Equilibrium Equations for Thermal Buckling Analysis of Annular Plates

Authors

  • Prakash A Nayakar   Department of Civil Engineering, New Horizon College of Engineering, Bangalore, India

Keywords:

Functionally graded materials, FSDT, Buckling

Abstract

In the following paper equations for buckling of annular plates which are made of functionally graded material are derived when subjected to temperature load. Equilibrium equations are derived using first order shear deformation theory under the thermal loads. The fundamental partial differential equations are derived using minimum potential energy. The material properties are assumed to be varying as a power form of the thickness coordinate variable z. These equations are solved by using number of methods like energy methods, analytical methods, finite difference method, and finite element methods.

References

  1. Aghelinejad, M., Zare, K., Ebrahimi, F. and Rastgoo, A. (2011) “Nonlinear thermo-mechanical post-buckling analysis of thin functionally graded annular plates based on Von-Karman's plate theory” Mechanics of Advanced Materials and Structures, Volume 18, Issue 5, pages 319-326.
  2. Dong, C.Y. (2008) “Three-dimensional free vibration analysis of functionally graded annular plates using the Chebyshev–Ritz method” Materials and Design, Volume 29, pages 1518–1525.
  3. Golmakani, M.E., and Kadkhodayan, M. (2011) “Nonlinear bending analysis of annular FGM plates using higher-order shear deformation plate theories” Composite Structures, Volume 93, pages 973–982.
  4. Hamad, M.H., and Tarlochan, F. (2013) “An axisymmetric bending analysis of functionally graded annular plate under transverse load via generalized differential quadrature method” International Journal of Research in Engineering and Technology, Volume 02, Issue 07, Jul-2013.
  5. Hosseini-Hashemi, Sh., Fadaee, M. and Es’haghi, M. (2010) “A novel approach for in-plane/out-of-plane frequency analysis of functionally graded circular/annular plates” International Journal of Mechanical Sciences, Volume 52, pages 1025–1035.
  6. Iman Davoodi Kermani., Mostafa Ghayour and Hamid Reza Mirdamadi. (2012) “Free vibration analysis of multi-directional functionally graded circular and annular plates” Journal of Mechanical Science and Technology, Volume 26 (11), pages 3399-3410.
  7. Koohkan, H., Kimiaeifar, A., Mansourabadi, A. and Vaghefi, R. (2010) “An analytical approach on the buckling analysis of circular, solid and annular functionally graded thin plates” Journal of Mechanical Engineering, Volume. ME 41, Issue No. 1.
  8. Lei, Zheng. and Zheng, Zhong. (2009) “Exact Solution for Axisymmetric Bending of Functionally Graded Circular Plate” Tsinghua science and technology, Volume 14, Number S2, pages 64-69.
  9. Li, Shi-Rong., Zhang, Jing-Hua. and Zhao, Yong-Gang. (2007) “Nonlinear thermomechanical post-buckling of circular FGM plate with geometric imperfection” Thin-Walled Structures, Volume 45, pages 528–536.
  10. Ma, L.S. and Wang, T.J. (2003) “Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings.” International Journal of Solids and Structures, Volume 40, pages 3311–3330.
  11. Ma, L.S. and Wang, T.J. (2004) “Relationships between axisymmetric bending and buckling solutions of FGM circular plates based on third-order plate theory and classical plate theory” International Journal of Solids and Structures, Volume 41, pages 85–101.
  12. Najafizadeh, M. M. and Eslami, M. R. (2002a) “Thermoelastic stability of orthotropic circular plates” Journal of Thermal Stresses, Volume 25, Issue10, pages 985-1005.
  13. Najafizadeh, M.H. and Eslami, M.R. (2002b) "Buckling analysis of circular plates of functionally graded materials under uniform radial compression." International Journal of Mechanical Sciences, Volume 44, Issue 12, December 2002, Pages 2479-2493.
  14. Najafizadeh, M.M. and Hedayati, B. (2004) “Refined theory for thermoelastic stability of functionally graded circular plates” Journal of Thermal Stresses, Volume 27, Issue 9, pages 857-880.
  15. Najafizadeh, M.M. and Heydari, H.R. (2008) “An exact solution for buckling of functionally graded circular plates based on higher order shear deformation plate theory under uniform radial compression” International Journal of Mechanical Sciences, Volume 50, pages 603–612.
  16. Nie, G.J. and Zhong, Z. (2007a) “Semi-analytical solution for three-dimensional vibration of functionally graded circular plates” Comput. Methods Appl. Mech. Engrg., Volume 196, pages 4901–4910.
  17. Nie, G.J. and Zhong, Z. (2007b) “Axisymmetric bending of two-directional functionally graded circular and annular plates” Acta Mechanica Solida Sinica, Volume 20, issue 4, December, 2007.
  18. Nie, G.J. and Zhong, Z. (2010) “Dynamic analysis of multi-directional functionally graded annular plates” Applied Mathematical Modelling, Volume 34, pages 608–616.
  19. Prakash, T. and Ganapathi, M. (2006) “Asymmetric flexural vibration and thermoelastic stability of FGM circular plates using finite element method” Composites: Part B, Volume 37, pages 642–649.
  20. Reddy, J.N., Wang, C.M. and Kitipornchai, S. (1999) "Axisymmetric bending of functionally graded circular and annular plates” European Journal of Mechanics - A/Solids, Volume 18, Issue 2, March-April 1999, Pages 185-199.
  21. Sahraee, S. and Saidi, A.R. (2009) “Axisymmetric bending analysis of thick functionally graded circular plates using fourth-order shear deformation theory” European Journal of Mechanics A/Solids, Volume 28, pages 974–984.
  22. Saidi, A.R. and Hasani Baferani, A. (2010) “Thermal buckling analysis of moderately thick functionally graded annular sector plates” Composite Structures, Volume 92, pages 1744–1752.
  23. Saidi, A.R., Rasouli, A. and Sahraee, S. (2009) “Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained third-order shear deformation plate theory” Composite Structures, Volume 89, pages 110–119.
  24. Serge Abrate (2006) “Free vibration, buckling, and static deflections of functionally graded plates” Composites Science and Technology, Volume 66 pages 2383–2394.
  25. Shen, Hui-Shen (2007) “Thermal post buckling behavior of shear deformable FGM plates with temperature-dependent properties” International Journal of Mechanical Sciences, Volume 49, pages 466–478.
  26. Shi, P. and Dong, C.Y. (2012) “Vibration analysis of functionally graded annular plates with mixed boundary conditions in thermal environment” Journal of Sound and Vibration, volume 331, pages 3649–3662.

IInternational Journal of Scientific Research in Computer Science, Engineering and Information Technology

Downloads

Published

2019-12-30

Issue

Volume 4, Issue 9, November-December-2019

Section

Research Articles

License

Copyright (c) IJSRCSEIT

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
Prakash A Nayakar , " Equilibrium Equations for Thermal Buckling Analysis of Annular Plates" International Journal of Scientific Research in Computer Science, Engineering and Information Technology(IJSRCSEIT), ISSN : 2456-3307, Volume 4, Issue 9, pp.370-374, November-December-2019.