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Innovative dome design: Applying geodesic patterns with shape annealing

Published online by Cambridge University Press:  27 February 2009

Kristina Shea  and
Jonathan Cagan
Kristina Shea
Affiliation:
Computational Design Lab, Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A.
Jonathan Cagan
Affiliation:
Computational Design Lab, Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A.
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Abstract

Shape annealing, a computational design method applied to structural design, has been extended to the design of traditional and innovative three-dimensional domes that incorporate the design goals of efficiency, economy, utility, and elegance. In contrast to deterministic structural optimization methods, shape annealing, a stochastic method, uses lateral exploration to generate multiple designs of similar quality that form a structural language of solutions. Structural languages can serve to enhance designer creativity by presenting multiple, spatially innovative, yet functional design solutions while also providing insight into the interaction between structural form and the trade-offs involved in multi-objective design. The style of the structures within a language is a product of the shape grammar that defines the allowable structural forms and the optimization model that provides a functional measure of the generated forms to determine the desirable designs. This paper presents an application of geodesic dome patterns that have been embodied in a shape grammar to define a structural language of domes. Within this language of domes, different dome styles are generated by changing the optimization model for dome design to include the design goals of maximum enclosure space, minimum surface area, minimum number of distinct cross-sectional areas, and visual uniformity. The strengths of the method that will be shown are 1) the generation of both conventional domes similar to shape optimization results and spatially innovative domes, 2) the generation of design alternatives within a defined design style, and 3) the generation of different design styles by modifying the language semantics provided by the optimization model.

Keywords

Topological LayoutStructural OptimizationDome DesignSimulated AnnealingShape Grammars
Type
Articles
Information
AI EDAM , Volume 11 , Issue 5 , November 1997 , pp. 379 - 394
Copyright
Copyright © Cambridge University Press 1997

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References

REFERENCES

Addis, W. (1990). Structural Engineering: The Nature of Theory and Design. Ellis Horwood, New York.Google Scholar
Anagnostou, G., Ronquist, E.M., & Patera, A.T. (1992). A computational procedure for part design. Computer Methods in Applied Mechanics and Engineering 97, 33–48.CrossRefGoogle Scholar
Baldwin, J. (1996). BuckyWorks: Buckminster Fuller's Ideas for Today. Wiley, New York.Google Scholar
Baumgartner, A., Harzheim, L., & Mattheck, C. (1992). SKO (soft kill option): The biological way to find an optimum structural topology. International Journal of Fatigue 14(6); 387–393.CrossRefGoogle Scholar
Bendsoe, M.P. (1995). Optimization of Structural Topology, Shape, and Material. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Bendsoe, M.P., & Kikuchi, N. (1988). Generating optimal topologies in structural design using homogenization method. Computer Methods in Applied Mechanics and Engineering 71, 197–224.CrossRefGoogle Scholar
Bendsoe, M.P., & Soares, C. (eds.) (1993). Topology Design of Structures, NATO ASI Series—NATO Advanced Research Workshop. Kluwer Academic Publishers, Dordredht.CrossRefGoogle Scholar
Bendsoe, M.P., Ben-Tal, A., & Zowe, J. (1994). Optimization methods for truss geometry and topology design. Structural Optimization 7, 141–159.CrossRefGoogle Scholar
Billington, D.P. (1983). The Tower and the Bridge: The New Art of Structural Engineering. Basic Books, New York.CrossRefGoogle Scholar
Bono, R. (1996). www.crisis.com/~rjbono/html/domes.html.Google Scholar
Bremicker, M., Chirehdast, M., Kikuchi, M., & Papalambros, P.Y. (1991). Integrated topology and shape optimization in structural design. Mechanics of Structures and Machines International Journal 19(4), 551–587.CrossRefGoogle Scholar
Brown, K.N., McMahon, C.A., & Sims Williams, J.H. (1995). Features, aka the semantics of a formal language of manufacturing. Research in Engineering Design 7, 151–172.CrossRefGoogle Scholar
Cagan, J., & Mitchell, W.J. (1993). Optimally directed shape generation by shape annealing. Environment and Planning B 20, 5–12.CrossRefGoogle Scholar
Chapman, C., Saitou, K., & Jakiela, M.J. (1994). Genetic algorithms as an approach to configuration and topology design. ASME Journal of Mechanical Design 116, 1005–1012.CrossRefGoogle Scholar
Chirehdast, M., Gea, H.-C., Kikuchi, N., & Papalambros, P.Y. (1994). Structural configuration examples of an integrated optimal design process. ASME Journal of Mechanical Design 116, 997–1004.CrossRefGoogle Scholar
Diaz, A.R., & Belding, B. (1993) On optimum truss layout by a homogenization method. ASME Journal of Mechanical Design 115, 367–373.CrossRefGoogle Scholar
Dorn, W.S., Gomory, R.E., & Greenberg, H.J. (1964). Automatic design of optimal structures. Journal de Mècanique 3(1), 25–52.Google Scholar
El-Sayed, M.E.M., & Jang, T.S. (1991). Multi-objective structural optimization via goal formulation. Computer Aided Optimum Design of Structures 91: Optimization of Structural Systems and Industrial Applications. pp. 87–97. Cambridge, MA, Compt. Mech. Publications.Google Scholar
Eschenauer, H., Koski, J., & Osyczka, A. (1990). Multicriteria Design Optimization: Procedures and Applications. Springer-Verlag, New York.CrossRefGoogle Scholar
Fuller, R.B. (1954). Building Construction. Patent No. 2,682,235.Google Scholar
Fuller, R.B. (1970). Hexa-Pent. Patent No. 3,810,336.Google Scholar
Gobat, J.I., & Atkinson, D. (1994). FElt: User's guide and reference manual. Computer Science Report No. CS94–376. University of California, San Diego.Google Scholar
Grandhi, R.V., Bharatram, G., & Venkayya, V.B. (1993). Multiobjective optimization of large-scale structures. AIAA Journal 31(7), 1329–1337.CrossRefGoogle Scholar
Hemp, W.S. (1973). Optimum Structures. Claredon, Oxford.Google Scholar
Hiesserman, J., & Woodbury, R. (1994). Geometric design with boundary solid grammars. In Formal Design Methods for CAD (B-18), Gero, J.S. & Tyugu, E. Eds., pp. 85–105. Elsevier Science B.V., North-Holland.Google Scholar
Kirkpatrick, S., Gelatt, C. D. Jr, & Vecchi, M.P. (1983). Optimization by simulated annealing. Science 220(4598) 671–679.CrossRefGoogle ScholarPubMed
Kirsch, U. (1989). Optimal topologies of structures. Applied Mechanics Review 42(8), 223–238.CrossRefGoogle Scholar
Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., & Teller, E. (1953). Equation of state calculations by fast computing machines. Journal of Chemical Physics 21, 1087–1092.CrossRefGoogle Scholar
Michell, A.G.M. (1904). The limits of economy of materials in frame structures. Philosophical Magazine Series 6, 8(47), 589–597.CrossRefGoogle Scholar
Mitchell, W.J. (1990). The Logic of Architecture: Design, Computation and Cognition, Chapter 2: Architectural Form. MIT Press, Cambridge, MA.Google Scholar
Ochotta, E.S. (1994). Synthesis of high-performance analog cells in ASTRX/OBLX. Ph.D. Dissertation. Report No. CMUCAD-94–17. Carnegie Mellon University, Pittsburgh, PA.Google Scholar
Pedersen, P. (1973). Optimal joint positions for space trusses. Proc. American Society of Civil Engineers 99(ST12), 2459–2475.Google Scholar
Pedersen, P. (1992). Topology optimization of three dimensional trusses. Topology Design of Structures, NATO ASI Series–NATO Advanced Research Workshop, pp. 19–30. Kluwer Academic Publishers, Dordredht.Google Scholar
Prennis, J. (Ed.) (1973). The Dome Builder's Handbook. Running Press, Philadelphia.Google Scholar
Reddy, G., & Cagan, J. (1993). Optimally directed truss topology generation using shape annealing. Advances in Design Automation, Vol. 65, pp. 749–759. Albuquerque, NM, ASME.Google Scholar
Reddy, G., & Cagan, J. (1995). An improved shape annealing algorithm for truss topology generation. ASME Journal of Mechanical Design 117(2A), 315–321.CrossRefGoogle Scholar
Rozvany, G.I.N., & Zhou, M. (1991). A new direction in cross-section and layout optimization: The COC algorithm. Computer Aided Optimum Design of Structures 91: Optimization of Structural Systems and Industrial Applications, pp. 39–50. Cambridge, MA, Compt. Mech. Publications.Google Scholar
Shea, K., Cagan, J., & Fenves, S. (1996). A shape annealing approach to optimal truss design with dynamic grouping of members. ASME Journal of Mechanical Design.Google Scholar
Sheppard, R., Threadgill, R., & Holmes, J. (1974). Paper Houses. Schocken Books, New York.Google Scholar
Simon, H.A. (1975). Style in design. In Spatial Synthesis in Computer-Aided Building Design. (Eastman, C.M. Ed.). John Wiley, New York.Google Scholar
Spillers, W.R. (1975). Iterative Structural Design. North-Holland Monographs In Design Theory, North-Holland/American Elsevier, New York.Google Scholar
Stal, D.M., & Turkiyyah, G.M. (1996). Skeleton-based shape design. In Artificial Intelligence in Design '96 (Gero, J.S. & Sudweeks, F. Eds.), pp. 761–780. Kluwer Academic, The Netherlands.Google Scholar
Swartz, W., & Sechen, C. (1990). New algorithms for the placement and routing of macro cells. IEEE Proc. Cat. No. 90CH2924–9, IEEE Conference on Computer-Aided Design, pp. 336–339. Santa Clara, CA, IEEE Computer Society Press.Google Scholar
Stiny, G. (1980). Introduction to shape and shape grammars. Environment and Planning B 7, 343–351.CrossRefGoogle Scholar