An adaptive B-spline representation of topology optimization design for Additive Manufacturing

Topology optimization is a renowned structural optimization approach used to compute the optimal topol-ogy for the enhancement of structural performance. It has been in common practice in different engineering fields such as automobile and aerospace. However, there still exist gaps between topology optimization and its engineering operations, which considerably impedes topology optimization's applications. One of these gaps is how to make (especially finite element-based) topology optimization results machine-readable, which means, how to transform these into computer-aided design (CAD) models, which are ready-to-use models for manufacturing. In the proposed work the authors adopted a unique methodology that plugs the gap between topology optimization and manufacturing. This methodology seamlessly integrates the structural analysis tool, boundary description tool and standard CAD geometry representation; equipped with the Hausdorff distance approach for 3D printing/additive manufacturing of optimal structures. Initially, we extract the skeleton of the optimal design (in the form of a points cloud) using the level set method, followed by an interpolation technique with shape preservation property, the extracted skeleton is made dense. Incorporating the shape and curvature information of the data set, an adaptive B-spline approximation is devised for fitting a smooth curve through the points cloud. This approach interprets topology optimization results as a parametric CAD model with minimum possible control points and minimum approximation error. The CAD-based optimal designs are then used for additive manufacturing. The numerical results exhibit in detail the validity and accuracy of the proposed method.