Electro-magneto-thermo-mechanical Behaviors of a Radially Polarized FGPM Thick Hollow Sphere

Document Type: Research Paper


Department of Mechanical Engineering, Faculty of Engineering, University of Kashan


In this study an analytical method is developed to obtain the response of electro-magneto-thermo-elastic stress and perturbation of a magnetic field vector for a thick-walled spherical functionally graded piezoelectric material (FGPM). The hollow sphere, which is placed in a uniform magnetic field, is subjected to a temperature gradient, inner and outer pressures and a constant electric potential difference between its inner and outer surfaces. The thermal, piezoelectric and mechanical properties except the Poisson’s ratio are assumed to vary with the power law functions through the thickness of the hollow sphere. By solving the heat transfer equation, in the first step, a symmetric distribution of temperature is obtained. Using the infinitesimal electro-magneto-thermo-elasticity theory, then, the Navier’s equation is solved and exact solutions for stresses, electric displacement, electric potential and perturbation of magnetic field vector in the FGPM hollow sphere are obtained. Moreover, the effects of magnetic field vector, electric potential and material in-homogeneity on the stresses and displacements distributions are investigated. The presented results indicate that the material in-homogeneity has a significant influence on the electro-magneto-thermo-mechanical behaviors of the FGPM hollow sphere and should therefore be considered in its optimum design.


[1] Chen W.Q., Lu Y., Ye J. R., Cai J.B., 2002, 3D electroelastic fields in a functionally graded piezoceramic hollow sphere under mechanical and electric loading, Archive of Applied Mechanics 72: 39-51.

[2] Lim C.W., He L.H., 2001, Exact solution of a compositionally graded piezoelectric layer under uniform stretch, bending and twisting, International Journal of Mechanical Sciences 43: 2479-2492.

[3] Shi Z. F., Chen Y., 2004, Functionally graded piezoelectric cantilever beam under load, Archive of Applied Mechanics 74: 237-247.

[4] Wu C. P., Syu Y.S., 2007, Exact solution of functionally graded piezoelectric shells under cylindrical bending, International Journal of Solids and Structures 44: 6450-6472.

[5] Dai H.L., Fu Y.M., Yang J.H., 2007, Electromagnetoelastic behaviors of functionally graded piezoelectric solid cylinder and sphere, Acta Mechanica Sinica 23: 55-63.

[6] Ootao Y., Tanigawa Y., 2007, Transient piezothermoelastic analysis for a functionally graded thermopiezoelectric hollow sphere, Composite Structures 81: 540-549.

[7] Khoshgoftar M.J., Ghorbanpour Arani A., Arefi M., 2009, Thermoelastic analysis of a thick walled cylinder made of functionally graded piezoelectric material, Smart Materials and Structures 18: 115007.

[8] Ghorbanpour Arani A., Loghman A., Abdollahitaheri A., Atabakhshian V., 2010, Electro-thermo-mechanical behaviors of a radially polarized rotating functionally graded piezoelectric cylinder, Journal of Mechanics of Materials and Structures, in press.

[9] Ghorbanpour Arani A., Salari M., Khademizadeh H., Arefmanesh A., 2010, Magnetothermoelastic stress and perturbation of magnetic field vector in a functionally graded hollow sphere, Archive of Applied Mechanics 80: 189-200.

[10] Ghorbanpour Arani A., Salari M., Khademizadeh H., Arefmanesh A., 2009, Magnetothermoelastic transient response of a functionally graded thick hollow sphere subjected to magnetic and thermoelastic fields, Archive of Applied Mechanics 79: 481-497.

[11] Dai H.L., Hong L., Fu Y.M., Xiao X.,2010, Analytical solution for electromagnetothermoelastic behaviors of a functionally graded piezoelectric hollow cylinder, Applied Mathematical Modelling 34: 343-357.

[12] Kraus J.D., 1984, Electromagnetic, McGraw-Hill, New York.

[13] Dai H.L., Wang X., 2004, Dynamic responses of piezoelectric hollow cylinders in an axial magnetic field, International Journal of Solids and Structures 41: 5231-5246.

[14] Heyliger P., 1996, A note on the static behavior of simplysupported laminated piezoelectric cylinders, International Journal of Solids and Structures 34: 3781-3794.

[15] Wang H.M., Xu Z.X., 2010, Effect of material inhomogeneity on electromechanical behaviors of functionally graded piezoelectric spherical structures, Computational Materials Science 48: 440-445.