Volume fraction optimization for minimizing thermal stress in Ni–Al2O3 functionally graded materials

Functionally graded heat-resisting material, in which the volume fraction of constituents varies continuously and functionally, is investigated for high-temperature engineering applications. In this advanced material, the thermomechanical behavior of FGMs is strongly influenced by the spatial distribution of the volume fraction. So, the determination of volume fraction distribution becomes a crucial part in the FGM design, for a given specification and loading condition. This paper is concerned with the volume fraction optimization for minimizing steady-state thermal stresses in Ni–Al2O3 heat-resisting FGM composites. Interior penalty-function method and golden section method are employed as optimization techniques, together with finite difference method for the sensitivity analysis and an appropriate material-property estimate for calculating thermomechanical properties of the graded layer. The introduced optimization method, through the numerical experiments, is found to provide optimal volume fraction distributions that minimize thermal stresses significantly, as well as the rapid and stable convergence.