Thermal Buckling of Rectangular FGM Plate with Variation Thickness

Equilibrium and stability equations of a thin rectangular plate with length a, width b, and thickness h(x)=C1x+C2, made of functionally graded materials under thermal loads are derived based on the first order shear deformation theory. It is assumed that the material properties vary as a power form of thickness coordinate variable z. The derived equilibrium and buckling equations are then solved analytically for a plate with simply supported boundary conditions. One type of thermal loading, uniform temperature rise and gradient through the thickness are considered, and the buckling temperatures are derived. The influences of the plate aspect ratio, the relative thickness, the gradient index and the transverse shear on buckling temperature difference are all discussed.





References:
[1] Koizumi M. FGM activities in Japan. Composites 1997;28(1- 2):1-4.
[2] Tanigawa Y, Matsumoto M, Akai T. Optimization of material
composition to minimize thermal stresses in non-homogeneous plate
subjected to unsteady heat supply. Jpn Soc Mech Engrs Int J Ser A
1997;40(1):84-93.
[3] Takezono S, Tao K, Inamura E. Thermal stress and deformation in
functionally graded material shells of revolution under thermal loading
due to fluid. Jpn Soc Mech Engrs Int J Ser A 1996;62(594):474-81.
[4] Aboudi J, Pindera M, Arnold SM. Coupled higher-order theory for
functionally grade composites with partial homogenization. Compos Eng
1995;5(7):771-92.
[5] Praveen GN, Reddy JN. Nonlinear transient thermal elastic analysis of
functionally graded ceramic-metal plates. Int J Solids Struct
1998;35(33):4457-76.
[6] Reddy JN, Wang CM, Kitipornchai S. Axisymmetric bending of
functionally graded circular and annular plates. Eur J Mech A/ Solids
1999;18(1):185-99.
[7] Sumi N. Numerical solution of thermal and mechanical waves in
functionally graded materials. Third International Congress on Thermal
Stresses, Branti Zew, Krakow, Poland, 1999. p. 569-72.
[8] Javaheri R, Eslami MR. Buckling of functionally graded plates under
inplane compressive loading. ZAMM 2002;82(4):277-83.
[9] Javaheri R, Eslami MR. Thermal buckling of functionally graded plates.
AIAA J 2002;40(1):162-9.
[10] Javaheri R, Eslami MR. Thermal buckling of functionally graded plates
based on higher order theory. J Thermal Stresses 2002;25: 603-25.
[11] Lanhe W. Thermal buckling of a simply supported moderately thick
rectangular FGM plate. Compos Struct 2004;64:211-8
[12] Birman V. Buckling of functionally graded hybrid composite plates[C].
Proceedings of the 10th conference on engineering mechanics,
Boulder, CO, 1995. p. 1199-1202.
[13] Ng TY, Lam KY, Liew KM. Dynamic stability analysis of functionally
graded cylindrical shells under periodic axial load-ing[J]. Int J Solids
Struct 2001;38(9):1295-309.
[14] Tauchert TR. Thermal buckling of thick antisymmetic angle ply
laminates. J Thermal Stresses 1987;10(1):113-24.
[15] Thornton EA. Thermal buckling of plates and shells, J. Appl Mech Rev
1993;46(10):485-506.
[16] Wu Lanhe, Wang Libin, Liu Shuhong. On thermal buckling of a simply
supported rectangular FGM plate. Chin J Eng Mech, in press [in
Chinese].
[17] Brush DO, Almroth BO. Buckling of bars, plates, and shells. New-York:
McGraw-Hill; 1975
[18] C. A. Meyers and M. W. Hyer, Thermal Buckling and Postbuckling of
Symmetrically Laminated Composite Plates, J. Thermal Stresses, vol. 14,
pp. 519+540, 1991.