Multiscale Topology Design Based on Non-Penalisation Smooth-Edged Material Distribution for Optimising Topology (SEMDOT)

This study presents an extension of the Smooth-Edged Material Distribution Optimisation Technique (SEMDOT) to multiscale topology optimisation (MSTO). While the SEMDOT has shown promise in producing smooth and fabrication-friendly structures in various single-scale problems, its application to multiscale design remains unexplored. To extend SEMDOT to MSTO, a discrete sensitivity approach without penalisation is introduced, in which sensitivities are directly determined by classifying elements. Microstructural properties are computed using energy-based homogenisation with periodic boundary conditions (PBCs), enabling efficient and accurate prediction of effective elastic moduli. Physical fidelity of the smooth boundaries estimated by level-set functions are validated. Numerical results from 2D and 3D compliance minimization benchmarks demonstrate the effectiveness of the SEMDOT method, resulting in smooth boundaries between solid and void phases at both macro- and microscales, overcoming the jagged boundaries and grayscale issues seen in conventional methods. The results also show that the SEMDOT achieves comparable performance to other MSTO methods, with fewer iterations and reduced computational time.