Keywords: functionally graded material, finite element, optimization, thermal stresses.

It is well known that abrupt transitions among different materials with different properties often result in a sharp local concentration of stress, either being the stress be internal or applied externally. Therefore, such stress concentration is greatly reduced if the transition from one material to the other is gradually made. By definition, Functionally Graded Materials, FGM, are used to produce components featuring gradual transitions in microstructure and composition, the presence of which is motivated by functional performance requirements that vary with location within the part. Functionally Graded Materials have the potential to improve the thermomechanical mechanical characteristics of a component: the magnitude of thermal stresses can be minimized; severe stress concentration and singularities at intersections between free edges can be suppressed. In general, heat-resisting Functionally Graded Materials are composed of three layers, ceramic and metal layers and a graded layer, such that the material composition in the middle graded layer varies from 100% ceramic at the ceramic-graded layer interface to 100% metal at the opposite interface. In such advanced material, the thermomechanical-mechanical behavior of FGM 's is strongly influenced by the spatial distribution of the volume fraction. Therefore, determining the volume fraction distribution becomes a crucial part in a FGM design. Selecting the most suitable volume fraction distribution becomes an essential part for tailoring a FGM that optimally meets the desired performances under preset geometry, loading and boundary conditions. This volume fraction optimization problem is defined and the "downhill" optimization algorithm is used to solve the problem. It is worth mentioning that the use of this kind of algorithm avoids computation of gradients. The novelties of this paper are the development of a simple one-dimensional finite element approach to describe the thermal and mechanical behavior of a metal/ceramic FGM hollow cylinder and the adoption of the heuristic algorithm "downhill" in the numerical solution of the volume fraction optimization problem.

1

Suresh, S., Mortensen, A. "Fundamentals of Functionally Graded Materials", IOM Communications, 1998.

2

Zhi-He Jin, Paulino, G.H., Dodds Jr, R.H. "Cohesive Fracture Modeling of Elastic-plastic Crack Growth in Functionally Graded Materials ", Engineering Fracture Mechanics,70, 1885-1012, 2003. doi:10.1016/S0013-7944(03)00130-9

3

Daros, C.H., Back, R.L. "Análise de Tensões Térmicas em Cilindros Gradualmente Funcionias através do Método dos Elementos Finitos ", Iberian Latin-American Congress on Computational Methods in Engineering, 2001.

4

Cho, J.R., Ha, D.Y. "Volume Fraction optimization for Minimizing Thermal Stress in Ni-Al₂O₃ Functionally Graded Materials ", Materials Science & Engineering A, 147-155, 2002. doi:10.1016/S0921-5093(01)01791-9

5

Cho, J.R., Oden, J.T. "Functionally Graded Material: a Parametric Study on Thermal-stress Characteristics Using the Crank-Nicolson-Galerkin scheme ", Computer Methods in Applied Mechanics and Engineering, 17-38, 2000. doi:10.1016/S0045-7825(99)00289-3

6

Cho, J.R., Ha, D.Y. "Averaging and Finite-element Discretization Approaches in the Numerical Analysis of Functionally Graded Materials ", Materials Science & Engineering A, 187-196, 2001. doi:10.1016/S0921-5093(00)01835-9

7

Koizumi, M. "FGM Activities in Japan ", Composites Part B,28B 1-4, 1997. doi:10.1016/S1359-8368(96)00016-9

8

Boussaa, D. "Optimizing a Compositionally Graded Interlayer to Reduce thermal Stresses in a Coated Tube", Mechanics of Solids and Structures, C. R. Acad. Sci. Paris, 209-215, 2000. doi:10.1016/S1287-4620(00)00118-6

9

Chakraborty, A., Gopalakrishnan, S., Reddy, J.N. "A New Beam Nite Element for the Analysis of Functionally Graded Materials", International Journal of Mechanical Sciences, 519-539, 2003. doi:10.1016/S0020-7403(03)00058-4

10

Giannakopoulos, A.E., Suresh, S., Finot, M., Olsson, M. "Elastoplastic Analysis of Thermal Cycling: Layered Materials with Compositional Gradients ", Acta Metall. Mater., 1335-1354, 1995. doi:10.1016/0956-7151(94)00360-T

11

Williamson, R.L., Rabin, B.H., Drake, J.T. Olsson "Finite Element Analysis of Thermal Residual Stresses at Graded Ceramic-metal Interfaces. Part I. Model Description and Geometrical Effects ", J. Appl. Phys.,vol. 74, 1310-1320, 1993. doi:10.1063/1.354910

12

Crandall, S.H., Dahl, N.C., Lardner, T.J. "An Introduction to the Mechanics of Solids", McGraw-Hill International Editions ,1978.

13

Reddy, J.N. "An Introduction to the Finite Element Method", McGraw-Hill Editions ,1984.

14

Bazaraa, M.S., Shetty, C.M. "Unconstrained Optimization", John Willey &Sons, New York, 1979.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £135 +P&P)