Parameterized level set method based topology optimization of transient heat conduction structures

In recent years, topology optimization on heat conduction structures has received extensive attention. However, most existing optimization methods focus on steady-state conditions and do not consider the transient effects of heat conduction. We propose a parameterized level set method that offers good stability and smooth boundary representation for solving the topology optimization problem of transient heat conduction structures. The parameterized level set method converts solving a series of partial differential equations into solving ordinary differential equations, thereby improving the efficiency of the optimization process. The interpolation coefficients of the level set functions are updated by sensitivity-driven Lagrange multipliers to facilitate the evolution of the level set functions. By considering heat compliance as the objective function and volume fraction as the constraint, an optimization model is established. This method is applied to various topological optimization problems with different boundary conditions and multi-material, and the efficacy of the proposed method is validated through numerical examples.