Effective volume-fraction optimization for thermal stress reduction in FGMs using irregular h-refinement

The volume fraction of constituent particles in functionally graded materials (FGM) varies continuously and functionally, and its optimal tailoring could be made by the numerical optimization incorporated with the nite element method. In such a case, the mesh density in nite element discretization of the volume fraction eld in uences the nal design quality such that the further objective function reduction requires the re nement of volume fraction meshes. However, the uniform re nement of the volume fraction mesh is not e ective, from the numerical point of view, particularly when the nite di erence scheme is employed. This numerical ine ciency could be resolved by locally increasing the mesh density only where more volume-fraction exibility (i.e. more mesh density) is required. In this paper, we propose an e ective volume-fraction optimization procedure by applying the irregular h-re nement to the volume fraction discretization