A computer program offers enhanced capabilities for calculating two-dimensional (2D) patterns needed to construct specified three-dimensional (3D) surfaces to within acceptably close approximations, with minimal waste of sheet material. Examples of complexly shaped sheet-material items that could be designed by use of

this program include aircraft fuselages, hulls of ships, clothing, and automotive bodies.

This program offers two advantages over the flattening subprograms of prior computer-aided-design, computer-aided manufacturing (CAD-CAM) programs:

  • The program utilizes all available pertinent information, including not only information on the desired 3D shape but also information about the manufacturing process in which the two-dimensional pattern(s) would be formed into the 3D surface. The more information about the 3D surface and the manufacturing process that is available, the better can be the match between the 3D surface and the 2D pattern(s) used to construct it.
  • The program affords options that enable the user to define and build a method of solution based on the unique characteristics of, and the available data about, the 3D surface. In particular, the program can implement any or all of four independent procedures, and for each procedure there is a choice of several algorithms. This array of options enables the user to integrate any available pertinent information into the solution via at least one procedure.

In the event that the desired 3D surface is one that can be fabricated by bending only (such a surface is termed “developable” in the art) then procedures 1 and 2 are the only ones needed. However, if in-plane deformations (stretching or shrinking) are needed, or if there is a need to fold any portion of sheet material upon itself to form multiple layers, then procedure 3 or procedures 3 and 4 must also be used.

In procedure 1, boundaries that divide a 3D surface into regions are placed into a plane. Because the algorithms defining these boundaries can be chosen from a library of algorithms, these boundaries serve as initial conditions which help define a unique flattening process. The placement of these boundaries depends on several factors unique to the 3D surface. One factor, which can be controlled by placement of the boundaries, is to allow or not allow distortions to move from one 2D region into another 2D region. Also, the user might want to satisfy some general 2D outer-boundary constraints, which can be addressed only at the boundary-placement level. Some 3D surface boundaries cannot be placed directly into the 2D plane by procedure 1. Such a boundary is not amenable to placement by use of one or two algorithms alone; instead, it is necessary to “grow” the boundary into the 2D plane during the execution of procedure(s) 2, 3, and/or 4.

In procedure 2, 3D cell walls are placed into the plane, such that the lengths of the 3D arcs of each cell wall are preserved in the plane. At this point, the program is working in the 2D plane but is using information which geometrically defines the corresponding 3D surface triangle. After procedure 2 has been performed at the local level on an individual cell, the user is then given the option of using either procedure 3 or procedures 3 and 4. These two procedures involve the relationship between the area and geometry of a 3D cell and the area and geometry of the corresponding recently formed 2D cell. In particular, if the user knows there was a local expansion, contraction, or folding of the 2D sheet during the manufacturing process, then procedure 3 or procedures 3 and 4 must be used. These procedures modify the local 2D cell by incorporating, into the 2D cell, the inverse stresses and strains inherent in the manufacturing process of forming a 3D surface from a 2D surface. Procedure 4 is used and coupled to procedure 3 if the expansion or contraction factors are associated with preferred directions.

Another important element of the program logic is the coupling of procedure 2 directly to procedure 3 by feeding the geometric solution of procedure 2 into procedure 3. The geometric solution from procedure 2 serves as an initial geometry from which procedure 3 (or 3 and 4) can geometrically and algebraically iterate. During this iteration, the 3D cell is transformed from a predefined 3D cell geometry to a 2D cell geometry which satisfies input data defining the manufacturing process.

This work was done by Bruce M. Auer of Glenn Research Center. For further information, access the Technical Support Package (TSP) free on-line at www.nasatech.com/tsp  under the Manufacturing category.

Inquiries concerning rights for the commercial use of this invention should be addressed to NASA Glenn Research Center, Commercial Technology Office, Attn: Steve Fedor, Mail Stop 4–8, 21000 Brookpark Road, Cleveland, Ohio 44135. Refer to LEW-17029.

NASA Tech Briefs Magazine

This article first appeared in the March, 2002 issue of NASA Tech Briefs Magazine.

Read more articles from the archives here.