Topology optimization of thermoelastic structures using level set method

This paper describes the topology optimization of thermoelastic structures, using level set method. The objective is to minimize the mean compliance of a structure with a material volume constraint. In level set method, free boundary of a structure is considered as design variable, and it is implicitly represented via level set model. Objective function of the optimization problem is defined as a function of the shape of a structure. Sensitivity analysis based on continuum model is conducted with respect to the free boundary, which suggests the steepest descent direction. A geometric energy term is introduced to ensure smooth structural boundary. Augmented Lagrangian multiplier method is adopted to enforce volume constraint. Numerical examples are provided for 2D cases, considering design independent temperature distribution.