Phase-field method combined with optimality criteria approach for topology optimization

This paper introduces a novel topology optimization framework by combining the phase-field method and optimality criteria approach. This novel approach allows for the automatical addition of holes in the initial shape, a capability that is not achievable with the conventional phase-field model based on boundary changes for topology optimization. The distribution of the material is changed according to the sensitivity of the optimality criteria approach to nucleate holes. After the nucleation of the new holes, they are utilized for topology optimization using the phase-field method. To demonstrate the accuracy and effectiveness of the proposed approach, we conduct several numerical examples based on the two-dimensional minimum compliance problem. The obtained numerical results show the proposed method's fast convergence compared to the conventional phase-field method.