Exploring optimal topology of thermal cloaks by CMA-ES

Abstract

This paper presents topology optimization for thermal cloaks expressed by level-set functions and explored using the covariance matrix adaptation evolution strategy (CMA-ES). Designed optimal configurations provide superior performances in thermal cloaks for the steady-state thermal conduction and succeed in realizing thermal invisibility, despite the structures being simply composed of iron and aluminum and without inhomogeneities caused by employing metamaterials. To design thermal cloaks, a prescribed objective function is used to evaluate the difference between the temperature field controlled by a thermal cloak and when no thermal insulator is present. The CMA-ES involves searches for optimal sets of level-set functions as design variables that minimize a regularized fitness involving a perimeter constraint. Through topology optimization subject to structural symmetries about four axes, we obtain a concept design of a thermal cloak that functions in an isotropic heat flux.