Universal Parametric Geometry Representation Method

TLDR

The fundamental parametric geometry representation method uses simple mathematical functions with observable physical features to describe an essentially limitless design space of analytically smooth geometries. By extending the class function/shape function methodology to three dimensions, the authors define a geometry in design space through distributions of class and shape functions and then transform this design space into physical space. The approach successfully represents arbitrary three‑dimensional geometries such as wings, nacelles, and bodies with few variables, and its versatility is illustrated by applications to nacelles, ducts, wings, and bodies.

Abstract

andsimplemathematicalfunctionshavingeasilyobservedphysicalfeatures.Thefundamentalparametricgeometry representation method is shown to describe an essentially limitless design space composed entirely of analytically smooth geometries. The class function/shape function methodology is then extended to more general threedimensional applications such as wing, body, ducts, and nacelles. It is shown that a general three-dimensional geometry can be represented by a distribution of fundamental shapes, and that the class function/shape function methodology can be used to describe the fundamental shapes as well as the distributions of the fundamental shapes. Withthisveryrobust,versatile,andsimplemethod, athree-dimensional geometry isdefinedinadesignspacebythe distribution of class functions and the shape functions. This design space geometry is then transformed into the physical space in which the actual geometry definition is obtained. A number of applications of the class function/ shape function transformation method to nacelles, ducts, wings, and bodies are presented to illustrate the versatility of this new methodology. It is shown that relatively few numbers of variables are required to represent arbitrary three-dimensional geometries such as an aircraft wing, nacelle, or body.