Effect of Geometry Precision and Load Distribution on Branch Mechanical Response

Abstract

Tree risk assessment requires mechanical response studies, but simplification of the shape, material, or boundary conditions is necessary when dealing with such complex structures. To observe overall tree response, sub-structuring to several levels of detail can be used, enabled by recent developments in numerical methods and three-dimensional laser scanning (3D scan). This study aimed to determine an appropriate level of geometry and loading simplification allowed for high-order branches at the crown border, which is useful for the mechanical analysis of structured tree models. Four higher-order branches were pruned and experimentally tested by single-point loading. Beam and solid finite-element models (FEMs) were created based on measured geometric parameters and detailed 3D scans, respectively. The FEMs were used to analyze seven loading scenarios with force applied at (a) the center of gravity, (b) the top of side branches, (c) key discrete points, and (d) uniformly to the whole volume (to each finite element). Force was distributed by ratios weighted according to the mass, area, and diameter of side branches; or according to the mass of each finite element. The results showed no significant difference between the beam model and 3D scan-based model. The scenarios with finite elements’ mass-based force distribution deviated significantly from those of the other scenarios. The most simplified single-point loading caused a deviation in the deflection curve. The deviation of single-point loading in the case of the bending moment was related to force distribution ratios given by the branches architecture. Therefore, such loading simplification is not considered always appropriate. Consistency between the bending moment and branch deflection provided a representative mechanical response, recommended for further modeling of trees by sub-structuring.