Figure 1: Self-supporting 3D equilibrium puzzle of the “dfab” logo

Self-supporting assemblies can teach us how to simplify the erection of complex architectural construction and how to design for prefabricated modules coming together easily and efficiently. This research, as part of the project “Equilibrium design of discrete-element assemblies” at the NCCR Digital Fabrication, develops spatial equilibrium puzzles that are stable by themselves without requiring glue or other connectors.

In recent decades, the manufacturing and handling of prefabricated modules and building parts have changed significantly. Advances in fabrication and on-site construction, such as CNC milling, robotic fabrication and assembly create new possibilities for the prefabrication of highly individual modules and the realization of complex architectural geometries. With the goal of improving structural performance and efficiency, this research investigates novel design and assembly strategies for such geometries with focus on unreinforced masonry and other discrete-element structures. It is part of the interdisciplinary research within the Swiss National Centre of Competence in Research (NCCR) Digital Fabrication. The research started in September 2014 by Ursula Frick at the Block Research Group, First results were recently presented at the Design Modelling Symposium Copenhagen 2015.

Discrete-element assemblies

In general, discrete-element assemblies are structures formed by individual units and are frequently found in architectural construction. These range from structures consisting of relatively small units, well known from masonry, to large-scale assemblies composed of prefabricated, multi-material building parts. like flights of stairs, facade elements, or entire building units.

How to connect the units is just one of many challenges when designing such assemblies. In particular, tensile mechanical joints often result in complicated detailing, which can be expensive and visually intrusive. Glued connections are simple, but make it difficult to adjust or disassemble a structure. Another challenge is the actual construction of the assemblies. Most designs going beyond mere vertical stacking, especially those with complex, three-dimensional arrangements, require scaffolding during the assembly process. This often leads to significant additional costs.

The aim of this research project is to extend existing and develop novel digital design and engineering approaches that address these particular, practical problems. It tackles individual aspects of stability, assembly, and structural optimization of discrete-element assemblies in architectural construction.

3D equilibrium puzzles

One of the accomplishments at this stage of the research is a prototypical, interactive decomposition tool as a means to digitally cut arbitrary volumetric shapes into 3D equilibrium puzzles. These assemblies, formed by individual, disjointed units, rely on a combination of compression, friction, and balancing actions to stand in equilibrium. This means they are stable without additional mechanical or physical connectors (Figure 2 and 3).

Figure 2: Decomposition example showing the initial geometry (a), the result of the decomposition (b), and the corresponding interface-force diagrams illustrating axial forces (c) and friction forces (d).

Figure 3: Photograph of the physical model that remains in equilibrium without mechanical connections or glue.

From a design perspective, this enables the design of assemblies that go beyond the scope of well-known configurations for masonry, such as walls, arches, domes, and vaults. The tool is based on real time user interaction and provides an interactive design environment, in which the design space of self-supporting assemblies can be explored and expanded.

Despite the promising preliminary results (see further reading) the interactive decomposition procedure can be time-consuming and the handling of large models can be difficult. The research will continue on the development of general, automated decomposition processes. Future investigations will focus on automated ‘cut’ generation and optimisation alternatives based on prefabrication, transport, and assembly constraints.

Application in architectural construction

In practice, structures acting in pure compression are rare, since modern engineering tools don’t allow for the design of such structural systems or are unable to verify their stability under all loading cases. Nevertheless, the optimization of joints is also relevant for structures that are not based on compression-only principles. When applied to the design and production of prefabricated elements in the building industry, joint optimization can be achieved by limiting connections to predominantly no-tension force transfers for the dominant loading case. This keeps the connections simple.

Designing for equilibrium allows for stability at interim stages of construction and enables the design of structures that are self supporting during assembly. This way, formwork can be minimized or replaced with an optimized set of temporary supports that is as sparse as possible, which can also function as stay-in-place formwork. Additionally, it allows for the development of more efficient complex additive fabrication processes, such as robotically-assisted assembly. For instance, robots can temporarily support or place material exactly where it is needed to keep or establish equilibrium. This avoids waiting time for mortar or glue to dry, reduces formwork, and in general contributes to fast and efficient erection of potentially complex structures.

Further reading

Frick, U., Van Mele, T., and Block, P. (2015) Decomposing three-dimensional shapes into self-supporting discrete element assemblies, Proceedings of the Design Modelling Symposium 2015, Copenhagen, 2015.