Nonlinear Finite Element Analysis of Thermoelastic Stresses of FGM Rotating Disk Considering Temperature-Dependency of Material Properties

Document Type: Persian


1 Ph.D Student of mechanical engineering, Islamic Azad University, Science and Technology branch

2 Ph.D Student of mechanical engineering, Sharif University of Technology


In the present paper, nonlinear radial and hoop thermoelastic stresses analysis of a disk made of FGMs material is investigated. According to this purpose, finite element method is used. In the present method, second-order one-dimensional element (with three node points) is proposed. The geometrical and stress boundary conditions are defined in the state of non-existence of external pressure and then zero radial stress in the outer layer of the disk, and zero displacement in the center of the disk. Also the temperature distribution is assumed as linear. The material properties changes including temperature-dependency are modeled. Finally, a numerical example is proposed to show the radial displacements, radial and hoop thermoelastic stresses versus radius of the disk for different power (N) from Power-law and different angular velocities. The results show that by increasing both two parameters, N and angular velocity of the disk, the amounts of displacement and stress are increased. At last, temperature-dependency and temperature-independency of material properties is investigated.


[1]        Suresh S., Mortensen A., Fundamental of Functionally Graded Materials, Barnes and Noble Pub, 1998.

[2]        Koizumi M., Nino M., Overview of FGM research in Japan, MRS Bulletin, Vol. 20, 1995, pp. 19-21.

[3]        Kaysser W.A., Ilschner B., FGM research activities in Europe, MRS Bulletin, Vol. 20 1995, pp. 22-26.

[4]        Research on the basic technology for the development of functionally graded materials for relaxation of thermal stress, Science on Technology Agency of Japanese Government Report, 1987.

[5]        Timoshenko S.P., Goodier J.N., Theory of Elasticity, McGraw-Hill, New York, 1987

[6]        Lekhnitskii S.G. , Anisotropic Plates, Gordon and Breach, London, 1968.

[7]        Seireg A., Surana K.S., Optimum design of rotating disks, J. Engineering, Vol. 92, 1970, pp. 1–10.

[8]        Murthy D.N.S., Sherbourne A.N., Elastic stresses in anisotropic disks of variable axial, J. Mechanical Science, Vol. 12,1970,  pp. 627–640.

[9]        Yeh K.Y., Han R.P.S., Analysis of high-speed rotating disks with variable axial and in-homogeneity, J. Applied Mechanics, Vol. 61, 1994, pp. 186–191.

[10]    Leissa A.W., Vagins M., The design of orthotropicmaterials for stress optimization,    J. Solids  Structures, Vol. 14,1978, pp. 517–526.

[11]    Jain R., Ramachandra K., Simha K.R.Y., Rotating anisotropic disc of uniform strength, J. Mechanical Science, Vol. 41, 1999, pp. 639–648.

[12]    Jain R., Ramachandra K., Simha K.R.Y., Singularity in rotating orthotropic discs and shells, J. Solids Structures, Vol. 37, 2000,
pp. 2035–58

[13]    Zhou F., Ogawa A., Elastic solutions for a solid rotating disk with cubic anisotropy, J. Applied Mechanics, Vol. 69 , 2002, pp. 81–83

[14]    Ramu S.A., Iyengar K.J., Quasi-three dimensional elastic stresses in rotating disks, J.  Mechanical Science, Vol. 16 ,1974, pp. 473–477





[15]    Chen W.Q., Lee K.Y., Stresses in rotating cross-ply laminated hollow cylinders with arbitrary axial, J. Strain Analysis, Vol. 39, 2004,
pp. 437–445

[16]    Mian M.A, Spencer A.J.M., Exact solutions for functionally graded and laminated elastic materials, J.  Solid Mechanics, Vol. 46, 1998, pp. 2283–95.

[17]    Chen J., Ding H., Chen W., Three-dimensional analytical solution for a rotating disc of functionally graded materials with transverse isotropy, J. Applied Mechanics, Vol. 77, 2007, pp. 241–251.

[18]    Hosseini Kordkheili S.A., Naghdabadi R., Thermoelastic analysis of a functionally graded rotating disk, J. Composite Structures, Vol. 79, 2007, pp. 508-516.

[19]    Zenkour A.M., Stress distribution in rotating composite structures of functionally graded solid disks, J. Materials Processing Technology, Vol. 209(7), 2009, pp. 3511-17.

[20]    Bayat  M., Sahari B.B., Saleem M., Ali  A., Wong  S.V., Thermoelastic solution of a functionally graded variable thickness rotating disk with bending based on the first-order shear deformation theory, J. Thin-walled Structure, Vol. 47, Issue 5, 2009, Pages 568-582 .

[21]    Reddy J.N., Chin C.D., Thermomechanical analysis of functionally graded cylinders and plates, J. Thermal Stresses, Vol. 21,1998,
pp. 593-626.

[22]    Budynas R.G., Advanced Strength And Applied Stress Analysis, McGraw-Hill Kogakusha, Ltd., Tokyo, 1977.

[23]    T.J.R. Hughes, The Finite Element Method, Prentice-Hall International Inc., 1987.