Summary
Layered manufacturing (LM), alias solid freeform fabrication or rapid prototyping, is an important emerging manufacturing technique. It builds up a manufactured artefact by depositing successive layers of material under computer control. Until recently, objects manufactured by LM methods have been regarded as composed of homogeneous material. However, new methods of optimal design specify `functionally graded’ or inhomogeneous materials. Layered manufacturing provides a means for producing such variable material distributions. Furthermore, methods are under development for embedding reinforcing fibres in the deposited material, and additional means are therefore needed for the representation of material nonisotropy. The problem reduces essentially to that of parametrizing the interior of a boundary representation solid model, ideally in terms of the surfaces involved in its boundary. The paper surveys several methods with the potential for representing 3D material distributions, and examines their compatibility with ISO 10303 (STEP) an international standard for the representation of product life-cycle data. Some consideration is also given to the related problem of representing the microstructure resulting from the deposition of the material (in most LM methods) in strands or filaments.
Also affiliated with Center for Automation Technologies, Rensselaer Polytechnic Institute, Troy, NY 12180-3590,USA
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
C. L. Bajaj. Modelling physical fields for interrogative visualization. In T. N. T. Goodman and R. R. Martin, editors, The Mathematics of Surfaces VII. Information Geometers Ltd., Winchester, UK, 1997.
M. P. Bendsoe, A. Diaz, and N. Kikuchi. Topology and generalized layout optimization of elastic structures. In M.P. Bendsoe and C.A. MotaSoares, editors, Topology Design of Structures. Kluwer Academic Publishers, Amsterdam, 1993.
M. Burns. Automated Fabrication. Prentice-Hall, Englewood Cliffs, New Jersey, 1992.
R. W. Gray IV, D. G. Baird, and J. H. Bøhn.Effects of processing conditions on short TLCP fiber reinforced FDM parts. Rapid Prototyping Journal, 4, 1, 14–25, 1998.
J. Hoschek and D. Lasser. Computer Aided Geometric Design. A. K. Peters, Wellesley, MA, 1993.
International Organization for Standardization. Industrial Automation Systems and Integration- Product Data Representation and Exchange, 1994. (The ISO catalogue is at http://www.iso.ch/cate/cat.html search on 10303 for a listing of parts of the standard).
C. L. Jackins and S. L. Tanimoto. Oct-trees and their use in representing three-dimensional objects. Computer Graphics e.4 Image Processing, 14, 249–270, 1983.
T. R. Jackson, N. M. Patrikalakis, E. M. Sachs, and M. J. Cima. Modeling and designing components with locally controlled composition. In Proceedings of the Solid Freeform Fabrication Symposium,Austin, TX, 1998.
K. K. Jurrens. Rapid prototyping’s second decade. Rapid Prototyping (quarterly newsletter of the SME Rapid Prototyping Association), 4, 1, 1–4, 1998.
V. Kumar. Solid Modeling and Algorithms for Heterogeneous Objects. PhD thesis, University of Michigan, Ann Arbor, MI, 1999.
V. Kumar, D. Burns, D. Dutta, and C. M. Hoffmann. A framework for object modeling. Computer Aided Design, 31, 9, 541–556,1999.
J. Mazumder, J. Koch, K. Nagarathnam, and J. Choi. Rapid manufacturing by laser aided direct deposition of metals. Technical report, University of Illinois, Department of Mechanical Engineering, 1996.
D. Meagher. Geometric modelling using octree encoding. Computer Graphics & Image Processing, 19, 129–147, 1982.
C. Nash and S. Sen. Topology and Differential Geometry for Physicists. Academic Press, New York, NY, 1983.
J. Owen. STEP: An Introduction. Information Geometers, Winchester, UK, 2nd edition, 1997.
L. Patil, D. Dutta, A. D. Bhatt, K. K. Jurrens, K. W. Lyons, M. J. Pratt, and R. D. Sriram. Representation of heterogeneous objects in ISO 10303 (STEP). Submitted to ASME International Mechanical Engineering Congress and Exposition, Orlando, FL, November 2000.
A. A. G. Requicha. Representations of rigid solids - Theory, methods and systems. ACM Computing Surveys, 12, 437–464, 1980.
V. L. Rvachev, T. I. Sheiko, V. Shapiro, and I. Tsukanov. Transfinite interpolation over implicitly defined sets. Technical Report SAL 2000–1, Spatial Automation Laboratory, University of Wisconsin - Madison, 2000.
J. J. Shah and M. Mäntylä. Parametric and Feature-based CAD/CAM. Wiley, 1995.
V. Shapiro and I. Tsukanov Implicit functions with guaranteed differential properties. In W. F. Bronsvoort and D. C. Anderson, editors, Proc. 5th ACM Symposium on Solid Modeling and Applications. Association for Computing Machinery, New York, NY, 1999.
D. Shepard. A two-dimensional interpolation function for irregularly spaced data. In Proceedings of 23rd ACM National Conference, pages 517–524. Association for Computing Machinery, New York, NY, 1968.
J. Vida, R. R. Martin, and T. Vârady. A survey of blending methods that use parametric surfaces. Computer Aided Design,26, 5, 341–365, 1994.
J. R. Woodwark. Blends in geometric modelling. In R. R. Martin, editor, The Mathematics of Surfaces II. Oxford University Press, 1987. (Proc. 2nd IMA Conf. on the Mathematics of Surfaces, Cardiff, Wales, Sept. 1986).
Z. Wu, S. H. Soon, and L. Feng. NURBS-based volume modeling. In International Workshop on Volume Graphics, Swansea, Wales, pages 321 - 330, 1999.
J. Zagajac. Engineering Analysis over Subsets. PhD thesis, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag London
About this paper
Cite this paper
Pratt, M.J. (2000). Modelling of Material Property Variation for Layered Manufacturing. In: Cipolla, R., Martin, R. (eds) The Mathematics of Surfaces IX. Springer, London. https://doi.org/10.1007/978-1-4471-0495-7_29
Download citation
DOI: https://doi.org/10.1007/978-1-4471-0495-7_29
Publisher Name: Springer, London
Print ISBN: 978-1-4471-1153-5
Online ISBN: 978-1-4471-0495-7
eBook Packages: Springer Book Archive