Design of bi-metallic devices based on the topological derivative concept

• Topological derivative of semi-coupled problem.
• Novel, extremely simple closed formula for the topological sensitivity.
• Full mathematical justifications for the obtained formulas.
• Potential applications to topology design of thermal actuators.

In this work the topological derivative concept is applied in the context of topology design of thermo-mechanical devices, where the linear elasticity system (modeled by the Navier equation) is coupled with the steady-state heat conduction problem (modeled by the Laplace equation). The mechanical coupling term comes out from the thermal stress induced by the temperature field. We consider the topology design of bi-metallic devices. The idea is to maximize the displacement in a given direction defined on the boundary of the thermo-elastic body with respect to a bi-metallic material distribution. The topological derivative is obtained by considering the nucleation of a small circular inclusion with different thermal expansion coefficients. A level-set domain representation method is used, together with the derived topological sensitivity formula, to devise a topology design algorithm. Finally, some numerical experiments regarding the conceptual design of thermo-mechanical devices are presented.