Generative Design - Topology Optimization from CAD to CAD

The extension of topology optimization from a 'design by simulation' process into a generative design process, that takes as input a CAD geometry of the design space and returns a CAD geometry of the optimized part design, is presented. Originally motivated by the needs of a virtual product design method for hybrid additive manufacturing in a recent research project, the developed methods apply for a general extension of FEM based optimization to a "CAD to CAD" process chain for general applications. The proposed process comprises not only the conversion of tessellated surfaces as result of the topology optimization into new parametric CAD surfaces. It also strives to keep unchanged parts such as functional surfaces in its original representation as defined by the designer and stitch them together with the newly generated faces. The identification of unchanged parts to be reused is based on a link between the CAD geometry of the design space with the FE model, that is directly established during meshing and maintained during the entire process chain. The creation of the new parametric CAD surfaces starts with the quadrangulation of their triangulation. The resulting quadrangular patches, that are well adapted to geometry, mostly consistently connected and modest in number, then serve to fit spline surfaces. The key ingredients, namely the linkage of a FE model with its underlying CAD geometry and the surface parameterization, whose generation is a challenge on its own, are discussed here in some technical detail. The integration of all methods and algorithms, has been done for the FE solver PERMAS resp. its graphical user interface VisPER, is verified by means of some comprehensive and practical examples. These not only demonstrate the complete embedding of topology optimization into a "CAD to CAD" generative design process, but also that the resulting parametrization of the optimized part is ideally suited for a subsequent parametric shape optimization in a future extension.