A level set method for topology optimization of heat conduction problem under multiple load cases

In this paper we present a numerical approach of topology optimization under multiple load cases for heat conduction problem. This framework is based on the theories of topological derivative and shape derivative for elliptic system. We employ level set model to implicitly represent geometric boundary of thermal conductive material. Introducing topological derivative will generate new topology in the design domain, which suppresses the dependence of initial topology guess to some extent. The shape optimization is obtained by combining shape derivative with level set method. The functional of quadratic temperature gradient is taken as the objective function in our analysis, which is subjected to the state equation of steady heat conduction and volume constrain. The shape of material domain is treated as the design variable and the final result is achieved by updating level set function gradually. We develop an effective numerical technique to implement the optimal design with multiple load cases for heat conduction problem. Numerical examples demonstrate that our proposed approach is effective and robust for topology optimization of heat conduction problem.