This paper studies the behavior of Tessellated Structural-Architectural (TeSA) beams using numerical modeling. A tessellation is an arrangement of shapes closely fitted together in a repeated pattern without gaps or overlaps. Historically, tessellations were used mainly as aesthetic elements in buildings. Examples of architectural tessellations include the Alhambra palace in Granada, Spain , and the Mosque of Ibn Tulun in Cairo, Egypt . Tessellations have also been recently used in building envelopes for natural light control, e.g., the Arab World Institute in Paris, France  and Al Bahar towers in Abu Dhabi, United Arab Emirates . In this study, tessellations are used both as structural and architectural elements.
Tessellations can be non-interlocking or interlocking. Topologically interlocking tessellations transfer load through the tiles by shear, bending, and axial forces generated by the contact between tiles. On the other hand, load transfer between tiles in non-interlocking tessellations requires adhesive materials or mechanical connections. Examples of non-interlocking and interlocking tessellations are shown in Fig. 1. In this paper, 2D interlocking tessellations are considered, for which the contact between tiles does not allow for separation in either of the two orthogonal directions .
Small scale studies on topologically interlocking tiles showed that tessellated structures are more damage tolerant compared to the same size solid structures [8,11,22]. Cracks in damaged tiles are contained in the boundaries and do not propagate to nearby tiles as seen in solid structures [12,13,18]. In addition, damaged tiles were replaced by intact ones and resulted only in limited performance loss in the small scale structure .
Previous research mostly focused on small scale topologically interlocked systems [4,15,20,24]. There is a need to investigate tessellations at scales suitable for building structures . discuss the concept of TeSA systems as applied to a reinforced concrete shear wall, and as part of a building structural system. They concluded that although TeSA walls have smaller stiffness and strength than conventional walls, they can be used as lateral load resisting elements with adjustments to design . discuss the practical benefits and challenges of designing and constructing a reinforced concrete TeSA shear wall specimen in detail. The experimental results of testing the specimen shown in Fig. 2 in reverse cyclic loading will be discussed in a forthcoming paper . showed that wall strength can be reasonably predicted using equilibrium based approaches.
Research presented in this paper builds upon the studies by Refs. [19,23] and focuses on the numerical modeling of 2D interlocking tessellated beams for application at the building scale. The modeling approach was validated using the results of an experimental study on a Medium Density Fiberboard (MDF) beam. MDF was a convenient and efficient material choice for the test specimen because it was cost efficient and could be fabricated using a CNC machine. The experiment facilitated the primary goal of this study, which is understanding the behavior of TeSA beams through a numerical finite element (FE) study and identifying the parameters that have a strong influence on the model accuracy.
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