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Optimization methods modelled after growth patterns of trees and bones

Based on observations on the growth forms of trees and other mechanically heavily loaded natural structures like bones, Claus Mattheck of the Institute for material sciences at the research center derived general rules for their shaping. He could demonstrate that structures can meet the demands of strength if the same stresses are acting all along the entire surface. The hypothesis of constant stresses was already put forward in 1893 by K. Metzger, a forrester, who applied this hypothesis on spruce trunks. Such a construction guide line leads to the development of things like trees, bones, teeth and claws with a minimum of material used and a maximum of loadability, while avoiding local weak points. Based on his studies of natural structures, Claus Mattheck devised several computer methods for shape optimization of technical parts. They are very successfully employed by the industry for more than a decade.

Computer Aided Optimization (CAO)

With the “Computer Aided Optimization” (CAO) the growth pattern of trees is emulated. In particular, the secondary thickening of the growth zone (meristem) is simulated. The underlying principle is that stresses are equal everywhere at the surface of a tree. Accordingly, mechanically loaded parts accumulate material on their outside until the shape is optimized and all surface stresses are equal.

The “Soft Kill Option” (SKO) is modelled after bone-eating cells, the so-called osteoclasts. Material is eaten away from computer model of structural elements from any point that is loaded less than average. Used on its own, SKO produces ultralight constructions as all unnecessary material is removed from both, the outside as well as the inside. Unfortunately, these constructions will have high peak stresses at the surface, Together with CAO, however, a construction will be designed without peak stresses, long durability and optimized weight. The two optimization tools used in conjunction combines the advantages of both methods. Alloy wheels designed in this wa yielded a weight reduction of 26 %. The durability of orthopedic screws, used in spine surgeries, could be increased 20 times, whilst minimizing the danger of fracture.

Moreover, Claus Mattheck developed a “Computer Aided Internal Optimization” (CAIO), which optimizes the arrangement of fibres in composites. The fibres are arranged along the major forces lines, thus preventing the occurrence of cracks and ruptures.