Thermal Stability of Thin Rectangular Plates with Variable Thickness Made of Functionally Graded Materials

Subject Areas : Engineering

M Pouladvand ¹ (Faculty of Engineering, University of Applied Science and Technology, Borojerd Branch)

Received: 2009-07-29 Accepted : 2009-10-10 Published : 2009-09-30

Keywords: Thermal buckling, FGM plates, Thin rectangular Plate, Classical plate theory, Variable thickness plate, Galerkin Method,

Abstract :

In this research, thermal buckling of thin rectangular plate made of Functionally Graded Materials (FGMs) with linear varying thickness is considered. Material properties are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The supporting condition of all edges of such a plate is simply supported. The equilibrium and stability equations of a FGM rectangular plate (FGRP) under thermal loads derived based on classical plate theory (CPT) via variational formulation, and are used to determine the pre-buckling forces and the governing differential equation of the plate. The buckling analysis of a functionally graded plate is conducted using; the uniform temperature rise, having temperature gradient through-the-thickness, and linear temperature variation in the thickness and closed-form solutions are obtained. The buckling load is defined in a weighted residual approach. In a special case the obtained results are compared by the results of functionally graded plates with uniform thickness. The influences of the plate thickness variation and the edge ratio on the critical loads are investigated. Finally, different plots indicating the variation of buckling load vs. different gradient exponent k, different geometries and loading conditions were obtained.

References:

[1] Koizumi M., 1997, FGM activities in Japan, Composites part B: Engineering 28(1-2): 1-4.

[2] Fuchiyama T., Noda N., 1995, Analysis of thermal stress in a plate of functionally gradient material, JSME Review 16: 263-269.

[3] Tanigawa Y., Matsumoto M., Akai T., 1997, Optimization of material composition to minimiza thermal stresses in non-homogeneous plate subjected to unsteady heat supply, JSME International Journal Series A-Solid Mechanics and Material Engineering 40(1): 84-93.

[4] Takezono S., Tao K., Inamura E., 1996, Thermal stress and deformation in functionally graded material shells of revolution under thermal loading due to fluid, JSME International Journal Series A-Solid Mechanics and Material Engineering 62(594): 474-481.

[5] Aboudi J., Pindera M., Arnold S.M., 1995, Coupled higher-order theory for functionally grade composites with partial homogenization, Composites part B: Engineering 5(7): 771-792.

[6] Reddy J.N., Chin C.D., 1998, Thermomechanical analysis of functionally graded cylinders and plates, Journal of Thermal Stresses 2: 593-626.

[7] Reddy J.N., Cheng Z.Q., 2001, Three-dimensional thermomechanical deformations of functionally graded rectangular plates, European Journal of Mechanics A/Solids 20: 841-855.

[8] Cheng Z.Q., Batra R.C., 2000, Three-dimensional thermoelastic deformations of a functionally graded elliptic plate, Composites part B: Engineering 31: 97-106.

[9] Javaheri R., Eslami M.R., 2002, Thermal buckling of functionally graded plates, AIAA Journal 40(1): 162-169.

[10] Javaheri R., Eslami M.R., 2002, Thermal buckling of functionally graded plates based on higher order theory, Journal of Thermal Stresses 25(7): 603-625.

[11] Najafizadeh M.M., Eslami M.R., 2002, First order theory based thermoelastic stability of functionally graded material circular plates, AIAA Journal 40: 1444-1450.

[12] Najafizadeh M.M., Heydari H.R., 2004, Thermal buckling of functionally graded circular plates based on higher order shear deformation plate theory, European Journal of Mechanics A/Solids 23: 1085-1100.

[13] Wetherhold R.C., Seelman S., Wang J., 1996, The use of functionally graded materials to eliminate or control thermal deformation, Composite Science and Technology 56: 1099-1104.

[14] Tanigawa Y., Morishita H., Ogaki S., 1999, Derivation of system of fundamental equations for a three dimensional thermoelastic field with non-homogeneous material properties and its application to a semi-infinite body, Journal of Thermal Stresses 22: 689-711.

[15] Praveen G.N., Reddy J.N., 1998, Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates, International Journal of Solids and Structures 35: 33: 4457-4476.

[16] Brush D.O., Almroth B.O., 1975, Buckling of Bars, Plate and Shell, McGraw Hill, New York.