A method for eliminating local modes caused by isolated structures in dynamic topology optimization

In the dynamic topology optimization of structures with single-phase material, isolated structures, often appear, resulting in the occurrence of local modes. Each isolated structure has three or six zero eigenvalues for 2D or 3D problems, but are meaningless and harmful to the topology optimization. Furthermore, these zero eigenvalues will cause extra unneeded huge computational cost, especially for large-scale problems. To tackle this issue, this paper proposes a novel method for eliminating local modes caused by isolated structures. Firstly, the Nonlinear Virtual Temperature Method (N-VTM) is introduced to identify isolated structures. Subsequently, a new mass interpolation is developed to eliminate the local modes caused by the isolated structures. Since the developed method has an explicit and simple formulation, and the sensitivity of eigen-frequencies with respect to the design variables can be derived. Typical application examples, including vibrating structures and phononic crystals, are used to validate the effectiveness of the proposed method. The results indicate that the proposed method can effectively identify and eliminate isolated structures in the optimization process, avoiding local mode problems, and ensures stable convergence of the optimization iterations.