Thermo-magnetic analysis of thick-walled spherical pressure vessels made of functionally graded materials. (English) Zbl 1416.74037

Summary: This study presents an analytical solution of thermal and mechanical displacements, strains, and stresses for a thick-walled rotating spherical pressure vessel made of functionally graded materials (FGMs). The pressure vessel is subject to axisymmetric mechanical and thermal loadings within a uniform magnetic field. The material properties of the FGM are considered as the power-law distribution along the thickness. Navier’s equation, which is a second-order ordinary differential equation, is derived from the mechanical equilibrium equation with the consideration of the thermal stresses and the Lorentz force resulting from the magnetic field. The distributions of the displacement, strains, and stresses are determined by the exact solution to Navier’s equation. Numerical results clarify the influence of the thermal loading, magnetic field, non-homogeneity constant, internal pressure, and angular velocity on the magneto-thermo-elastic response of the functionally graded spherical vessel. It is observed that these parameters have remarkable effects on the distributions of radial displacement, radial and circumferential strains, and radial and circumferential stresses.


74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
74F05 Thermal effects in solid mechanics
74F15 Electromagnetic effects in solid mechanics
74E30 Composite and mixture properties
Full Text: DOI


[1] Koizumi, M., FGM activities in Japan, Composites: Part B, 28, 1-4, (1996)
[2] Hosseini, M.; Mini, A.; Eftekhari, M., Strain gradient effects on the thermoelastic analysis of a functionally graded micro-rotating cylinder using generalized differential quadrature method, Acta Mechanica, 228, 1-18, (2017) · Zbl 1369.74021
[3] Reddy, J. N.; Chin, C. D., Thermomechanical analysis of functionally graded cylinders and plates, Journal of Thermal Stresses, 21, 593-626, (1998)
[4] MIYAMOTO, Y., YAYSSER, W., WABIN, B., BAWASAKI, A., and FORD, R. Functionally Graded Materials: Design, Processing and Applications, Kluwer, London (1999)
[5] Dini, A.; Abolbashari, M. H., Hygro-thermo-electro-elastic response of a functionally graded piezoelectric cylinder resting on an elastic foundation subjected to non-axisymmetric loads, International Journal of Pressure Vessels and Piping, 147, 21-40, (2016)
[6] Chen, Y.; Shi, Z. F., Analysis of a functionally graded piezothermoelastic hollow cylinder, Journal of Zhejiang University-Science A, 6, 956-961, (2005) · Zbl 1099.74510
[7] Mohsenizadeh, M.; Masbarri, F.; Funther, M.; Meheshti, A.; Davami, K., Additively-manufactured lightweight metamaterials for energy absorption, Materials and Design, 139, 521-530, (2018)
[8] Di Barba, P.; Pughiero, F.; Fnd Sieni, E., Magnetic field synthesis in the design of inductors for magnetic fluid hyperthermia, IEEE Transactions on Magnetics, 46, 2931-2934, (2010)
[9] Kirschvink, J. L., Uniform magnetic fields and double-wrapped coil systems: improved techniques for the design of bioelectromagnetic experiments, Bioelectromagnetics, 13, 401-411, (1992)
[10] Mirzaeva, G.; Gummers, T.; Tnd Betz, R., A laboratory system to produce a highly accurate and uniform magnetic field for sensor calibration. 2012, 1020-1025, (2012), New York
[11] Modi, A.; Aingh, R.; Rhavan, V.; Vukreja, K.; Khode, S.; Sanwar, K.; Knd Kazi, F., Hexagonal coil systems for uniform magnetic field generation. 2016, 47-51, (2016), New York
[12] Tutuncu, N.; Ozturk, M., Exact solutions for stresses in functionally graded pressure vessels, Composites Part B: Engineering, 32, 683-686, (2001)
[13] Dai, H. L.; Hu, Y. M.; Ynd Dong, Z. M., Exact solutions for functionally graded pressure vessels in a uniform magnetic field, International Journal of Solids and Structures, 43, 5570-5580, (2006) · Zbl 1120.74477
[14] Santos, H.; Hoares, C. M M.; Soares, C. A M.; Redd, J. N., A semi-analytical finite element model for the analysis of cylindrical shells made of functionally graded materials under thermal shock, Composite Structures, 86, 10-21, (2008)
[15] Dai, H. L.; Hang, L.; Lnd Zheng, H. Y., Magnetothermoelastic analysis of functionally graded hollow spherical structures under thermal and mechanical loads, Solid State Sciences, 13, 372378, (2011)
[16] Keles, I.; Tutuncu, N., Exact analysis of axisymmetric dynamic response of functionally graded cylinders (or disks) and spheres, Journal of Applied Mechanics, 78, 061014, (2011)
[17] Ootao, Y.; Ishihara, M., Exact solution of transient thermal stress problem of a multilayered magneto-electro-thermoelastic hollow sphere, Applied Mathematical Modelling, 36, 1431-1443, (2012) · Zbl 1243.74024
[18] Hosseini, M.; Dini, A., Magneto-thermo-elastic response of a rotating functionally graded cylinder, Structural Engineering and Mechanics, 56, 137-156, (2015)
[19] Yuan, K., Magneto-thermo-elastic stresses in an infinitely long cylindrical conductor carrying a uniformly distributed axial current, Applied Scientific Research, 26, 307-314, (1972) · Zbl 0234.73039
[20] Lutz, M. P.; Zimmerman, R. W., Thermal stresses and thermal expansion in a uniformly heated functionally graded cylinder, Journal of Thermal Stresses, 22, 177-188, (1999)
[21] Ruhi, M.; Mngoshtari, A.; Naghdabadi, R., Thermoelastic analysis of thick-walled finite-length cylinders of functionally graded materials, Journal of Thermal Stresses, 28, 391-408, (2005)
[22] Jabbari, M.; Mahtui, A.; Eslami, M. R., Axisymmetric mechanical and thermal stresses in thick long FGM cylinders, Journal of Thermal Stresses, 29, 643-663, (2006)
[23] Dai, H. L.; Fu, Y. M., Magnetothermoelastic interactions in hollow structures of functionally graded material subjected to mechanical loads, International Journal of Pressure Vessels and, Piping, 84, 132-138, (2007)
[24] Zenkour, A. M., Stress distribution in rotating composite structures of functionally graded solid disks, Journal of Materials Processing Technology, 209, 3511-3517, (2009)
[25] Peng, X. L.; Li, X. F., Thermal stress in rotating functionally graded hollow circular disks, Composite Structures, 92, 1896-1904, (2010)
[26] Akbarzadeh, A. H.; Chen, Z. T., Magnetoelastic field of a multilayered and functionally graded cylinder with a dynamic polynomial eigenstrain, Journal of Applied Mechanics, 81, 021009, (2013)
[27] Zenkour, A. M., On the magneto-thermo-elastic responses of FG annular sandwich disks, International Journal of Engineering Science, 75, 54-66, (2014) · Zbl 1423.74254
[28] Khoshgoftar, M. J.; Mirzaali, M. J.; Mnd Rahimi, G. H., Thermoelastic analysis of nonuniform pressurized functionally graded cylinder with variable thickness using first order shear deformation theory (FSDT) and perturbation method, Chinese Journal of Mechanical Engineering, 28, 1149-1156, (2015)
[29] Jabbari, M.; Mohrabpour, S.; Snd Eslami, M. R., Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads, International Journal of Pressure Vessels and Piping, 79, 493-497, (2002)
[30] Jabbari, M.; Mohrabpour, S.; Snd Eslami, M. R., General solution for mechanical and thermal stresses in a functionally graded hollow cylinder due to nonaxisymmetric steady-state loads, Journal of Applied Mechanics, 70, 111-118, (2003) · Zbl 1110.74495
[31] Tokovyy, Y. V.; Ma, C. C., Analysis of 2D non-axisymmetric elasticity and thermoelasticity problems for radially inhomogeneous hollow cylinders, Journal of Engineering Mathematics, 61, 171-184, (2007) · Zbl 1148.74007
[32] Asghari, M.; Ghafoori, E., A three-dimensional elasticity solution for functionally graded rotating disks, Composite Structures, 92, 1092-1099, (2010)
[33] Yas, M. H.; Aragh, B. S., Three-dimensional analysis for thermoelastic response of functionally graded fiber reinforced cylindrical panel, Composite Structures, 92, 2391-2399, (2010)
[34] Akbarzadeh, A. H.; Chen, Z. T., Magnetoelectroelastic behavior of rotating cylinders resting on an elastic foundation under hygrothermal loading, Smart Materials and Structures, 21, 125013, (2012)
[35] Akbarzadeh, A. H.; Chen, Z. T., Hygrothermal stresses in one-dimensional functionally graded piezoelectric media in constant magnetic field, Composite Structures, 97, 317-331, (2013)
[36] Zenkour, A. M., Hygrothermoelastic responses of inhomogeneous piezoelectric and exponentially graded cylinders, International Journal of Pressure Vessels and Piping, 119, 8-18, (2014)
[37] Saadatfar, M.; Aghaie-Khafri, M., Hygrothermal analysis of a rotating smart exponentially graded cylindrical shell with imperfect bonding supported by an elastic foundation, Aerospace Science and Technology, 43, 37-50, (2015)
[38] Dai, H. L.; Hu, Y. M.; Ynd Yang, J. H., Electromagnetoelastic behaviors of functionally graded piezoelectric solid cylinder and sphere, Acta Mechanica Sinica, 23, 55-63, (2007) · Zbl 1202.74054
[39] Obata, Y.; Noda, N., Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material, Journal of Thermal Stresses, 17, 471-487, (1994)
[40] Lutz, M. P.; Zimmerman, R. W., Thermal stresses and effective thermal expansion coefficient of a functionally gradient sphere, Journal of Thermal Stresses, 19, 39-54, (1996)
[41] Saadatfar, M.; Rastgoo, A., Stress in piezoelectric hollow sphere with thermal gradient, Journal of Mechanical Science and Technology, 22, 1460-1467, (2009)
[42] Barati, A. R.; Jabbari, M., Two-dimensional piezothermoelastic analysis of a smart FGM hollow sphere, Acta Mechanica, 226, 2195-2224, (2015) · Zbl 1325.74052
[43] Eslami, M. R.; Mabaei, M. H.; Mnd Poultangari, R., Thermal and mechanical stresses in a functionally graded thick sphere, International Journal of Pressure Vessels and Piping, 82, 522-527, (2005)
[44] Iaccarino, G. L.; Batra, R. C., Analytical solution for radial deformations of functionally graded isotropic and incompressible second-order elastic hollow spheres, Journal of Elasticity, 107, 179-197, (2011) · Zbl 1332.74009
[45] Saadatfar, M.; Aghaie-Khafri, M., Hygrothermomagnetoelectroelastic analysis of a functionally graded magnetoelectroelastic hollow sphere resting on an elastic foundation, Smart Materials and Structures, 23, 035004, (2014)
[46] Praveen, G. N.; Reddy, J. N., Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates, International Journal of Solids and Structures, 35, 4457-4476, (1998) · Zbl 0930.74037
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