016/J.IJPVP.2005.01.002
• [10] M. Z. Nejad, M. Abedi, M. H. Lotfian, and M. Ghannad, “An exact solution for stresses and displacements of pressurized FGM thick-walled spherical shells with exponential-varying properties,” Journal of Mechanical Science and Technology, vol. 26, no. 12, pp. 4081–4087, Dec. 2012, doi:10.1007/s12206-012-0908-3
• [11] N. Tutuncu and M. Ozturk, “Exact solutions for stresses in functionally graded pressure vessels,” Composite Part:B Engineering, vol. 32, no. 8, pp. 683–686, Dec. 2001, doi:10.1016/S1359-8368(01)00041-5
• [12] L. H. You, J. J. Zhang, and X. Y. You, “Elastic analysis of internally pressurized thick-walled spherical pressure vessels of functionally graded materials,” International Journal of Pressure Vessels and Piping, vol. 82, no. 5, pp. 347–354, May 2005, doi:10.1016/J.IJPVP.2004.11.001
• [13] K. Celebi, D. Yarimpabuc, and I. Keles, “A unified method for stresses in FGM sphere with exponentially-varying properties,” Structural Engineering and Mechanics, vol. 57, no. 5, pp. 823–835, 2016, doi:10.12989/sem.2016.57.5.823
• [14] İ. Kacar, “Exact elasticity solutions to rotating pressurized axisymmetric vessels made of functionally graded materials (FGM),” Materwiss Werksttech, vol. 51, no. 11, pp. 1481–1492, Nov. 2020, doi:10.1002/mawe.202000148
• [15] D. Yarımpabuç and A. Temo, “The Effect of Uniform Magnetic Field on Pressurized FG Cylindirical and Spherical Vessels,” European Mechanical Science, vol. 3, no. 4, pp. 133–141, Dec. 2019, doi:10.26701/ems.585130
• [16] M. A. Nematollahi, A. Dini, and M. Hosseini, “Thermo-magnetic analysis of thick-walled spherical pressure vessels made of functionally graded materials,” Applied Mathematics and Mechanics (English Edition), vol. 40, no. 6, pp. 751–766, Jun. 2019, doi:10.1007/s10483-019-2489-9
• [17] Y. Z. Chen and X. Y. Lin, “An alternative numerical solution of thick-walled cylinders and spheres made of functionally graded materials,” Computational Materials Science, vol. 48, no. 3, pp. 640–647, May 2010, doi:10.1016/J.COMMATSCI.2010.02.033
• [18] Y. Z. Chen and X. Y. Lin, “Elastic analysis for thick cylinders and spherical pressure vessels made of functionally graded materials,” Computational Materials Science, vol. 44, no. 2, pp. 581–587, 2008, doi:10.1016/J.COMMATSCI.2008.04.018
• [19] N. Tutuncu and B. Temel, “A novel approach to stress analysis of pressurized FGM cylinders, disks and spheres,” Composite Structures, vol. 91, no. 3, pp. 385–390, Dec. 2009, doi:10.1016/J.COMPSTRUCT.2009.06.009
• [20] S. Kumar Shrivastava, L. Sondhi, and J. Kumar Tiwari, “Elastic Analysis of Rotating Spherical Pressure Vessel of Functionally Graded Material Modeled by Mori-Tanaka Scheme,” International Journal of Engineering Research & Industrial Applications, vol. 9, no. 3, pp. 1–12, 2016.
• [21] E. Arslan, W. Mack, and T. Apatay, “Thermo-mechanically loaded steel/aluminum functionally graded spherical containers and pressure vessels,” International Journal of Pressure Vessels and Piping, vol. 191, 2021, doi:10.1016/j.ijpvp.2021.104334
• [22] A. Yıldırım, D. Yarımpabuç, V. Arikan, M. Eker, and K. Celebi, “Nonlinear thermal stress analysis of functionally graded spherical pressure vessels,” International Journal of Pressure Vessels and Piping, vol. 200, p. 104830, Dec. 2022, doi:10.1016/J.IJPVP.2022.104830
• [23] J. C. Halpin Affdl and J. L. Kardos, “The Halpin‐Tsai equations: A review,” Polymer Engineering & Science, vol. 16, no. 5. pp. 344–352, 1976. doi: 10.1002/pen.760160512
• [24] Y. Fukui, H. Okada, N. Kumazawa, Y. Watanabe, N. Yamanaka, and Y. Oya-Seimiya, “Manufacturing of Al-Al3Fe functionally graded material using the vacuum centrifugal method and measurements of its mechanical properties,” Journal of Japan Institute of Light Metals, vol. 49, no. 1, pp. 35–40, 1999.
• [25] J. M. Lee, S. B. Kang, T. Sato, H. Tezuka, and A. Kamio, “Microstructures and Mechanical Properties of Al3Fe Reinforced Aluminum Matrix Composites Fabricated by a Plasma Synthesis Method,” Materials Transactions, vol. 43, no.10, pp. 2487-2493, 2002.
• [26] L. N. Trefethen, Spectral Methods in Matlab. Philadelphia: SIAM, 2000.
• [27] M. Eker, D. Yarımpabuç, and K. Çelebi, “Thermal stress analysis of functionally graded solid and hollow thick-walled structures with heat generation,” Engineering Computations (Swansea, Wales), vol. 38, no. 1, pp. 371–391, Jan. 2021, doi:10.1108/EC-02-2020-0120
• [28] D. Yarımpabuç, “A Unified Approach to Hyperbolic Heat Conduction of the Semi-infinite Functionally Graded Body with a Time-Dependent Laser Heat Source,” Iranian Journal of Science and Technology- Transactions of Mechanical Engineering, vol. 43, no. 4, 2019, doi:10.1007/s40997-019-00312-0
• [29] A. Çalışkan, “Fonksiyonel Derecelenmiş Dönen Basınçlı Kapların Elastik Analizi,” Yüksek Lisans Tezi, Osmaniye Korkut Ata Üniversitesi, Fen Bilimleri Enstitüsü, Osmaniye, Türkiye, 2021.
• [30] C. Boğa, “Elastic Analysis of an Hollow Cylinder Made from Functionally Graded Material Exposed to Internal Pressure,” ISVOS Journal, vol. 2, no. 2, pp. 56–66, 2018