Study on the Volume Fraction Optimization of Functionally Graded Heat-Resisting Composites

기능경사 내열 복합재의 체적분율 최적화에 관한 연구

  • Published : 2001.06.01


Functionally graded materials(FGMs) are highlighted to be suitable for high temperature engineering due to their continuous distribution of material properties. In this paper, an optimal design is executed for determining the optimal material volume distribution pattern that minimizes the steady-state thermal stress of FGM heat-resisting composites. The interior penalty function method and the golden section method are employed as optimization techniques while the finite element method is used for thermal stress analysis. Through numerical simulations we suggest the volume fraction distributions that considerably improve initial thermal stress distributions.


Functionally Graded Material;Interior Penalty Function Method;Golden Section Method;Modified Rule of Mixtures;Schaperys Estimate;Volume fraction


  1. ANSYS Inc., 1999, ANSYS User's Manual for Release 5.6
  2. GiannakopuJos, A. E., Suresh, S. and Olsson, M., 1995, 'Elastoplastic Analysis of Thermal Cycling: Layered Materials with Compositional Gradients,' Acta Metall. Mater., Vol. 43, No.3, pp, 1335-1354
  3. Reite, T., Dvorak, G. J. and Tvergaard, V.,1997, 'Micromechanical Models for Graded Composite Materials,' J. physics of Solids, Vol. 45, pp. 1281-1302
  4. Grujicic, M and Zhang, Y., 1998, 'Determination of Elastic Properties of Functionally Graded Materials using Voronoi Cell Finite Element Method,' Materials Science and Engrgineering, Vol. 104, pp. 64-76
  5. Cho, J. R. and Ha, D. Y., 2001, 'Averaging and Finite-Element Discretization Approaches in the Numerical Analysis of Functionally Graded Materials,' Materials Science and Engineering A, Vol. 302, No.2, pp. 187-196
  6. Tomata, Y., Kukori, K., Mori, K. and Tamura, K' 1976, 'Tensile Deformation of Two-Ductile-Phase Alloys: Flow Curves of Fe-Cr-Ni Alloys,' Materials Science Engineering, Vol. 24, pp. 85-94
  7. Schapery, R. A., 1968, 'Thermal Expansion Coefficients of Composite Materials based on Energy Principles,' J. Computational Materials, Vol. 2, pp, 380-404
  8. Vanderplaats, G. N., 1984, Numerical Optimization Techniques for Engineering Design with Applications, McGraw-Hill
  9. Cho, J. R. and Ha, D. Y., 2001, 'Thermo-Elastoplastic Characteristics of Heat Resisting Functionally Graded Composites,' Structural Engineering and Mechanics, Vol. 11, No. 1, pp. 36-49
  10. Koizumi, M., 1992, 'Recent Progress of Functionally Gradient Materials in Japan,' Ceram. Engrg. Sci. Proc .. Vol. 13, pp. 333-347
  11. Ootao, Y., Tanigawa, Y. and Nakamura, T., 1999, 'Optimization of Material Composition of FGM Hollow Circular Cylinder under Thermal Loading a Neural Network Approach,' Composites: Part B, Vol. 30, pp. 415-422
  12. Chen, B. C. and Kikuchi, N., 1999, 'Structure Topology Optimization of Functionally Gradient Materials,' Proceedings of Fifth U.S. National Congress on Computational Mechanics, pp. 401-402
  13. Tanaka, K., Tanaka, Y., Enomoto, K., Poterasu, V. F. and Sugano, Y., 1993, 'Design of Thermoelastic Materials using Direct Sensitivity and Optimization Methods: Reduction of Thermal Stresses in Functionally Gradient Materials,' Computer Methods in Applied Mechanics and Engineering, Vol. 106, pp. 271-284
  14. Cho, J. R. and Kim, B. G., 1999, 'Finite Element Analysis of Thermal Stresses in Functionally Gradient Layered Composites,' KSME International Journal, Vol. 13, No.2, pp. 108-115
  15. Cho, J. R. and Oden, J. T., 2000, 'Functionally Graded Material A Parametric Study on Thermal-Stress Characteristics using the Crank-Nicolson-Galerkin Scheme,' Computer Methods in Applied Mechanics and Engineering, Vol. 188, pp. 17-38