Level Set-Based Topological Shape Optimization of Heat Conduction Problems Considering Design-Dependent Convection Boundary

A level set-based topological shape optimization method considering design-dependent convection boundaries is developed for steady-state heat conduction problems. We embed the level set function obtained from a Hamilton-Jacobi type of equation into a fixed initial domain to implicitly represent thermal boundaries. The effects of the implicit convection boundary obtained from topological shape variations are represented by numerical Dirac delta and Heaviside functions. The method minimizes the thermal compliance of systems by varying the implicit boundary, satisfying the constraint of allowable material volume. During design optimization, the boundary velocity to integrate the Hamilton-Jacobi equation is derived from an optimality condition.