3595. Calculating Mass Properties from a Triangulated Solid

Paper

Abstract

The introduction of solid modelling in Computer—Aided Design (CAD) tools has proven to be a tremendous boon to weight engineering. Analysis of the solid models provides weight, center of gravity, and inertia data with an ease and precision undreamt of by earlier generations. However, CAD packages such as Dassault’s Catia and SolidWorks are designed for a wide range of applications. As a result, the models are highly complex and even simple operations require a significant amount of resources. This can make sophisticated weights analyses slow and unwieldly, and occasionally prone to error.
Alternative means of representing solid objects
can address these problems. One of the simplest
representations of a solid is by triangulation: the
surface of the solid is approximated by adjoining
triangles. The representation is not exact, but can
be refined to any desired level of precision. By
Stoke’s theorem, any quantity that can be
expressed by an integration of a well—behaved
function over the volume of a solid can also be
expressed by an integration of a related function
over the solid’s surface. So, for a given mass
distribution, it is only necessary to know the surface of the solid in order to do mass properties calculations. Representations such as this are the heart of Finite Element Modelling (FEM), and various sophisticated software packages are also available to perform analysis on FE models. However, sometimes a custom application may be preferable. Since FEM is widely used, CAD packages commonly support the extraction of FE models from their solids, making the creation of these models easy to accomplish. Once created, the data for the FE model can be made available to other applications by exporting it to a text file. Although analysis packages exist that can handle triangulated solids, very little information [1][2][3] is publicly available on how the analysis is done. This article attempts to fill this hole by developing the necessary formulas and procedures.
For the author, the genesis of this article was a new routine for simulating the ditching of an aircraft in water. The routine worked by tracking the movement of water as it flowed into various parts of the aircraft. I originally attempted to craft a Catia macro, but quickly ran into problems. The routine required splitting solids by planes representing the water surface. Regularly, Catia would encounter errors in attempting the splits. I had to add special handling to work around these errors by estimating the results. When I finally produced a working program, it took over 8 hours to produce a very coarse simulation. And to my surprise, Catia had filled over 12 gigabytes of virtual memory, forcing me to reboot. It was clear that another approach would be needed to make this simulation viable. Rather than licensing and learning an existing FEM package, which might have its own computation overhead issues, I chose to program it on my own.
I would like to express my appreciation to Patrick Brown and especially to Victor Graham, who assisted me in the preparation of this paper.