An adaptive material-field series-expansion method for structural topology optimization

The material-field series-expansion (MFSE) method reduces the dimension of design variables in density-based topology optimization and avoids the checkerboard patterns. However, the constant correlation function of the MFSE method only accounts for the spatial dependency between material field points. Accordingly, the expanded material field using the constant correlation function has an obscure topology, which increases the iterations and computation burden of the MFSE method. This paper proposes an adaptive correlation function that considers the spatial dependency and the values of material field points simultaneously. It describes the correlation between material field points more accurately. As a result, the expanded material field based on the adaptive correlation function has a clearer topology than the constant correlation function. Moreover, the adaptive material-field series-expansion (AMFSE) method with dual-loop optimization is introduced leveraging the adaptive correlation function. The outer loop updates the adaptive correlation functions and expanded material fields. The inner loop searches for the optimal solution of the current topology optimization model based on the expanded material field. Finally, several examples of static compliance and dynamic modal loss factor topology optimization validate the effectiveness and applicability of the AMFSE method. Results show that the AMFSE method converges faster with fewer iterations than the MFSE method, despite it increasing the computing time of matrix decomposition in the outer loops. Therefore, the AMFSE method is suitable for topology optimization with complex responses such as modal loss factors to decrease the iterations and computation burden simultaneously.