Symplectic Method-Based Analysis of Axisymmetric Dynamic Thermal Buckling of Functionally Graded Circular Plates

  • J. H. ZhangEmail author
  • X. Liu
  • X. Zhao

The dynamic thermal buckling of circular thin plates made of a functionally graded material is investigated by the symplectic method. Based on the Hamilton principle, canonical equations are established in the symplectic space, and the problems of axisymmetric dynamic thermal buckling of the plates are simplified. The buckling loads and modes of the plates are translated into generalized eigenvalues and eigensolutions, which can be obtained from bifurcation conditions. The effects of gradient properties, parameters of geometric shape, and dynamic thermal loads on the critical temperature increments are considered.


functionally graded materials dynamic stability thermal buckling symplectic method 



This work was supported by the National Natural Science Foundation of China [grants Nos.11662008 and 11862012] and the abroad exchange funding for young backbone teachers of Lanzhou University of Technology.


  1. 1.
    J. H. Zhang, G. Z. Li, S. R. Li, and Y. B. Ma, “DQM-based thermal stresses analysis of a functionally graded cylindrical shell under thermal shock,” J. Thermal Stresses, 38, No. 9, 959-982 (2015).CrossRefGoogle Scholar
  2. 2.
    B. Diveyev, I. Butyter, and Y. Pelekh, “Dynamic properties of symmetric and asymmetric Beams made of Functionally Graded materials in bending,” Mech. Compos. Mater, 54, No. 1, 111-118 (2018).CrossRefGoogle Scholar
  3. 3.
    J. H. Zhang, S. C. Pan, and L. K. Chen, “Dynamic thermal buckling and postbuckling of clamped–clamped imperfect functionally graded annular plates,” Nonlinear Dyn., 95, 565-577 (2019).CrossRefGoogle Scholar
  4. 4.
    S. R. Li, J. H. Zhang, and Y. G. Zhao, “Thermal post-buckling of functionally graded material Timoshenko beams,”Appl. Math. Mech., 27, No. 6, 803-811 (2006).CrossRefGoogle Scholar
  5. 5.
    S. R. Li, J. H. Zhang, and Y.G. Zhao, “Nonlinear thermo-mechanical post-buckling of circular FGM plate with geometric imperfection,” Thin-Wall. Struct., 45, No.5, 528-536 (2007).CrossRefGoogle Scholar
  6. 6.
    K. S. Anandrao, R. K. Gupta, P. Ramchandran, and G.V. Rao, “Thermal post-buckling analysis of uniform slender functionally graded material beams”, Struct. Eng. and Mech., 36, No. 5, 545-560 (2010).CrossRefGoogle Scholar
  7. 7.
    G. L. She, F. G. Yuan, and Y. R. Ren, “Nonlinear analysis of bending, thermal buckling and post-buckling for functionally graded tubes by using a refined beam theory,” Compos. Struct., 165, 74-82 (2017).CrossRefGoogle Scholar
  8. 8.
    G. L. She, F. G. Yuan, and Y.R. Ren, “Thermal buckling and post-buckling analysis of functionally graded beams based on a general higher-order shear deformation theory,” Appl. Math. Model., 47, 340-357 (2017).CrossRefGoogle Scholar
  9. 9.
    L. S. Ma and T. J. Wang, “Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings,” Int. J. Solids. Struct., 40, No. 13-14, 3311-3330 (2003).CrossRefGoogle Scholar
  10. 10.
    L. S. Ma and T. J. Wang, “Relationships between the solutions of axisymmetric bending and buckling of functionally graded circular plates based on the third-order plate theory and the classical solutions for isotropic circular plates,” Int. J. Solids. Struct., 41, No. 1, 85-101 (2004).CrossRefGoogle Scholar
  11. 11.
    X. L. Jia, L. L. Ke, X. L. Zhong, Y. Sun, J. Yang, and S. Kitipornchai, “Thermal-mechanical-electrical buckling behavior of functionally graded micro-beams based on modified couple stress theory,” Compos. Struct., 202, 625-634 (2018)CrossRefGoogle Scholar
  12. 12.
    J. Sun, X. Xu, and C.W. Lim, “Buckling of functionally graded cylindrical shells under combined thermal and compressive loads,” J. Thermal Stresses, 37, No. 3, 340-362 (2014).CrossRefGoogle Scholar
  13. 13.
    J. Sun, X. Xu, and C. W. Lim, “Torsional buckling of functionally graded cylindrical shells with temperature-dependent properties,” Int. J. Struct. Stab. Dy., 14, No.1, 1350 048 (2014).Google Scholar
  14. 14.
    B. Mirzavand, M. R. Eslami, and M. Shakeri, “Dynamic thermal postbuckling analysis of piezoelectric functionally graded cylindrical shells,” J. Thermal Stresses, 33, No. 7, 646-660 (2010).CrossRefGoogle Scholar
  15. 15.
    B. Mirzavand, M. R. Eslami, and J. N. Reddy, “Dynamic thermal postbuckling analysis of shear-deformable piezoelectric FGM cylindrical shells,” J. Thermal Stresses, 36, No. 3, 189-206 (2013).CrossRefGoogle Scholar
  16. 16.
    M. Shariyat, “Dynamic thermal buckling of suddenly heated temperature-dependent FGM cylindrical shells under combined axial compression and external pressure,” Int. J. Solids. Struct., 45, No. 9, 2598-2612 (2008).CrossRefGoogle Scholar
  17. 17.
    M. Shariyat, “Vibration and dynamic buckling control of imperfect hybrid FGM plates with temperature-dependent material properties subjected to thermo-electro-mechanical loading conditions,” Compos. Struct., 88, No. 2, 240-252 (2009).CrossRefGoogle Scholar
  18. 18.
    D. H. Bich, D. Van Dung, V. H. Nam, and N.T. Phuong, “Nonlinear static and dynamic buckling analysis of imperfect eccentrically stiffened functionally graded circular cylindrical thin shells under axial compression,” Int. J. Mech. Sci., 74, 190-200 (2013).CrossRefGoogle Scholar
  19. 19.
    K. Gao, W. Gao, D. Wu, and C. Song, “Nonlinear dynamic buckling of the imperfect orthotropic E-FGM circular cylindrical shells subjected to the longitudinal constant velocity,” Int. J. Mech. Sci., 138, 199-209 (2018).CrossRefGoogle Scholar
  20. 20.
    C. W. Lim and X. S. Xu, “Symplectic elasticity: theory and applications,” Appl. Mech. Rev., 63, No. 5, 1-10 (2010).Google Scholar
  21. 21.
    X. Xu, H. Chu, and C.W. Lim, “A symplectic Hamiltonian approach for thermal buckling of cylindrical shells,” Int. J. Struct. Stab. Dy., 10, No. 2, 273-286 (2010).CrossRefGoogle Scholar
  22. 22.
    J. H. Zhang and S. R. Li, “Dynamic buckling of FGM truncated conical shells subjected to non-uniform normal impact load,” Compos. Struct., 92, No. 12, 2979-2983 (2010).CrossRefGoogle Scholar
  23. 23.
    J. H. Zhang, S. C. Pan, and S. R. Li, “Dynamic buckling of functionally graded circular plate under thermal shock,” Chinese J. of Applied Mechanics [in Chinese], 32, No. 6, 901-907 (2015).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Science, Lanzhou University of TechnologyLanzhouP.R. China
  2. 2.Taiyuan Boiler Group Co.,LtdTaiyuanP.R. China

Personalised recommendations