A multi-regional MFSE topology optimization method for large-scale structures with arbitrary design domains

Due to its exceptional mechanical properties, large-scale topology optimization with arbitrary design domains has become an attractive mission and facilitated the application of topology optimization methods in practical engineering applications. In this work, an extended material-field series expansion (MFSE) method that employs a multi-regional strategy with spatial-varied correlation length is proposed for arbitrary design domain and overcoming several shortcomings of the original MFSE method. The proposed approach involves dividing the design domain into multiple sub-regions through background grid mapping technology, where each sub-region is characterized by its own material field function. The evolution of these material-field functions is carried out independently driven by the design sensitivity of the objective function and constraints. As expected, the structures in any two adjacent sub-regions can be connected perfectly due to the continuity of the solution by mono-scale analysis. The proposed framework is scalable and can be utilized for parallel computation, arbitrary design domains, and different topology optimization problems. Several numerical examples, including 2D and 3D design domains with arbitrary geometries, are presented to validate the effectiveness of the proposed method in applying large-scale structures with arbitrary design domains.