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
Geometry dierentiation 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 dierentiation capability is also unavailable within
the CAD system, other methods of dierentiation 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.  utilized nite-dierencing
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 dierent approaches. For example,
to approximate geometry dierentiation (assuming no topology changes) for
aerodynamics analysis of an aircraft outer mold-line, Nemec et al. [2, 3] used
centered nite-dierencing of surface tessellations while tracking mesh nodes
to determine the design velocity w.r.t. model parameters. Chen et al. proposed
a method in  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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