Session: 02-06-01: Product and Sustainable Design

Paper Number: 116420

116420 - Variable Radius Fillet Shape Analysis to Minimize Stress Concentration Effects: Learning From Trees for Sustainable Design 

Nature is full of complex engineering. Even something as seemingly simple as a tree is an intricate structure that has been optimized over thousands of years of evolution. Every part of a tree, from the roots to the leaves, must be able to handle a variety of working conditions: mechanical loads, light, water nutrients, external biota. As such there are many different plant features, where engineers can learn from studying trees. One area of particular interest for mechanical engineers is how trees handle areas of high stress concentration where the branches intersect with the trunk.

In engineering when there is a shape discontinuity it is common to add fillets (or notches) to reduce the stress concentration in the problematic area. Trees behave in a similar way and grow natural notches at these high stress areas. This paper presents an analysis of these natural fillets and looks at how they can effectively reduce the maximum stress.

Although extensively literature has been written on the base of trees, where the trunk meets the ground above surface, little work has been done on the natural curvature where tree branches intersect with the trunk. This is another area of the tree where high stress concentration occurs. To reduce the stress concentration the tree grows in a way, integrating development with growth, as to create what is essentially a natural fillet.

On that line of thought, the desired outcome of this work was to explore the possibilities of using trees for engineering design inspiration as well as better understand how trees handle areas of high stress concentration. This work analyzed the effectiveness of the natural curvature where the tree branch intersects with the trunk. The tree used in this scheme is of the species Pinus taeda which is also known as a loblolly pine.

The natural tree fillet was compared with both circular fillets as well as shapes developed using the Method of Tensile Triangles, a graphical method of creating an optimized fillet design in nature. Mentioned comparison was carried out by means of Finite Element Method (FEM) analysis. Static FEM study was done on 2D models with various fillet geometry and the stresses determined from these simulations were compared. In addition to this a 3D model of the branch was created to analyze the stresses in the tree branch.

Results indicated that all the different fillet geometries looked at in this work showed significant improvement over the model with only sharp edges, as expected. The model created using the Method of Tensile Triangles also performed very well and had a maximum stress that was only 2% larger than that of the natural tree model. The radius of the circular fillet model had to be increased, which created a cross sectional area of material more than two times as large as the other models, just to achieve the same maximum stress as the other two fillet designs. In addition, even though worse case wind loading was applied the stress on the sides of the branch was still negligible in comparison to that on the top and bottom.

More data on different trees needs to be collected to draw definite conclusions on the effectiveness of the natural curvature of tree branches at reducing stress. However, this work has demonstrated that the Method of Tensile Triangles is able to closely replicate the geometry of trees as well as provide an example of how sustainable natural phenomena can be applied to improve human-made designs.

Presenting Author: Mariappan Jawaharlal College of Engineering and Computer Science, California State University, Sacramento

Presenting Author Biography: Dr. Mariappan “Jawa” Jawaharlal, Associate Dean for Faculty Affairs and Professor of Mechanical Engineering at the College of Engineering and Computer Science of California State University - Sacramento, has more than 20 years of academic, industrial and entrepreneurial experience in engineering and is renowned for his innovative, engaging teaching pedagogy. Dr. "Jawa" was also a Professor of Mechanical Engineering at California State Polytechnic University in Pomona, He received the California State University System’s highest honor, the Wang Family Excellence Outstanding Faculty Award, as well as the Provost’s Award, the Northrop Grumman Award for Excellence in Teaching, and a Fellowship in the Biomimicry Institute. At Rowan University in Glassboro, NJ, he was one of the first faculty members recruited to develop a new engineering program with a $100 million donation. Dr. Jawa is founder and director of Robotics Education through Active Learning (REAL), a K-12 outreach robotics program that educates thousands each year and culminates in the Annual Robot Rally, the nation’s largest robotics event. He also co-founded the Femineers (Female Engineers), which the White House recognized for its empowerment of young women to become engineers. Since founding an online education company in 1998, Dr. Jawa has developed hundreds of interactive, engrossing learning modules, online tutorials, and CSU course redesigns focusing on bottleneck courses. He has brought many new engineering and robotic products to market from mere concept stages. He also writes columns for The Huffington Post on various K-12 and higher education topics. A marathon runner and scuba diver, he has completed 25 marathons and has run across the Grand Canyon from rim to rim to rim.

Authors:

Mark Warner Department of Mechanical Engineering, California State Polytechnic University-Pomona
Gustavo VARGAS-SILVA Public University of Navarra
Mariappan Jawaharlal College of Engineering and Computer Science, California State University, Sacramento