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Model Sensitivity of Edges to a Parameter

Lazzara, David S., Mark Drela, and Robert Haimes

Reserach Notes, 18th International Meshing Roundtable, Springer-Verlag, pp.16-20, October 25-28 2009


18th International Meshing Roundtable
Salt Lake City, UT, USA.
October 25-28, 2009

Massachusetts Institute of Technology
77 Massachusetts Ave., Cambridge, MA 02139

First Paragraph
Geometry di erentiation is necessary when using solid model representations within design frameworks that employ gradient-based optimization. This pre- requisite becomes a greater challenge if the solid model was obtained from a Computer Aided Design (CAD) system. In these cases, the solid model is usually a manifold boundary representation (BRep) created from a master model that contains driving parameters and a three-dimensional (3D) feature- construction recipe. Since access to the CAD system source code is normally unavailable and a geometry di erentiation capability is also unavailable within the CAD system, other methods of di erentiation must be employed. With access to the master-model, parameters driving the solid model can be perturbed by some step-size in order to determine the design velocity (i.e. the mapping of a geometry feature from an initial to a perturbed domain) of each feature. This translates into a design velocity for each face, trim curve and node in the BRep. Armstrong et al. [1] utilized nite-di erencing to nd the design velocity normal to the model boundary in this manner. Although doing this for each driving parameter and topology feature in a complex model is tedious (requiring at least one new instance for each param- eter perturbation), others have attempted di erent approaches. For example, to approximate geometry di erentiation (assuming no topology changes) for aerodynamics analysis of an aircraft outer mold-line, Nemec et al. [2, 3] used centered nite-di erencing of surface tessellations while tracking mesh nodes to determine the design velocity w.r.t. model parameters. Chen et al. proposed a method in [4] that required deriving implicit representations of active prim- itives in a solid model to determine the design velocity of active boundaries driven by model parameters.

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