Study on two-phase material topology optimization for transient heat conduction

Abstract

In the field of topology optimization for heat conduction problems, the steady-state thermal conditions are usually assumed because of its theoretical ease of handling. However, for design problems such as casting dies and heat-dissipating parts, where not only the spatial distribution of temperature but also its temporal transition is important, a topology optimization method considering unsteady-state conditions is required. With this background, the present study deals with an unsteady-state heat conduction problem with a special objective function, namely minimizing temperature at the targeted time and space. The optimization problem is solved using a gradient-based optimization scheme and its accuracy of sensitivities with respect to design variables is investigated. Finally, the performance of the proposed method and a common problem for unsteady-state thermal problems are discussed through a series of the numerical examples.