 Fractal equilibrium configuration of a mechanically loaded binary treeJavier Rodríguez-Cuadrado and Jesús San Martín Chaos, Solitons & Fractals, 2021, vol. 152, issue C Abstract: In this paper we study the equilibrium mechanics problem that originates in a binary tree with infinite levels subjected to loads on its topmost branches. The application of the laws of mechanics to find the equilibrium configuration shows that the functional forms of the vertical and horizontal displacements of its end nodes converge to a Takagi curve and a linear combination of inverses of β-Cantor functions respectively as the number of levels tend to infinity. As a consequence, the shape of the canopy results from the combination of these two emerging fractals that were not present in the unloaded tree. Besides, our study also shows that the analytical expressions of the emerging fractals depend on the mechanical properties of the binary tree, indicating that the binary tree is a link between these two emerging fractals. In addition, we prove that the fractal dimensions of Takagi and β-Cantor are related in this model. Keywords: Takagi curve; β-Cantor function; Principle of virtual work; Fractal binary tree; Equilibrium configuration (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007694 DOI: 10.1016/j.chaos.2021.111415 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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