Topology optimization of nonlinear heat conduction problems involving large temperature gradient

In this work, we develop a topology optimization method for steady-state nonlinear heat conduction problems involving large temperature gradient to minimize the maximum structural temperature. Temperature-dependent material properties (TDMPs) are taken into account to break the widely-used assumption of constant material properties (CMPs) in conventional topology optimization. The Kreisselmeier–Steinhauser function is adopted as an aggregated measure of the maximum temperature over a specific region and the adjoint method is used to derive the sensitivity expressions. To effectively solve the well-known unsymmetric adjoint problem caused by material nonlinearity, an engineering-oriented stationary iterative method (ESIM) is constructed to transform the unsymmetric adjoint problem into a symmetric one with a series of right-hand sides that can be efficiently solved with mature linear system solvers. Both 2D and 3D numerical examples are provided to illustrate the validity and utility of the proposed method, including the accuracy and convergence of the ESIM. The results show that the assumption of CMPs can result in significant inaccuracy in the analysis and design of heat conduction systems working under large temperature gradient. On the contrary, by considering TDMPs and employing the proposed method, reasonable designs are achieved and thermal performance is greatly improved.