# ICS 269, Fall 1996: Theory Seminar

## 11 Oct 1996:

Evaluating Geometric Sensitivities at Singular and Non-singular
Points of Variational CAD Models for Design Optimization

Mac Casale, ICS, UC Irvine

Much has been published on the topic of design optimization of
mechanical components. Most of the research has concentrated on the
finite element or boundary element part of the problem. Little
effort has been applied to integrating design optimization with
CAD.

With the introduction of parametric and variational CAD, it is
more desirable than ever to merge these technologies, i.e., to
perform the analysis directly on the CAD geometry and to use the
CAD parameters/dimensions as design variables. In this talk, one
part of the problem is examined, the calculation of geometric
sensitivities on variational CAD geometry. It is shown that for a
well-conditioned set of constraint equations, the geometric
sensitivities are easily obtained by a straight-forward application
of the implicit function theorem.

When the constraint equations become singular, the situation is
more complex. The nature of singularities is explored, and a
method, based on rational transformations that are common in
algebraic curve tracing, is suggested to resolve singular points.
It is shown that the geometric sensitivity is a natural by-product
of the transformation. The talk concludes with an overview of a
symbolic algebra package, coded in Mathematica, that was found to
be useful in the investigation.