Domain Segmentation Optimization of Multiple Anisotropic Materials With Varying Orientation Angles Using a Topology Optimization Based on the Extended Level Set Method

In this study, we propose a method to optimize a domain segmentation of multiple anisotropic materials having varying orientation angles (OAs). The feature of this method is that anisotropic materials having different OAs are considered as different materials for each angle and the domain segmentation is optimized. First, the formulation of a multi-material topology optimization problem is described in which anisotropic materials with different OAs are considered as different materials. Then, linear elasticity topological derivatives are calculated when an anisotropic material is replaced with a different anisotropic material. Subsequently, we outline a topology optimization method based on the extended level set method, which is used to solve the multi-material topology optimization problem. Finally, we apply the proposed method to a stiffness maximization problem and demonstrate its effectiveness using multiple numerical examples.