Requirements for finite element model generation from CAD data—An approach using numerical conformal mapping

Abstract

A critical problem facing the mechanical design community is that of bridging the gap between mechanical CAD data (typically boundary rep trimmed NURB surfaces) and finite element models. A number of papers have discussed this issue and identified it as a critical technology for developing future mechanical design methodologies [Crabb, In Implementation Road Map for Design and Manufacturing, D. H. Brown Sponsored Conference, Ann Arbor, MI (1994)]. While a variety of procedures for finite element model generation from CAD data have been proposed and commercialized, the resulting models have, in general, received much resistance from the professional analyst community. A set of criteria by which the quality of a proposed finite element model generation procedure can be evaluated analytically using elementary control theory is discussed. Additional observations of mesh behavior based on the dimensional anisotropy of general geometric components are presented. Finally a criterion for qualitatively evaluating optimal edge orientations for many of the classical element families is discussed. It is suggested that a combination of these approaches provides an opportunity to semi-quantitatively rank order proposed finite element model generation procedures. A finite element model generation procedure based on numerical conformal mapping is then proposed. It is demonstrated that this procedure ranks very highly when evaluated against the previous criteria. Further, a technical proof of concept implementation demonstrates that numerical conformal mapping appears to be suitable for application to a wide variety of boundary rep solid models.