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.