NDLI: Elastic fractal trees: a correspondence among geometry, stress, resilience and material quantity

Content Provider	Springer Nature Link
Author	Barros, Marcelo Miranda Bevilacqua, Luiz
Copyright Year	2014
Abstract	A two-dimensional elastic fractal tree model is proposed considering the trunk clamped to the ground and extremities under the action of moments. For the proposed problem the normal stress is lower in the trunk and higher in the extremities. The limiting case in which stress is constant in all orders corresponds to the physiological principle of minimum work proposed by Murray (Proc Natl Acad Sci USA 12:207–214, 1926). When longitudinal and transverse proportions coincide the tree is said to be geometrically similar. Geometric similarity, constancy of stress, uniform distribution of elastic energy and of material quantity among orders occur in group. These four states are correlated to each other: the occurrence of two implies that the other two also occur. The proposed approach considers both individual and systemic properties and highlights the inherent connection among them. Flexibility is shown to increase from the trunk to the extremities. Considering a stochastic distribution of external moments the branching design is shown to minimize relative dispersion of stress while concentrating forces through the trunk.
Starting Page	1479
Ending Page	1483
Page Count	5
File Format	PDF
ISSN	16785878
Journal	Journal of the Brazilian Society of Mechanical Sciences and Engineering
Volume Number	37
Issue Number	5
e-ISSN	18063691
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-12-09
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Biomechanics Fractal systems Physiology Mechanical Engineering Morphometry Allometry
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Industrial and Manufacturing Engineering Automotive Engineering Mechanical Engineering Aerospace Engineering

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