Behavior of the Tree Branches, Trunk, and Root Anchorage by Nonlinear Finite Element Analysis

Abstract

The finite element method that takes into account geometric nonlinearity is adopted to investigate the static behavior of the tree branches, trunk, and root anchorage. The formulation of a nonlinear beam element is first outlined, followed by a summary of the procedures for buckling analysis and incremental-iterative nonlinear analysis. Using the nonlinear analysis procedure presented, parametric studies are conducted for the critical lengths of tree branches and the buckling loads of tree trunks. The following parameters are considered for the branches: diameter, growth angle and elastic modulus, and the following for the trunk: taper ratio, bottom diameter, and static weight. Also presented is a procedure for evaluating the root anchorage stiffness of a tree based on the data previously recorded from a bending test. In order to deal with the ambiguities in the mechanical properties of tree components, parametric values of a wide range are considered in the analysis, which are believed to cover those of the real tree structures and components. Some interesting rules underlying the tree biomechanics are drawn from the numerical studies.