
Model Sensitivity of Edges to a Parameter
Lazzara, David S., Mark Drela, and Robert Haimes
Reserach Notes, 18th International Meshing Roundtable, SpringerVerlag, pp.1620, October 2528 2009

IMR PROCEEDINGS

18th International Meshing Roundtable
Salt Lake City, UT, USA.
October 2528, 2009
Massachusetts Institute of Technology
77 Massachusetts Ave., Cambridge, MA 02139
First Paragraph
Geometry dierentiation is necessary when using solid model representations
within design frameworks that employ gradientbased 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 threedimensional (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 mastermodel, parameters driving the solid model can
be perturbed by some stepsize 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 nitedierencing
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 moldline, Nemec et al. [2, 3] used
centered nitedierencing 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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