Thesis topic proposal
Péter Várkonyi
Computational form finding of structures


Institute: Budapest University of Technology and Economics
Pál Csonka Doctoral School of Architecture

Thesis supervisor: Péter Várkonyi
Location of studies (in Hungarian): Department of Mechanics, Materials & Structures
Abbreviation of location of studies: BME

Description of the research topic:

Shells, tents, cable structures and funicular arches offer economical structural solutions due to being free from significant bending moments. At the same time, they are attractive architectural elements. However, their shapes have to be designed carefully to ensure proper behavior. Form finding algorithms currently used in architectural design cannot generate but certain special types of these structures. For example, dynamic relaxation can only be used to find shapes of membrane shells under pure tension. The aim of this project is to classify moment-free structures, and to develop and analyze new computer algorithms, which support the conceptual design of these structures, and give a powerful tool in the hands of the architectural designer.

Significant bibliography:
- Macdonald, A. J. (2007). Structure and architecture. Routledge.
- Adriaenssens, S., Block, P., Veenendaal, D., & Williams, C. (Eds.). (2014). Shell structures for architecture: form finding and optimization. Routledge.
- Bletzinger, K. U., Wüchner, R., Daoud, F., & Camprubí, N. (2005). Computational methods for form finding and optimization of shells and membranes. Computer methods in applied mechanics and engineering, 194(30-33), 3438-3452.
- Kilian, A., & Ochsendorf, J. (2005). Particle-spring systems for structural form finding. Journal of the international association for shell and spatial structures, 46(2), 77-84. - Tran, H. C., & Lee, J. (2010). Advanced form-finding of tensegrity structures. Computers & structures, 88(3-4), 237-246.

Significant periodicals:
- Computers & structures
- J. Solids and Structures
- Proc. Roy. Soc. London A
- IMA J. Applied Mathematics
- Építés- és Építészettudomány

Structures under pure compression or tension are popular in architecture. These structures include cables, chains, funicular arches as well as shells, vaults, tents, cable nets, and grid shells. Different types of these structures can also be combined. For example, a funicular arch can support a pre-stressed tent surface [1].
A common property of all types of moment-free structures is their ability to cover large spans or to carry high loads with moderate amount of structural material. Their most important disadvantage is the special shapes required by their mechanical behavior, and the induced production costs. Computer-aided design, manufacturing, and construction methods may largely eliminate these disadvantages, and thus the popularity of moment-free structures in building industry is increasing.
Most important design challenge of moment-free structures is to find geometric shapes, which enable their special structural behavior. Traditionally, form finding was based on physical models, whereas today, such methods are replaced by computational algorithms [2]. More and more of commercial CAD systems of architectural design include structural form finding modules [3].
An important limitation of popular form-finding algorithms is that they cannot produce shapes but for a limited range of structural types. For examples, dynamic relaxation can only create shapes for tensile membrane shells. As a consequence, the shapes of cantilevered shells cannot be generated this way. It is another remarkable limitation that there are no off-the-shelf solutions for the automated geometric design of several moment-free structures combined together. As a consequence, most of these structures follow simple geometric schemes (e.g. Bridge in Seville by S. Calatrava [4]; Gateshead Millenium bridge [5]).
The task of a PhD student will be to classify moment-free structures according to their functional scheme, to explore the freedom in the geometric design of structures following various schemes, as well as to develop from finding algorithms for various schemes.
[1] Macdonald, A. J. (2007). Structure and architecture. Routledge. [2] Adriaenssens, S., Block, P., Veenendaal, D., & Williams, C. (Eds.). (2014). Shell structures for architecture: form finding and optimization. Routledge. [3] https://www.grasshopper3d.com/
[4] https://calatrava.com/projects/alamillo-bridge-cartuja-viaduct-seville.html
[5] http://www.lusas.com/case/bridge/gateshead.html

Deadline for application: 2021-08-31

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