A modified leaky ReLU scheme (MLRS) for topology optimization with multiple materials

Based on the leaky rectified linear unit (ReLU) function, the paper proposes a modified leaky ReLU scheme (MLRS) for topology optimization with multiple materials. A continuous function formed by sequence of modified leaky ReLU functions are used for the material property interpolation. No extra design variables will be introduced for whatever number of materials considered. Thus, the computational cost is independent to material types. Since the modified leaky ReLU function only consists of two linear functions, the sensitivity of objective and constraint functions is easy to derive. Besides, the sensitivity of MSRL stays a proper constant number even when the design variable is sufficiently small, which may help the convergence. The discontinuous points of derivatives can be jumped across smoothly so that stable transitions can be guaranteed from one type of material to another. An optimal criteria (OC) based solution method is derived from the KKT condition, and an interior point method based solution procedure is introduced for more complex cases. The proposed method is general and straightforward, and is compatible with the existing optimization algorithms. Numerical examples including structural and thermal topology optimization are used to verify the proposed method. The results demonstrate its efficiency and stability. (C) 2019 Elsevier Inc. All rights reserved.