Title: A combinatorial framework for parametric additive manufacturing

Authors: J.C. Boudreaux

Addresses: National Institute of Standards and Technology, Gaithersburg, MD 20899, USA

Abstract: The design of engineered artefacts is often a difficult and costly task. Thus, substantial technical efforts have been directed at developing methods to reuse design data sets by identifying, and exploiting, latent functional connections between data sets. Parametric design is based on the premise that an inventory existing designs can be used to create design templates such that the identified functional connections are coded by embedded parametric expressions. Novel variant designs may then be generated by assigning reasonable values to the parameters and then evaluating the resulting expressions in a carefully controlled manner. The potential of parametric engineering is clearly shown in the context of additive manufacturing. It will also be shown that parametric engineering models can be based directly on finitary combinatorial structures, specifically simplicial complexes. This paper will also propose that a suitable computational framework for this approach can be based upon a functional model of computation.

Keywords: additive manufacturing; topological models; directed graphs; simplicial complexes; manifolds; Morse functions; Reeb graphs; functional computation; digraph automata; parametric design; modelling; parametric engineering models; combinatorial structures.

DOI: 10.1504/IJRAPIDM.2013.053684

International Journal of Rapid Manufacturing, 2013 Vol.3 No.2/3, pp.105 - 129

Available online: 04 May 2013 *

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