Multiphysics Topology Optimization of Thermal Actuators by Using the Level Set-Based Multiple-Type Boundary Method

Thermal actuators use thermal expansion and contraction of an elastic body to produce motion at its output port. In the present study, a thermal actuator comprises an elastic body and heating/cooling devices. Such devices have a thin-layer shape and are installed on the surface of the elastic body. The design optimization of thermal actuator is a multiphysics problem, including both heat conduction and elastic deformation. The design variables include multiple types of boundaries, i.e., the temperature boundary (high temperature and low temperature) and the free boundary. In order to solve such a multiphysics optimization problem involving multiple types of boundaries, the level set-based multiple-type boundary method is employed. In the analysis for the shape derivative of the temperature boundary, the constrained variational principle is employed to explicitly include the temperature boundary condition into the weak form of heat conduction equation. Numerical examples in two dimensions are investigated.