Analysis of steady heat conduction for 3D axisymmetric functionally graded circular plate

Abstract

The thermal conduction behavior of the three-dimensional axisymmetric functionally graded circular plate was studied under thermal loads on its top and bottom surfaces. Material properties were taken to be arbitrary distribution functions of the thickness. A temperature function that satisfies thermal boundary conditions at the edges and the variable separation method were used to reduce equation governing the steady state heat conduction to an ordinary differential equation (ODE) in the thickness coordinate which was solved analytically. Next, resulting variable coefficients ODE due to arbitrary distribution of material properties along thickness coordinate was also solved by the Peano-Baker series. Some numerical examples were given to demonstrate the accuracy, efficiency of the present model, and to investigate the influence of different distributions of material properties on the temperature field. The numerical results confirm that the influence of different material distributions, gradient indices and thickness of plate to temperature field in plate can not be ignored.

Keywords

functionally graded circular plate / variable separation method / steady heat conduction / Peano-Baker series

References

[1] KoizumiM. FGM activities in Japan [J]. Composites Part B, 1997, 28(1/2): 1-4

[2] MasoudA, MehdiA, SeyedM H. Dynamic analysis of two-dimensional functionally graded thick hollow cylinder with finite length under impact loading [J]. Acta Mechanica, 2009, 208(3/4): 163-180

[3] KhosravifardA, HematiyanM R, MarinL. Nonlinear transient heat conduction analysis of functionally graded materials in the presence of heat sources using an improved meshless radial point interpolation method [J]. Applied Mathematical Modelling, 2011, 35(9): 4157-4174

[4] FuZ J, ChenW, QinQ H. Boundary knot method for heat conduction in nonlinear functionally graded material [J]. Engineering Analysis with Boundary Elements, 2011, 35(5): 729-734

[5] TianJ H, HanX, LongS Y, XieG Q. An analysis of the heat conduction problem for plates with the functionally graded material using the hybrid numerical method [J]. Computers, Materials and Continua, 2009, 10(3): 229-242

[6] ByrdL, BirmanV. An investigation of numerical modeling of transient heat conduction in a one-dimensional functionally graded material [J]. Heat Transfer Engineering, 2010, 31(3): 212-221

[7] TarnJ Q, WangY M. End effects of heat conduction in circular cylinders of functionally graded materials and laminated composites [J]. International Journal of Heat and Mass Transfer, 2004, 47(26): 5741-5747

[8] KhosravifardA, HematiyanM R, MarinL. Nonlinear transient heat conduction analysis of functionally graded materials in the presence of heat sources using an improved meshless radial point interpolation method [J]. Applied Mathematical Modelling, 2011, 35(9): 4157-4174

[9] SutradharA, PaulinoG H. The simple boundary element method for transient heat conduction in functionally graded materials [J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193(42/44): 4511-4539

[10] SutradharA, PaulinoG H, GrayL J. Transient heat conduction in homogeneous and non-homogeneous materials by the Laplace transform Galerkin boundary element method [J]. Engineering Analysis with Boundary Elements, 2002, 26(2): 119-132

[11] WangX, PanE, RoyA K. Three-dimensional Green’s functions for a steady point heat source in a functionally graded half-space and some related problems [J]. International Journal of Engineering Science, 2007, 45(11): 939-950

[12] AzisM I, ClementsD L. Nonlinear transient heat conduction problems for a class of inhomogeneous anisotropic materials by BEM [J]. Engineering Analysis with Boundary Elements, 2008, 32(12): 1054-1060

[13] SladekJ, SladekV, ZhangC. Transient heat conduction analysis in functionally graded materials by the meshless local boundary integral equation method [J]. Computational Materials Science, 2003, 28(3/4): 494-504

[14] SladekJ, SladekV, HellmichC. Heat conduction analysis of 3-D axisymmetric and anisotropic FGM bodies by meshless local Petrov-Galerkin method [J]. Computational Mechanics, 2007, 39(3): 323-333

[15] GantmacherF RThe theory of matrix [M], 1960New YorkChelsea

[16] DacunhaJ J. Transition matrix and generalized matrix exponential via the Peano-Baker series [J]. Journal of Difference Equations and Applications, 2005, 11(15): 1245-1264

[17] LiuW X. Exact solution of steady-state heat conduction for axisymmetric functionally graded circular plate [J]. Journal of Tongji University: Natural Science, 2010, 38(5): 716-719