Stress Analysis of Magneto Thermoelastic and Induction Magnetic Filed in FGM Hallow Sphere

Document Type : Persian


1 Assistant Professor, Mechanical Engineering Dept., Isfahan University of Technology

2 Assistant Professor, Kashan University

3 M.Sc., Isfahan University of Technology


In this paper a closed form solution for one-dimensional magnetothermoelastic problem in a functionally graded material (FGM) hollow sphere placed in a uniform magnetic field and temperature field subjected to an internal pressure is obtained using the theory of magnetothermoelasticity. Hyper-geometric functions are employed to solve the governing equation. The material properties through the graded direction are assumed to be nonlinear with an exponential distribution. The nonhomogeneity of the material in the radial directions is assumed to be power-exponential. The temperature, displacement and stress fields and the perturbation of magnetic field vector are determined and compared with those of the homogeneous case. Hence, the effect of inhomogeneity on the stresses and the perturbation of magnetic field vector distributions are demonstrated. The results of this study are applicable for designing optimum FGM hollow spheres.


[1]            Tianhu He., and Xiaogeng Tian., and Yapeng Shen., 2005, A generalized electromagneto-thermoelastic problem for an infinitely long solid cylinder. European Journal of Mechanics A/solid,  24,349-359.
[2]            Pelletier J.L., 2003, Thermoelastic Analysis Optimizaion Of  Functionally Graded Plates and Shells. B.S. University of Maine,.
[3]            Koizumi M., 1992, The concept of FGM. Ryukoku University,.
[4]            Pines M.L., 2004, Pressureless Sintering Of  Powder Processed Functionally Graded Metal-Ceramic Plates. Michael Louis Pines, Master Of  Science,.
[5]            Nakai T., and Murat O., 2001, Exact Solutions for stresses in functionally graded pressure vessels. Journal of Composite ser. B, 32,683-686.
[6]            Fukui Y., and Yamanaka N., and Wakashima K., 1993, The stresses and strains in a thick-walled tube for functionally graded material under uniform thermal loading. JSME Int. J.  ser. A, 36,156-162.
[7]            Lutz MP., and Zimmerman RW., 1996, Thermal stresses and Effective thermal Expansion Coefficient of a functionally gradient sphere. Journal of Thermal stresses, 19, 39-54.
[8]            Dai H.L., and Fu Y.M., and Dong Z.M., 2006, Exact solution for functionally graded pressure vessels in a uniform magnetic field. Int. J. Solids and Structures, 43,5570-5580.
[9]            Dai H.L., and Fu Y.M., 2006, Magnetothermoelastic interaction in hollow structures of functionally graded material subjected to mechanical loads. Int. J. Pressure vessels and piping,  84,132-138.
[10]        Kraus J.D., 1984, Electromagnetic. McGraw-Hill Inc.,USA,.
[11]        Dai H.L., and Wang X., 2004, Dynamic responses of piezoelectric hollow cylinders in an axial magnetic field. Int. J. solids and structures, 41,5231-5246.