Ashraf M. Zenkour, Daoud S. Mashat

Abstract: Thermal buckling response of functionally graded plates is presented in this paper using sinusoidal shear deformation plate theory (SPT). The material properties of the plate are assumed to vary according to a power law form in the thickness direction. Equilibrium and stability equations are derived based on the SPT. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The buckling analysis of a functionally graded plate under various types of thermal loads is carried out. The influences of many plate parameters on buckling temperature difference will be investigated. Numerical results are presented for the SPT, demonstrating its importance and accuracy in comparison to other theories.

Keywords: Thermal Buckling; Non-Linear Strains; Functionally Graded Material; Sinusoidal Plate

Cite this paper: Zenkour, A. and Mashat, D. (2010) Thermal buckling analysis of ceramic-metal functionally graded plates. Natural Science, 2, 968-978. doi: 10.4236/ns.2010.29118.

References

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

[2]   Bhangale, R.K. and Ganesan, N. (2005) A linear thermoelastic buckling behavior of functionally graded hemispherical shell with a cut-out at apex in thermal environment. International Journal of Structural Stability and Dynamics, 5(2), 185-215.

[3]   Javaheri, R. and Eslami, M.R. (2002) Buckling of functionally graded plates under in-plane compressive loading. ZAMM – Journal of Applied Mathematics and Mechanics, 82(4), 277-283.

[4]   Chung, Y.-L. and Chang, H.-X. (2008) Mechanical behavior of rectangular plates with functionally graded coefficient of thermal expansion subjected to thermal loading. Journal of Thermal Stresses, 31(4), 368-388.

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

[6]   Reddy, J.N. (2000) Analysis of functionally graded plates. International Journal for Numerical Methods in Engineering, 47(1-3), 663-684.

[7]   Amini, M.H., Soleimani, M. and Rastgoo, A. (2009) Three-dimensional free vibration analysis of functionally graded material plates resting on an elastic foundation. Smart Materials and Structures, 18(8), 1-9.

[8]   Sladek, J., Sladek, V., Hellmich, Ch. and Eberhardsteiner, J. (2007) Analysis of thick functionally graded plates by local integral equation method. Communications in Numerical Methods in Engineering, 23(8), 733-754.

[9]   Kim, J.-H. and Paulino, G.H. (2002) Finite element evaluation of mixed mode stress intensity factors in functionally graded materials. International Journal for Numerical Methods in Engineering, 53(8), 1903-1935.

[10]   Altenbach, H. and Eremeyev, V.A. (2008) Analysis of the viscoelastic behavior of plates made of functionally graded materials. ZAMM – Journal of Applied Mathematics and Mechanics, 88(5), 332-341.

[11]   Ovesy, H.R. and Ghannadpour, S.A.M. (2007) Large deflection finite strip analysis of functionally graded plates under pressure loads. International Journal of Structural Stability and Dynamics, 7(2), 193-211.

[12]   Han, X., Liu, G.R. and Lam, K.Y. (2001) Transient waves in plates of functionally graded materials. International Journal for Numerical Methods in Engineering, 52(8), 851-865.

[13]   Zenkour, A.M. (2007) Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate. Archive of Applied Mechanics, 77(4), 197-214.

[14]   Zenkour, A.M. (2005) A comprehensive analysis of functionally graded sandwich plates: Part 1-Deflection and stresses. International Journal of Solids and Structures, 42(18-19), 5224-5242.

[15]   Zenkour, A.M. (2005) A comprehensive analysis of functionally graded sandwich plates: Part 2-Buckling and free vibration. International Journal of Solids and Structures, 42(18-19), 5243-5258.

[16]   Zenkour, A.M. (2005) On vibration of functionally graded plates according to a refined trigonometric plate theory. International Journal of Structural Stability and Dynamics, 5(2), 279-297.

[17]   Aliaga, J.W. and Reddy, J.N. (2004) Nonlinear thermoelastic analysis of functionally graded plates using the third-order shear deformation theory. International Journal of Computational Engineering Science, 5(4), 753- 779.

[18]   Arciniega, R.A. and Reddy, J.N. (2007) Large deformation analysis of functionally graded shells. International Journal of Solids and Structures, 44(6), 2036-2052.

[19]   Kadoli, R., Akhtar, K. and Ganesan, N. (2008) Static analysis of functionally graded beams using higher order shear deformation theory. Applied Mathematical Modelling, 32(12), 2509-2525.

[20]   Sina, S.A., Navazi, H.M. and Haddadpour, H. (2009) An analytical method for free vibration analysis of functionally graded beams. Materials & Design, 30(3), 741-747.

[21]   Zhao, X., Lee, Y.Y. and Liew, K.M. (2009) Mechanical and thermal buckling analysis of functionally graded plates. Composite Structures, 90(2), 161-171.

[22]   Matsunaga, H. (2009) Thermal buckling of functionally graded plates according to a 2D higher-order deformation theory. Composite Structures, 90(1), 76-86.

[23]   Morimoto, T., Tanigawa, Y. and Kawamura, R. (2006) Thermal buckling of functionally graded rectangular plates subjected to partial heating. International Journal of Mechanical Sciences, 48(9), 926-937.

[24]   Shariat, B.A.S. and Eslami, M.R. (2006) Thermal buckling of imperfect functionally graded plates. Internation- al Journal of Solids and Structures, 43(14-15), 4082- 4096.

[25]   Ganapathi, M. and Prakash, T. (2006) Thermal buckling of simply supported functionally graded skew plates. Composite Structures, 74(2), 247-250.

[26]   Lanhe, W. (2004) Thermal buckling of a simply supported moderately thick rectangular FGM plate. Composite Structures, 64(2), 211-218.

[27]   Najafizadeh, M.M. and 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(6), 1085-1100.

[28]   Babu, C.S. and Kant, T. (2000) Refined higher order finite element models for thermal buckling of laminated composite and sandwich plates. Journal of Thermal Stresses, 23(2), 111-130.

[29]   Zenkour, A.M. (2006) Generalized shear deformation theory for bending analysis of functionally graded plates. Applied Mathematical Modelling, 30(1), 67-84.

[30]   Zenkour, A.M. (2004) Buckling of fiber-reinforced viscoelastic composite plates using various plate theories. Journal of Engineering Mathematics, 50(1), 75-93.

[31]   Zenkour, A.M. (2004) Thermal effects on the bending response of fiber-reinforced viscoelastic composite plates using a sinusoidal shear deformation theory. Acta Mecha- nica, 171(3-4), 171-187.

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