Optimal tailoring of 2D volume-fraction distributions for heat-resisting functionally graded materials using FDM Original Research Article

Thermoelastic behavior of heat resisting functionally graded materials (FGMs), under given thermal loading and boundary conditions, is definitely characterized by the spatial distribution of volume fractions of constituent particles. Hence, the determination of volume-fraction distribution becomes a crucial step in tailoring an optimal heat-resisting FGM. In this paper, we address a two-dimensional volume-fraction optimization procedure for relaxing the effective thermal stress distribution. In order for the optimization efficiency and the volume-fraction continuity, we approximate the volume-fraction field with bilinear elements of n-times larger size than for the thermoelastic analysis. As well, the refined material-property estimate is employed to assure the design quality. Numerical experiments illustrating our theoretical work are also presented.