Biological rule of growth
The biological growth rule describes the growth behavior of organically grown structures, such as trees , claws and bones , which are exposed to mechanical stresses (e.g. wind load, snow load). From a mechanical point of view, these are biologically grown components, which are also referred to as biological power carriers. The rule of growth is:
- Store material in highly stressed areas.
- Remove material in low-impact areas.
The effect of this growth rule was investigated at the research center in Karlsruhe. It was found that biological structures grow into a form in which the surface tension is homogeneous under the loads that occur . In this way, biological force carriers avoid stress peaks, which represent the potential weak points of a mechanical component, and thus distribute the stress evenly on the surface. For example, at a branch connection there is no circular transition that would lead to notch stresses , but a so-called baud curve that ensures a notch stress-free transition.
The striving for the highest possible failure safety is only one criterion for biological power carriers. Safety must also be achieved with as little material as possible in order to be able to assert oneself in the tough competition in nature during evolution . One can therefore expect that the biological powerhouses represent an optimized lightweight design.
The 2nd rule of growth only applies to bones. This means that it is not possible for the trees to remove the superfluous material in the areas that are suddenly less polluted due to changed boundary conditions. The bones are superior in this regard, as they break down material with the help of phagocytes and can therefore always achieve a good lightweight design.
In everyday engineering, one often pursues the same goals as the biological powerhouse, namely to design a fail-safe component with as little material as possible. For this reason, the successful biological growth rule was simulated on the computer and used as the basis for optimization programs with regard to strength. The component to be optimized is allowed to grow virtually in accordance with the biological growth rule, as would a bone, for example, if it had to take over the function of the component. This then leads to a design with homogeneous surface tension. There are two ways in which the growth rule can be applied. If it is only applied to the surface areas of a component, a method for shape optimization is obtained, the CAO method. If, on the other hand, the area of application is expanded to include the inner areas, a method for topology optimization , the SKO method and the TopShape variant, is obtained . With the latter, in addition to the growth rule, casting restrictions are implemented in the algorithm in order to improve and facilitate the optimization of castings . A VDI guideline has existed since 2012, which aims to bring the application areas and functionality of these optimization methods closer to a wide range of engineers.
literature
- C. Mattheck: Design and Growth Rule for Biological Structures and their Application in Engineering. Fatigue Fract Eng Mater Struct 13, 5, 1990, 535-550.
- C. Mattheck: Design in Nature, Rombach GmbH + Co Verlagshaus KG, Freiburg i. B., 1997, ISBN 3793091503
- R. Baud: Contributions to the knowledge of the stress distribution in prismatic and wedge-shaped construction elements with cross-sectional transitions. Report 29, Switzerland, Association for Material Testing in Technology (Report 83 of the Eidgen. Mat. Prüf.-Anstalt, Zurich 1934)
- Thum, W. Bautz: The discharge transition. Most favorable formation of the transition on stepped waves u. Like. Research 6th volume / booklet 6, 1935, 269-273
- L. Harzheim: Structure optimization, fundamentals and applications. Scientific publishing house Harri Deutsch GmbH, Frankfurt am Main, 2007, ISBN 978-3-8171-1809-0
Individual evidence
- ↑ VDI 6224 sheet 2: 2012-08: Bionic optimization - application of biological growth laws for the structural-mechanical optimization of technical components link to VDI