Constructing self-supporting structures in biscale topology optimization

The self-supporting requirement is very necessary in additive manufacturing so that the printed structure will not collapse during fabrication. Imposing the self-supporting constraint on topology optimization allows for designing a performance optimized structure that is ready-to-print. However, although biscale topology optimization has been widely studied, conducting self-supporting topology optimization separately for the macro-structure and for each micro-structure is not sufficient to produce an overall self-supporting structure, as first observed in this study. The issue is resolved via an approach to bridge the gap between the requirements of self-supporting at the two scales via distinguishing the macro-cells based on their relative locations. In addition, the self-supporting constraint is expressed as a simple quadratic function included in the topology optimization in both scales, and a convolution operator is designed to efficiently implement its detection. Ultimately, a completely self-supporting overall structure is generated within a biscale topology optimization framework and extends its potentiality to produce design to be directly fabricated via additive manufacturing. Performance of the approach is demonstrated via various 2D and 3D examples.