Yes, you read that right. Topology optimization without the use of a computer.
If you have ever tried topology optimization in CAD programs such as Autodesk Fusion 360, SolidWorks or Creo, you know that topology studies take a long time to compute. Even simple setups can take hours to solve. And if you want finer results, the solve time increases exponentially.
Sometimes, you need a simpler and faster method. In my research for open source topology optimization tools, I stumbled upon a method that only requires pen and paper.
Claus Mattheck, Head of department of Biomechanics at the Institute for Materials Research II of the Karlsruhe Research Centre has developed a very clever method. Based on years of experience with computer algorithms, he saw that common shapes emerged, and they all followed the same principles.
The first principle is:
“Optimal designs have a uniform stress distribution.”
All optimal, light weight design tend to have a uniform stress distribution. This is seen all throughout nature. If you think about it, an area of high stress is a weak point. And an area of low stress has an unnecessary amount of material and weight.
The Force Cone Method
The force cone method is based on the observation that a force acting on a plane will produce internal reaction forces to counteract the external force. Most of the internal forces will appear within a 90 degree angle, or cone. Compressive forces will appear in front of the force, and tension forces will appear behind the force.
Furthermore, engineers have found that the optimal angle to create a light weight two-bar truss, is 90 degrees. Be aware that this does not consider buckling.
The fact that optimal solutions tend to have beams at 90 degrees was also recognized by Mitchell in 1904.
If you want to learn more about this method, check out C. Mattheck’s book: Thinking Tools After Nature.
It covers three thinking tools that can help you to understand how forces work and how to inform your light weight designs. An indepth explanation of the force cone method, ways to reduce stress concentrations, fatigue, cracks. As well as awesome examples from nature.
These are practical tools for the design engineer at the early phase of the development process. No equations or heavy math. You'll have to find that somewhere else. But I promise you, this book will make you look at mechanical and structural design in a new way.