Why Ellipsoids in Mechanical Analysis of Wood Structures

Authors

F. Niklas Schietzold, Technische Universitat DresdenFollow
Julio Urenda, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Wolfgang Graf, Technische Universitat DresdenFollow
Michael Kaliske, Technische Universitat DresdenFollow

Publication Date

2-2020

Comments

Technical Report: UTEP-CS-20-07

Abstract

Wood is a very mechanically anisotropic material. At each point on the wooden beam, both average values and fluctuations of the local mechanical properties corresponding to a certain direction depend, e.g., on whether this direction is longitudinal, radial or tangential with respect to the grain orientation of the original tree. This anisotropy can be described in geometric terms, if we select a point x and form iso-correlation surfaces -- i.e., surfaces formed by points y with the same level of correlation ρ(x,y) between local changes in the vicinities of the points x and y. Empirical analysis shows that for each point x, the corresponding surfaces are well approximated by concentric homothetic ellipsoids. In this paper, we provide a theoretical explanation for this empirical fact.