Topological Derivative-Based Shape Optimization with Pointwise Temperature Constraints and Applications

In this work we investigate a topological derivative-based strategy to address shape and topology optimization problems with temperature constraints, motivated by applications to the design of thermal management devices. A quadratic penalty functional is formulated to realize the constraint and its first-order topological asymptotic expansion is derived, considering two different model problems. First, we investigate the design of optimal heat-sink structures under steady-state heat conduction. Next, the design of a cooling system for a battery pack is considered with a weakly-coupled thermo-mechanical model. The topology optimization problem is addressed with an efficient algorithm based on the topological derivative method, combined with a level set representation of the design domain, and numerical results are presented.