Magneto-Thermo-Elastic Stresses and Perturbation of Magnetic Field Vector in a Thin Functionally Graded Rotating Disk

Subject Areas : Engineering

A  Ghorbanpour Arani ¹ (Faculty of Mechanical Engineering, University of Kashan--- Institute of Nanoscience & Nanotechnology, University of Kashan)
S  Amir ² (Faculty of Mechanical Engineering, University of Kashan)

Received: 2011-11-07 Accepted : 2011-12-15 Published : 2011-12-30

Keywords: Perturbation of Magnetic Field Vector, FG rotating disk, Magneto-thermo-elastic stress, Heat convection,

Abstract :

In this paper, a semi-analytical solution for magneto-thermo-elastic problem in an axisymmetric functionally graded (FG) hollow rotating disk with constant thickness placed in uniform magnetic and thermal fields with heat convection from disk’s surfaces is presented. Solution for stresses and perturbation of magnetic field vector in a thin FG rotating disk is determined using infinitesimal theory of magneto-thermo-elasticity under plane stress conditions. The material properties except Poisson’s ratio are modeled as power-law distribution of volume fraction. The non-dimensional distribution of temperature, displacement, stresses and perturbation of magnetic field vector throughout radius are determined. The effects of the material grading index and the magnetic field on the stress and displacement fields are investigated. The results of stresses and radial displacements for two different boundary conditions are compared with the case of a thin FG rotating disk with the same loading and boundary conditions but in the absence of magnetic field. It has been found that imposing a magnetic field significantly decreases tensile circumferential stresses. Therefore, the fatigue life of the disk will be significantly improved by applying the magnetic field. The results of this investigation can be used for optimum design of rotating disks.

References:

[1] Suresh S., Mortensen A.., 1998, Fundamentals of functionally graded materials, London, UK: IOM Communications Limited.

[2] Lutz M.P., Zimmerman R.W., 1966, Thermal stresses and effective thermal expansion coefficient of a functionally graded sphere, Journal Thermal Stresses 19: 39-54.

[3] Zimmerman R.W., Lutz M.P., 1999, Thermal stresses and effective thermal expansion in a uniformly heated functionally graded cylinder, Journal Thermal Stresses 22: 177-188.

[4] Kordkheili S.A.H., Naghdabadi R., 2007, Thermoelastic analysis of a functionally graded rotating disk, Composite Structures 79:508-516.

[5] Obata Y., Noda N., 1994, Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material, Journal Thermal Stresses 17: 471-488.

[6] Dai H.L., Fu Y.M., 2007, Magneto thermoelastic interaction in hollow structures of functionally graded material subjected to mechanical loads, International Journal of Pressure Vessels and Piping 84: 132-138.

[7] Dai H.L., Fu Y.M., Dong Z.M., 2006, Exact solution for functionally graded pressure vessels in a uniform magnetic field, International Journal of Solids and Structures43: 5570-5580.

[8] Ghorbanpour Arani A., Salari M., Khademizadeh H., Arefmanesh A., 2010, Magneto thermoelastic transient response of a functionally graded thick hollow sphere subjected to magnetic and thermoelastic fields, Journal of Achieve of Applied Mechanics 79: 481-497.

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

[10] Tang S., 1968, Elastic stresses in rotating anisotropic disks, International Journal of Mechanical Sciences 11: 509-517.

[11] Ruhi M., Angoshtari A., Naghdabadi R., 2005, Thermoelastic analysis of thick-walled finite-length cylinders of functionally graded materials, Journal Thermal Stresses 28: 391-408.

[12] Farshi B., Jahed H., Mehrabian A., 2004, Optimum design of inhomogeneous nonuniform rotating disks, International Journal of Computers and Structures 82: 773–779.

[13] Loghman A., Ghorbanpour Arani A., Amir S., Vajedi A., 2010, Magneto thermoelastic creep analysis of functionally graded cylinder, International Journal of Pressure Vessels and Piping 87: 389-395.

[14] Bayat M., Sahari B.B., Saleem M., Aidy A., Wong S.V., 2009, Thermoelastic solution of a functionally graded variable thickness rotating disk with bending based on the first-order shear deformation theory, Thin-Walled Structures 47: 568-582.

[15] Ghorbanpour Arani A., Loghman A., Shajari A.R., Amir S., 2010, Semi-analytical solution of magneto-thermo-elastic stresses for functionally graded variable thickness rotating disks, Journal of Mechanical Science and Technology 24: 2107-2118.

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

[17] Paul C.R., Nasar S.A., 1987, Introduction to Electromagnetic Fields, Mc. Grawhill, Second Edition.

[18] Bayat M., Saleem M., Sahari B.B., Hamouda A.M.S., Mahdi E., 2009, Mechanical and thermal stresses in a functionally graded rotating disk with variable thickness due to radially symmetry loads, International Journal of Pressure Vessels and Piping 86: 357-372.