Abstract:
In this paper we present a number of modeling methods that may be
used to automate the design of 3D broadcloth composite parts.
First, we describe a model (a Tchebychev net) which allows us to
simulate the deformation of woven materials into a specific 3D shape.
Two algorithms are described for performing the actual fitting.
The first algorithm simulates the fit by solving the
Tchebychev net formula using a finite difference technique.
The second algorithm simulates the fit by
reducing the problem to a surface-surface intersection problem.
Once we establish the techniques for simulating
a fit, we can discuss the quality and acceptibility of the fit.
In general, a good fit is the one that consumes the smallest area of the
material, that has the smallest deformation energy,
and that is free of manufacturing anomalies such as wrinkles and breaks.
We will present mathematical tools that
allow us to measure the ``goodness'' of a fit with a Tchebychev net,
and that allow us to visually identify
where a possible anomalous event may occur.
Specifically, we will introduce a path-dependent Gaussian curvature
integral that is defined at an arbitrary point in a surface region.
With a path-dependent Gaussian curvature integral,
we will show that it is possible not only to
predict anomalous events,
or wrinkles in particular, but to provide a solution to preventing them.
Finally, we will propose
three methods for preventing anomalous events:
(1) automatic generation of a good initial condition, (2) dart insertion,
and (3) surface shape modification.
Providing different methods for preventing
anomalous events allows a designer of broadcloth composites to select
any combination of them in accordance with his/her design task.
The ultimate goal of all of these techniques is to provide a designer the software
tools needed to easily determine the shape of the broadcloth plies
needed to cover a specific 3D shape.