Investigating the elastomechanics of Douglas fir. 1. Modelling with the Finite Element Method

Simulations of the elasto-mechanical reactions of trees subjected to wind and gravitational forces contribute deeper insight into stability aspects and mechanically triggered growth processes. In this study, the finite element method (FEM) was applied to a 64-year old Douglas fir tree of which in detail the stem and crown geometry (Tab. 1, 2) as well as the heterogeneity of the mechanical wood properties (Tab. 3) were taken into account. The stress distribution of the stem surface were calculated assuming a northwestern wind with a wind speed of 20 m/s (Fig. 3). The amount of stress caused only by wind forces dominates: whereas the stress values of the stem section below the crown base turned out to be relatively constant with about 10 MPa (but reduced at the swelling of the stem base), and being slightly smaller within the mid-crown section with about 8 MPa. the stress increases in the top region up to 25 MPa. The amount of stress evoked by gravitational forces due to the stem mass is negligible (Fig. 4). It was not possible to reliably estimate the stress contribution of the branches because the chosen concept of punctually transmitting the branch-specific forces and moments into the stem, implements unrealistic high stress peaks which fade off only very slowly (Fig. 5). Modelling with finite elements has been proven a feasible way of handling such complex objects as trees, but this requires high performance and thus, expensive hardware and software. One disadvantage of finite element software arises from its primary design for engineering applications so that modelling of natural objects being extremely irregular in shape and material properties is very time consuming. Therefore, extensive studies by varying the geometry of the object cannot be realised with this method.