Multi‐material topology optimization method for transient thermal structure with constraint on permissible temperatures

Abstract

Excessive temperature may lead material to performance degradation, ablation, and phase change. Thus, controlling the maximum temperature of used material within a safe range is of great significance to the safe operation of thermal structures. In this article, a density‐based multi‐material topology optimization method for transient thermal structures is proposed, in which the maximal temperature for each material is controlled not greater than its permissible temperature. In this method, a projection algorithm based on the PDE (partial differential equation) filter and Heaviside projection is set up and used to identify the domains occupied by each material. The maximal temperature of each specific material occupying domain is approximately expressed by the condensed integrals in the time and space domains. The permissible temperature constraint is satisfied by controlling the condensed integrals not great than a specific threshold value (depending on the corresponding material's permissible temperature). Several examples illustrate that the permissible temperature plays an important role in the selection and the distribution scheme of the candidate materials for the design of multi‐material thermal structures. The proposed method can effectively control the maximal temperature of each material within its constraint range, and achieve the rational design for multi‐material thermal structures. In addition, different thermal loading time may also lead to different material selection of structure. This work has potential applications in the lightweight design of thermal insulation structures.