Document Type : Original Article

Authors

1 Department of Mechanical Engineering, Parand Branch, Islamic Azad University , Parand, Iran

2 Department of Mechanical, Engineering, Parand Branch, Islamic Azad University, Parand, Iran

Abstract

In this paper, the effects of different rotational speed functions in the elastic-plastic deformation and stress analysis of a rotating annular thin disk of functionally graded material (FGM) in Reddy model is studied using the analytical and FEM methods. In this regard, differential equations governing dynamic equilibrium for displacements and stresses in the elastic region of the FGM rotating disk have been derived using the theory of elasticity in plane stress condition and have been solved by the shooting method. Then, the equations governing the distribution of plastic radial and circumferential stresses on the disk have been extracted using the Prandtl-Reuss theory of plasticity and based on the Ludwig hardening law in conjunction with the von Mises yield criterion. Also, by modeling the annular thin disk in the environment of finite element software ANSYS, the results obtained from the elastic analytical solution and the finite element numerical solution have been compared to each other and to the results reported in the literature for specific cases and validated accordingly. The effects of variation of the disk geometric parameters, functionally graded material power index as well as different type of the time-dependent rotational speed functions such as the constant speed, exponential, and accelerated/decelerated linear, quadratic, and square root functions on the elastic behavior of the disk and distribution of radial displacement, and also distribution of radial, circumferential, and shear stresses on the disk have been studied. Moreover, the results of plastic analysis have been presented for distribution of radial and circumferential stresses on the disk.

Keywords

Main Subjects

Article Title [فارسی]

Study on effects of different rotational speed functions in elastic-plastic analysis of annular thin disk of functionally graded material

Authors [فارسی]

  • Hadi Hamedani 1
  • Ahmad Mamandi 2

1 Department of Mechanical Engineering, Parand Branch, Islamic Azad University , Parand, Iran

2 Department of Mechanical, Engineering, Parand Branch, Islamic Azad University, Parand, Iran

Abstract [فارسی]

In this paper, the effects of different rotational speed functions in the elastic-plastic deformation and stress analysis of a rotating annular thin disk of functionally graded material (FGM) in Reddy model is studied using the analytical and FEM methods. In this regard, differential equations governing dynamic equilibrium for displacements and stresses in the elastic region of the FGM rotating disk have been derived using the theory of elasticity in plane stress condition and have been solved by the shooting method. Then, the equations governing the distribution of plastic radial and circumferential stresses on the disk have been extracted using the Prandtl-Reuss theory of plasticity and based on the Ludwig hardening law in conjunction with the von Mises yield criterion. Also, by modeling the annular thin disk in the environment of finite element software ANSYS, the results obtained from the elastic analytical solution and the finite element numerical solution have been compared to each other and to the results reported in the literature for specific cases and validated accordingly. The effects of variation of the disk geometric parameters, functionally graded material power index as well as different type of the time-dependent rotational speed functions such as the constant speed, exponential, and accelerated/decelerated linear, quadratic, and square root functions on the elastic behavior of the disk and distribution of radial displacement, and also distribution of radial, circumferential, and shear stresses on the disk have been studied. Moreover, the results of plastic analysis have been presented for distribution of radial and circumferential stresses on the disk

Keywords [فارسی]

  • Annular FGM rotating thin disk
  • Accelerated/decelerated rotational speed
  • Elastic-plastic analysis
  • Ludwig hardening law
  • von Mises yield criterion
[1] Durodola, J.F., and Attia, O. “Deformation and stresses in FG rotating disks”, Composite Science and Technology, Vol. 60, No. 7, pp. 987–995, 2000.
[2] Eraslan, A.N, and Argeso, H. “Limit angular velocities of variable thickness rotating disks” International Journal of Solids and Structures, Vol. 39, No. 12, pp. 3109–3130, 2002.
[3] Eraslan A.N., and Orcan, Y. “Elastic–plastic deformation of a rotating disk of exponentially varying thickness”, Mechanics of Materials, Vol. 34, No. 7, pp. 423–432, 2002.
[4] Orcan, Y., and Eraslan, A.N. “Elastic–plastic stresses in linearly hardening rotating solid disks of variable thickness”, Mechanics Research Communications, Vol. 29, No. 4, pp. 269-281, 2002.
[5] Eraslan A.N. “Von mises yield criterion and nonlinearly hardening variable thickness rotating annular disks with rigid inclusion”, Mechanics Research Communications, Vol. 29, pp. 339-350, 2002.
[6] Eraslan A.N. “Elastic-plastic deformation of rotating variable thickness annular disks with free, pressurized and radially constrained boundary conditions”, International Journal of Mechanical Science, Vol. 45, pp. 643–67, 2003.
[7] Zenkour, A.M. “Analytical solutions for rotating exponentially-graded annular disks with various boundary conditions”, International Journal of Structural Stability, Vol. 5 No. 4, pp. 557-577, 2005.
[8] Eraslan A.N., and Akis, T., “On the plane strain and plane stress solutions of functionally
graded rotating solid shaft and solid disk problems”, Acta Mechanica, Vol. 18, No. 1, pp. 43-63, 2006.
[9] Chen, J.Y., Ding, H.J., and Chen, W.Q. “Three-dimensional analytical solution for a rotating disc of functionally graded materials with transverse isotropy”, Archive of Applied Mechanics, Vol. 77, No. 4, pp. 241-251, 2007.
[10] Zenkour, A.M. “Stress distribution in rotating composite structures of functionally graded solid disks”, Jouranl of Materials Processing Technology, Vol. 209, No. 7, pp. 3511-3517, 2009.
[11] Asghari, M., and Ghafoori, E. “A three-dimensional elasticity solution for functionally graded rotating disks, Composite Structures, Vol. 92, No. 5, pp. 1092-1099, 2010.
[12] Callioglu, H., Bektas, N.B. and Sayer, M., Stress analysis of functionally graded rotating disks: analytical and numerical solutions, Acta Mechanica Sinica, Vol. 27, No. 6, pp. 950-955, 2011.
[13] Peng, X.-L., and Li, X.-F. “Elastic analysis of rotating functionally graded polar orthotropic disks”, International Journal of Mechanical Science, Vol. 60, pp. 84-91, 2012.
[14] Peng, X.L., and Li, X.F. “Effects of gradient on stress distribution in rotating functionally graded solid disks”, Journal of Mechanical Science and Technology, Vol. 26, No. 5, pp. 1483-1492, 2012.
[15] Zafarmand, H., and Hassani, B. “Analysis of two-dimensional functionally graded rotating thick disks with variable thickness”, Acta Mechanica, Vol. 225, No. 2, pp. 453-464, 2013.
[16] Aleksandrova, A. “Exact deformation analysis of a solid rotating elastic-perfectly plastic disk”, International Journal of Mechanical Sciences, Vol. 88, pp. 55-60, 2014.
[17] Zamani Nejad, M., Rastgoo, A., and Hadi, A. “Exact elasto-plastic analysis of rotating disks made of functionally graded material”, International Journal of Mechanical Science, Viol. 85, pp. 47-57, 2014.
[18] Dai, T. and Dai, H.-L., “Investigation of mechanical behavior for rotating FGM circular disk with a variable angular speed”, Journal of Mechanical Science and Technology, Vol. 29, No. 9, pp. 3779-3787, 2015.
[19] Callioglu, H., Sayer, M., and Demir, E. “Elastic-plastic stress analysis of rotating functionally graded disk”, Thin-Walled Structures, Vol. 94, pp. 38-44, 2015.
[20] Zhenga, Y., Bahalooa, H., Mousanezhad, D., Mahdi, E., Vaziria, A., and Nayeb-Has H., “Stress analysis in functionally graded rotating disks with non-uniform thickness and variable angular velocity”, International Journal of Mechanical Sciences, Vol. 119, pp. 283-293, 2016.
[21] Kalali, A.T., Hassani, B., and Hadidi-Moud, S., “Elastic-plastic analysis of pressure vessels and rotating disks made of functionally graded materials using the isogeometric approach”, Journal of Theoretical and Applied Mechanics, Vol. 54, No. 1, pp. 113-125, 2016.
[22] Sharma, S., and Yadav, S., “Numerical solution of thermal elastic-plastic functionally graded thin rotating disk with exponentially variable thickness and variable density”, Thermal Science, Vol. 23, No. 1, pp. 125-136, 2019.
[23] Ugural, A.C., “Theory of Plates and Shells”, McGraw-Hill Book Company, 1999.
[24] Boresi, A.P., Chong, K. and Lee, J.D., “Elasticity in Engineering Mechanics, John Wiley & Sons, 2010.
[25] Johnson, W. and Mellor, P.B., “Engineering Plasticity”, Ellis Horwood Limited, Van Nostrand Reinhold (UK), 1983.