journal article·2023-12-22Open access

Analysis of Lightweight Structure Mesh Topology of Geodesic Domes

Dominika Bysiec, Szymon Jaszczyński, Tomasz Maleska

Applied Sciences· Volume 14· Issue 1

Abstract

This paper presents two methods of shaping the mesh topology of lightweight structures as spherical domes. The two given methods of dividing the initial face of the polyhedra determine the obtained structures, which differ in the way of connecting the nodal points. These points were obtained by applying the algorithm for calculating spherical coordinates presented in the paper, which were then converted to the Cartesian system using transformation formulas. Two models of dome structures are presented, based on a 4608-hedron according to the first division method, and on a 4704-hedron, using the second proposed method with numerical analysis. Thus, the novelty of this paper is an implementation of the formulas and algorithms from geodesic domes based on the regular dodecahedron to the regular octahedron, which has not been presented so far. The choice of the shape of the structure has impacts on sustainable development, dictated by structural and visual considerations, leading to the design of a light structure with low consumption of construction material (steel), which can undoubtedly be helpful when making the final structure shape. In addition, according to this research, it can be concluded that using the first method to create a geodesic dome mesh is more straightforward, safer, and requires less design experience.
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Research context

OpenAlex topics: Architecture and Computational Design · Advanced Theoretical and Applied Studies in Material Sciences and Geometry · 3D Surveying and Cultural Heritage

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Faculty of Civil Engineering and Architecture, Opole University of Technology, 45-758 Opole, Poland

References (56)

Show source-provided references
1. Fuller, B.R. (1954). Geodesic Dome. (2,682,235), U.S. Patent.
2. Clinton, J.D. (1971). Advanced Structural Geometry Studies. Part I, Polyhedral Subdivision Concept for Structural Application.
3. Lowest common frequency: b2 + bc + c210.1177/026635119000500306 ↗
4. Tarnai, T. (1987). Spherical Grid Structures: Geometric Essays on Geodesic Domes, Hungarian Institute for Building Science.
5. Geodesic domes: Natural and man-made10.1177/026635119601-203 ↗
6. The roundest polyhedral with symmetry constraints10.3390/sym9030041 ↗
7. The use of polyhedral for building structures
8. Gabriel, J.F. (1997). The Polyhedral World. Beyond the Cube. The Architecture of Space Frames and Polyhedra, John Wiley & Sons, Inc.
9. Dome-type space structures of ellipsoidal form
10. The chiral polyhedra
11. Kunieda, H. (2001, January 9–13). Polyhedral patterns. Proceedings of the International Symposium on Theory, Design and Realization of Shell and Spatial Structures, Nagoya, Japan.
12. Huybers, P. (2002). ICCS’02: Proceedings of the International Conference on Computational Science—Part III, Amsterdam, The Netherlands, 21–24 April 2002, Springer.
13. Determination of parameters of crystal latticed surfaces composed of hexagonal plane faces10.1177/026635119000500303 ↗
14. Pavlov, G.N. (1993). Space Structures 4, Thomas Telford Ltd.
15. Kitrick, C.J. (1980). Tensegrity Module Structure and Method of Inter-Connecting the Modules. (4,207,715), U.S. Patent.
16. A unified approach to class I, II & III geodesic forms10.1177/026635119000500307 ↗
17. Structures on hyper-structures
18. Continuous transformations of subdivided periodic surfaces10.1177/026635119000500309 ↗
19. Lalvani, H., and Katz, N. (1993). Space Structures 4, Thomas Telford.
20. Higher dimension periodic table of regular and semi-regular polytopes10.1177/026635119601-204 ↗
21. Artistic tessellation patterns on spherical surface
22. Patterns of the spherical surface
23. Rębielak, J. (2005). Shaping of Space Structures. Examples of Applications of Formian in the Design of Tension-Strut Systems, Oficyna Wydawnicza Politechniki Wrocławskiej.
24. Coxeter, H.S.M. (1973). Regular Polytopes, Dover Publications. [3rd ed.].
25. Fuliński, J. (1973). Geometria Kratownic Powierzchniowych, Państwowe Wydawnictwo Naukowe. The Work of Wrocław Scientific Society.
26. Gradient-based size, shape, and topology optimization of single-layer reticulated shells subject to distributed loads10.1007/s00158-022-03225-w ↗
27. Optimum geometry design of geodesic domes using harmony search algorithm
28. Optimum topological design of geometrically nonlinear single layer latticed domes using coupled genetic algorithm10.1016/j.compstruc.2007.02.023 ↗
29. Geometry and topology optimization of geodesic domes using charged system search10.1007/s00158-010-0566-y ↗
30. Optimum topology design of various geometrically nonlinear latticed domes using improved harmony search method10.1007/s00158-011-0675-2 ↗
31. Optimal design of dome structures with recently developed algorithm: Rao series10.1016/j.istruc.2022.06.010 ↗
32. Continuous size optimization of large-scale dome structures with dynamic constraints
33. Optimizations of domes against instability
34. Optimization of the braced dome structures by using Jaya algorithm with frequency constraints
35. Rosso, M.M., Cucuzza, R., Aloisio, A., and Marano, G.C. (2022). Enhanced Multi-Strategy Particle Swarm Optimization for Constrained Problems with an Evolutionary-Strategies-Based Unfeasible Local Search Operator. Appl. Sci., 12.10.3390/app12052285 ↗
36. Reliability based bi-directional evolutionary topology optimization of geometric and material nonlinear analysis with imperfections10.1016/j.compstruc.2023.107120 ↗
37. Optimal design of skeletal structures via the charged system search algorithm10.1007/s00158-009-0462-5 ↗
38. Cucuzza, R., Rosso, M.M., Aloisio, A., Melchiorre, J., Giudice, M.L., and Marano, G.C. (2022). Size and Shape Optimization of a Guyed Mast Structure under Wind, Ice and Seismic Loading. Appl. Sci., 12.10.3390/app12104875 ↗
39. A Multi-volume constraint approach to diverse form designs from topology optimization10.1016/j.engstruct.2022.115525 ↗
40. A tensegrity approach to the optimal reinforcement of masonry domes and vaults through fiber-reinforced composite materials10.1016/j.compstruct.2015.08.087 ↗
41. Cucuzza, F., Bertetto, A.M., Domaneshi, M., Tarantini, R., Cardoni, A., and Cimellaro, G.P. (2023). Italian Workshop on Shell and Spatial Structures. In Lecture Notes in Civil Engineering, Springer.
42. Cucuzza, R., Domaneschi, M., Rosso, M.M., Martinelli, L., and Marano, G.C. (2023). Italian Workshop on Shell and Spatial Structures. 2023. In Lecture Notes in Civil Engineering, Springer.
43. Cucuzza, R., Cardoni, A., Manuello, A., Domaneschi, M., Cimellaro, G., and Marano, G. (August, January 31). Experimental Investigation of the Static and Dynamic behaviors of 3D-Printed Shell Structures. Proceedings of the 15th World Congress on Computational Mechanics (WCCM-APCOM2022), Yokohama, Japan.10.23967/wccm-apcom.2022.049 ↗
44. Pilarska, D. (2018, January 23–25). Octahedron—Based spatial bar structures–the form of large areas covers. Proceedings of the Third Scientific Conference Environmental Challenges in Civil Engineering, Opole, Poland.10.1051/matecconf/201817403007 ↗
45. Pilarska, D. (2018, January 7). Comparative analysis of various design solutions of octahedron—Based spatial bar structures. Proceedings of the XXIV Conference of Lightweight Structures in Civil Engineering, Lodz, Poland.10.1051/matecconf/201817403007 ↗
46. Two subdivision methods based on the regular octahedron for single-and double-layer spherical geodesic domes. Int10.1177/0956059920956944 ↗
47. Bysiec, D. (2023). Sustainable Shaping of Lightweight Structures Created According to Different Methods. Sustainability, 15.10.3390/su15043236 ↗
48. (2005). Eurocode 1; Actions on Structures (Standard No. EC 1991).
49. Pilarska, D., and Maleska, T. (2021). Numerical Analysis of Steel Geodesic Dome under Seismic Excitations. Materials, 14.10.3390/ma14164493 ↗
50. Bysiec, D., Maleska, T., and Janda, A. (2023, January 2–6). Dynamic characteristic of geodesic domes with different location of mass. Proceedings of the Eighth International Symposium on Life-Cycle Civil Engineering, Milan, Italy.10.1201/9781003323020-112 ↗
51. Influence of the mesh structure of geodesic domes on their seismic response in applied directions
52. (2005). Eurocode 3; Design of Steel Structures (Standard No. EC 1993).
53. Size optimization of space trusses using Big Bang−Big Crunch algorithm10.1016/j.compstruc.2009.04.011 ↗
54. Life-cycle cost-based risk assessment of aging bridge networks10.1080/15732479.2020.1845752 ↗
55. Lifetime seismic resilience of aging bridges and road networks10.1080/15732479.2019.1653937 ↗
56. Estimation of Scenario-based Liquefaction Probability with Consideration of Ground-motion Randomness