Thermal barrier coatings (TBCs) are used for increasing the efficiency and reducing pollutants of internal combustion engines (ICEs). In this paper, an optimization framework is developed in order to obtain the optimal dimensions for conventional coat, and the optimal dimensions and material property for functionally graded (FG) coat of a partially coated piston. A thermo mechanical analysis is investigated for Nano coat by finite element method. The conventional and Nano coats are made of MgZrO_3 as the insulating ceramic overlay and NiCrAl as the metallic bond-coat. The properties of the FG coat is assumed to vary according to power law through the thickness. For all tree conventional, FG...