材料分布の連続性を仮定した熱拡散問題のトポロジー最適化

抄録

In structural designs considering thermal loading, maximization of temperature diffusivity in structures is one of the most important essential factors in reducing operating temperature and maintaining product durability, in addition to the usual maximization of stiffness that optimal designs achieve. In this paper, a topology optimization method is constructed for thermal problems considering generic heat transfer boundaries, including heat convection boundaries, based on the homogenization method. First, the topology optimization method for thermal problems is discussed using a homogenization method that assumes a continuous material distribution. Next, a new objective function that can take into account heat transfer boundaries, such as temperature-constant and heat convection boundaries, is proposed, based on the concept of a total potential energy maximization problem in the structural problem, and an optimization problem is formulated using the proposed objective function. An optimization algorithm is constructed using the Finite Element Method (FEM) and Sequential Linear Programming (SLP). Finally, several numerical examples are presented in order to confirm the usefulness of the proposed method.