THERMAL SCIENCE

International Scientific Journal

Thermal Science - Online First

online first only

Comparative thermal buckling analysis of functionally graded plate

ABSTRACT
A thermal buckling analysis of functionally graded thick rectangular plates according to von Karman nonlinear theory is presented. The material properties of the functionally graded plate, except for the Poisson’s ratio, were assumed to be graded in the thickness direction, according to a power-law distribution, in terms of the volume fractions of the metal and ceramic constituents. Formulations of equilibrium and stability equations are derived using the high order shear deformation theory based on different types of shape functions. Analytical method for determination of the critical buckling temperature for uniform increase of temperature, linear and nonlinear change of temperature across thickness of a plate is developed. Numerical results were obtained in Маtlab software using combinations of symbolic and numeric values. The paper presents comparative results of critical buckling temperature for different types of shape functions. The accuracy of the formulation presented is verified by comparing to results available from the literature.
KEYWORDS
PAPER SUBMITTED: 2016-06-14
PAPER REVISED: 2016-07-08
PAPER ACCEPTED: 2016-07-21
PUBLISHED ONLINE: 2016-08-07
DOI REFERENCE: https://doi.org/10.2298/TSCI160614182C
REFERENCES
  1. Marković, S., Synthesis and characterization of BaTi1-xSnxO3 powders and multilayer ceramic materials, Ph. D. thesis, University of Belgrade, Belgrade, Serbia, 2008 (In Serbian)
  2. Praveen, G.N., Reddy, J.N., Nonlinear transient thermoelastic analysis of functionlly graded ceramic-metal plates, Int J Solids Struct, 35 (1998), 33, pp. 4457-4476,.
  3. Reddy, J.N., Analysis of functionally graded plates, Int J Numer Meth Eng, 47 (2000), 1-3, pp. 663-684
  4. Woo, J., Meguid, S.A., Nonlinear analysis of functionally graded plates and shallow shells, Int J Solids Struct, 38 (2001), 42-43, pp. 7409-7421
  5. Ma, L.S., Wang, T.J., Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings, Int J Solids Struct, 40 (2003), 13-14, pp. 3311-3330
  6. Lanhe, W., Thermal buckling of a simply supported moderately thick rectangular FGM plate, Compos Struct, 64, (2004) 2, pp. 211-218
  7. Chi, S-H., Chung, Y-L., Mechanical behavior of functionally graded material plates under transverse load-Part I: analysis, Int J Solids Struct, 43 (2006), 13, pp. 3657-3674 Chi, S-H., Chung, Y-L., Mechanical behavior of functionally graded material plates under transverse load-Part II: numerical results, Int J Solids Struct, 43 (2006), 13, pp. 3675-3691
  8. Chung, Y-L., Che, W-T., The flexibility of functionally graded material plates subjected to uniform loads, J Mech Mater Struct, 2 (2007), 1, pp. 63-86
  9. Akavci, S. S., Thermal buckling analysis of functionally graded plates on an elastic foundation according to a hyperbolic shear deformation theory, Mech Compos Mater, 50 (2014), 2, pp. 197-212
  10. Ambartsumyan, S. A., On the heory of Anisotropic Shells and Plates, Non-Homogeniety in Elasticity and Plasticity: Symposium, Edited by Olszak W., Warsaw, September 2-9, 1958.
  11. Reissner, E., Stavsky, Y., Bending and stretching of certain types of heterogeneous aeolotropic elastic plates, J Appl Mech-T-ASME, 28 (1961), pp. 402-408
  12. Stein, M., Nonlinear theory for plates and shells including the effects of transverse shearing, AIAA J, 24 (1986), 9, pp. 1537-1544
  13. Mantari, J.L., et al., Bending and free vibration analysis of isotropic and multilayered plates and shells by using a new accurate higherorder shear deformation theory, Compos Part B-Eng, 43 (2012), 8, pp. 3348-3360
  14. Mantari, J.L., et al., A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates, Int J Solids Struct, 49 (2012), 1, pp. 43-53
  15. Karama, M., et al., Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity, Int J Solids Struct, 40 (2003), 6, pp. 1525-1546
  16. Aydogdu, M., A new shear deformation theory for laminated composite plates, Compos Struct, 89 (2009), 1, pp. 94-101
  17. Mantari, J.L., et al., A new tangential-exponential higher order shear deformation theory for advanced composite plates, Compos Part B-Eng, 60 (2014), pp. 319-328
  18. Meiche, N. E. et al., "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate, Int J of Mech Sci, 53 (2011), 4, pp. 237-247
  19. Soldatos, K., A transverse shear deformation theory for homogeneous monoclinic plates, Acta Mech, 94 (1992), 3, pp. 195-220
  20. Akavci, S.S., Two new hyperbolic shear displacement models for orthotropic laminated composite plates, Mech Compos Mater, 46 (2010), 2, pp. 215-226
  21. Mechab, B., et al., Analysis of thick orthotropic laminated composite plates based on higher order shear deformation theory by the new function under thermo-mechanical loading, Compos Part B-Eng, 43 (2012), 3, pp. 1453-1458
  22. Milosavljevic D. I., at al., Failure criteria of fibre reinforced composites in homogenous temperature field, Therm Sci, 14 (2010), Suppl., pp. S285-S297
  23. Mantari, J.L., et al., Bending response of functionally graded plates by using a new higher order shear deformation theory, Compos Struct, 94 (2012), 2, pp. 714-723
  24. Grover, N., et al., Flexural behavior of general laminated composite and sandwich plates using a secant function based shear deformation theory, Lat Am J Solids Stru, 11 (2014), pp. 1275-1297
  25. Reddy. J.N., Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, New York, USA, 2004
  26. Bouiadjra, M. B., et al., Thermal buckling of functionally graded plates according to a four-variable refined plate theory, J Therm Stresses, 35 (2012), 8, pp. 677-694
  27. Javaheri, R., Eslami, M. R., Thermal buckling of functionally graded plates based on a higher order theory, J Therm Stresses, 25 (2002), 7, pp. 603-625
  28. Zenkour, A. M., Mashat, D. S., Thermal buckling analysis of ceramic-metal functionally graded plates, Natural Science., 2 (2010), 9, pp. 968-978