Topology optimization for coupled thermal and structural problems using the level set method

In structural designs considering thermal loading, maximization of temperature diffusivity as well as structural stiffness are important and indispensable goals that optimal solutions to design problems need to achieve to reduce operating temperatures and extend product durability. In this paper, a new topology optimization method, based on the level set method and Finite Element Method and including design-dependent effects, is constructed for coupled thermal and structural problems, and multi-objective optimization problems having generic heat transfer boundaries in a fixed design domain are formulated. First, a topology optimization method for coupled thermal and structural problems that uses a level set method incorporating fictitious interface energy is briefly explained. Next, a new objective function that can take into account both temperature diffusivity and stiffness maximization is formulated, based on the concept of total potential energy maximization for the thermal and structural problems. An optimization algorithm that uses the Finite Element Method when solving the equilibrium equation and updating the level set function is then constructed. Finally, several numerical examples are presented to confirm the usefulness of the proposed method.