Floor Slabs Made from Topologically Interlocking Prefabs of Small Size

Abstract

In this article, the issue of constructing slabs from unified small elements, which are connected together into a stable structure by topological interlocking, is considered. The state-of-the-art methods in this topic are presented, as well as the results of the author's original research. The author has expanded the well-known concept of shaping square slabs from square prefabs by the aggregation of triangular and hexagonal slabs from prefabs in the shape of equilateral triangles, regular hexagons, and rhombuses. Each of the slabs can be modelled with upper and bottom surfaces, either both relief, both smooth, or one relief and the other smooth. The slabs can be modelled in different ways, and each one results in intriguing floor and ceiling patterns. All of the slabs can co-operate with grillages made of steel beams, which can be constructed before filling with the prefabricated slab, which is a novel idea. Reversing the assembly order, as compared to that used in the literature, is made possible thanks to division of these elements into parts, to form a keystone which is inserted into the slab as a final step.Buildings 2020, 10, 76 2 of 23 of 8 × 8 m. As the manufacture of non-uniform elements with precision while ensuring a tight fit is difficult, researchers' efforts have been redirected to finding a solution which allows the construction of a flat vault out of identical elements.The first concepts of flat vaults built from unified small elements were presented in 1699 by Abeille and Truchet [2] and then in 1737 by Frezier [3]. The elements were arranged such that each element supported two other elements and was supported by another two elements. This idea was based on the concept of floor structures made of reciprocal timber beams, which has been known since the 17th century and popularized by Wallis (as Serlio's floors), immediately before the announcement of the mentioned inventions [4]. The differences between the concepts of Abeille, Truchet, and Frezier are manifested in the shapes of the blocks used. Abeille started from a vault characterized by the fact that one of its surfaces is smooth, while the other is relief (Figure 1a). Truchet designed a vault with both smooth surfaces, obtained as a result of the use of blocks with curvilinear edges and non-flat faces (Figure 1b). Frezier found two different straight-edged block shapes, the use of which resulted also in the construction of vaults with two smooth surfaces (Figure 1c,d).

Architectural Systemic Approach: The Serpentine Gallery 2005, a Reciprocal Frame Case Study

“…In the 18th century, Frézier [50] became interested in the principle (known as Serlio's floor) and linked it to the constructive solution of Abeille's flat vaults. The establishment of this relationship gave rise to numerous articles that jointly reviewed both solutions [51][52][53].…”

Architecturing materials at mesoscale: some current trends

“…This technique of reconstructing polyhedra-based TI structure from middleplane tessellations was adopted by other researchers, e.g. [18][19][20][21][22], but alternative algorithms were also considered [20]. Interlockable block geometries based on non-planar geometries of the contact surfaces are also possible, cf.…”

Mechanical Performance of Light Weight 3D Printed Interlocked Assemblies

“…Piekarski [13] utilized the concept of geometric interlocking in prefabricated construction slabs. The study used different equilateral geometric shapes such as triangles, hexagons, and rhombi.…”