Topology optimization for multi-material structures based on the level set method

Abstract

Topology optimization is the most flexible type of structural optimization method. This method has been applied in a variety of physics problems dealing with a multitude of design problems. In a given design problem, however, the optimization problem often has conflicting evaluative functions, such as the need for high rigidity in combination with minimal weight. The difficulty of simultaneously achieving high performance for two or more functions may be further compounded because current topology optimization methods typically only deal with a single material. On the other hand, when multiple kinds of materials having various properties can be selected for use, the range of a designer's choices is increased and an appropriate solution that greatly improves product functions may be achieved. Thus, this paper presents a new topology optimization method for multi-materials that obtains high-performance configurations. We apply the Multi-Material Level Set (MM-LS) topology description model in the topology optimization method, which uses a total of n level set functions to represent n materials, plus the void phase. The advantage of the MM-LS model is that clear optimal configurations are obtained and the design sensitivity for multi-material structures can be easily calculated. The level set functions that are design variables are updated using the topological derivatives, which also function as design sensitivities, and we derive the topological derivatives for multiple materials. Through several numerical examples, we demonstrate the validity of the proposed method.