Generation and Nomenclature of Tessellations and Double-Layer Grids
Publication: Journal of Structural Engineering
Volume 138, Issue 7
Abstract
The aim of this work is to establish a systematic methodology for generating automatically different tessellations and double-layer grids (DLGs) following a newly defined, specific nomenclature. This particular nomenclature defines the notation of mosaics and DLGs in a synthesized and unique manner, and can generate and design them after the parameters expressed in their own names. By means of an algorithm and some computational codes, it is possible to recreate in 3D any DLGs directly from their own names. The current nomenclature for tessellations is also analyzed and found to have severe disadvantages, such as the excessive length of their notations and their nonunique character. A new nomenclature is proposed to define and generate -uniform mosaics consistently and unequivocally in a manner consistent with the current nomenclature used for Archimedean (regular and semiregular) tessellations.
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Acknowledgments
We would like to thank the Basque Delegation of the Spanish College of Civil Engineers for their support while this research was carried out.
References
Critchlow, K. (1969). Order in Space: A Design Source Book, Thames and Hudson, London.
Cundy, H. M., and Rollett, A. P. (1981). Mathematical Models, Tarquin, Stradbroke, UK.
Cuoco, D., and the American Society of Civil Engineers, Task Committee on Double-Layer Grids (Couco/ASCE). (1997). Guidelines for the Design of Double-Layer Grids, ASCE, Reston, VA.
Eekhout, M. (1989). Architecture in Space Structures, 010 Publishers, Rotterdam.
Gomez-Jauregui, V. (2011). “Generation and nomenclature of tessellations and DLG.” 〈www.tensegridad.es/DLG-tessellations/DLG-tessellations.html〉 (Aug. 12, 2011).
Grünbaum, B., and Shephard, G. C. (1986). Tilings and Patterns, W. H. Freeman & Co, New York.
Joyce, D. E. (1997). “The 17 plane symmetry groups.” 〈http://www.clarku.edu/~djoyce/wallpaper/seventeen.html〉 (Dec. 23, 2010).
Lan, T. T. (1999). “Space frame structures.” Structural Engineering Handbook, CRC Press, Boca Raton, FL, 24.1–24.50.
Makowski, Z. S. (1968). Estructuras Espaciales de Acero, Gustavo Gili, Barcelona.
Makowski, Z. S. (1981). Analysis, Design and Construction of Double-Layer Grids, Applied Science Publishers, Ltd., London.
Malla, R. B., and Serrette, R. L. (1996). “Double-layer grids: Review of static and thermal analysis methods.” J. Struct. Eng.JSENDH, 122(8), 873–881.
Otero, C. (1990). “Diseño geométrico de cúpulas no esféricas aproximadas por mallas triangulares con un número mínimo de longitudes de barra.” Doctoral dissertation, Universidad de Cantabria, Spain.
Otero, C., Oti, J., Villar, F., and Otero, F. (1992). “Classical geometry in flat and simple curved meshes.” Bull. Int. Assoc. Shell Spatial Struct.BSSSCD, 33(1), 3–31.
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Information
Published In
Journal of Structural Engineering
Volume 138 • Issue 7 • July 2012
Pages: 843 - 852
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Jun 10, 2011
Accepted: Oct 20, 2011
Published online: Oct 24, 2011
Published in print: Jul 1, 2012
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