Abstract
Abstract
Abrupt changes in geometry create stress concentrations, which are highly localized stresses causing failure at these locations. Engineers create fillets, and round-off sharp corners to reduce these stresses. Stress concentrations occur in the natural world, and the objective of this paper is to understand how trees handle areas of high stresses, learn from nature, and are used for engineering design inspiration. The main areas of the tree where high stress concentration occurs are the trunk base, where the trunk meets the ground above surface, and the branch base, where tree branches intersect with the trunk. Although extensive work has been done on the trunk base of trees, little work has been done on the branch base.
In this paper, the effectiveness of the natural curvature where branches intersect with the trunk is analyzed. The tree used in this scheme comes from the species Pinus Taeda (a.k.a. Loblolly Pine). The natural tree fillet was compared with both circular fillets and shapes developed using the Method of Tensile Triangles, a graphical way to create an optimized fillet design in nature. The comparison was carried out by using Finite Element Method (FEM). Static bending studies were done on both 2D and 3D models comparing various fillet geometries and stresses.