The recently completed project “ELiSE AuST – Automation and standardization of the bionic ELiSE process” which was part of the research project „BIO-OPT – Automation, validation, benchmarking and standardization of bionic optimization processes”, funded by the German Federal Ministry for Economic Affairs and Energy (BMWi) led to exciting results with regard to the expert knowledge of bionic stiffening structures.
The content of the project was amongst others the development of generic algorithms for the automated, load-dependent and adaptive dimensioning of surface stiffening structures in the field of lightweight designs. This method shall support engineers in such a way that the future design process of stiffening structures is less time-consuming. Especially, in the ambit of the emerging additive manufacturing technologies the demand of automated design processes is rising constantly.
The following example should give a brief insight how generic algorithms are applied and how the resulting bionic structures for surface stiffening look alike.
Starting point is a surface fixed at all four corners and loaded with two static forces. (Fig. 1). In order to withstand the mechanical loads and avoid failure, a stiffening structure for additional support is required. The resulting structure should be effectively dimensioned to save resources and weight. Before starting the optimization procedure, some boundary conditions need to be defined. Hence, a material (an ABS plastic) is selected and the maximum permitted value for stress and displacement as well as some restrictions for the production process are defined. Injection molding is considered as a standard manufacturing process.
For the comparison study, the optimization was carried out in two different ways. On the one hand, a uniform rectangular grid-structure is considered as representing a conventional stiffening application. On the other hand, the surface is supported with adaptive honeycomb-structures based on the generic algorithms developed within the ELiSE Aust project. In order to be able to compare the optimized structures, some design parameters are kept constant. Therefore, following parameters are equal for both optimization methods: Displacement, maximum honeycomb height, thickness of surface (panel) and wall thickness of the honeycombs. Additionally, the optimized part (in case of the irregular adaptive stiffening) should not leave larger areas of the surface unsupported. The generic algorithm for the design of complex stiffening structures is based on the shell structures of diatoms and radiolaria. The basis of the adaptive honeycomb design algorithm is an irregular distribution of points on surfaces or three-dimensional bodies, which is based on a density distribution according to [Wel09].
One method delivers a uniformly stiffened surface with a constant honeycomb height and a final weight of 621 g. In contrast, the results of the bionic surface stiffening show an irregular honeycomb arrangement, varying in height and honeycomb size. The honeycomb arrangement is adapted in accordance to the mechanical loading and has a decreased honeycomb sizes and increased honeycomb heights in the areas of load introduction and clamped edges. Without violating the prior defined manufacturing constraints, the bionic surface stiffening leads to a final weight of 497 g and saves up to 20% of weight compared to the uniformly stiffened reference part.
In unserem Anwendungsbeispiel sehen wir, dass mit Hilfe von adaptiven Wabenmustern angepasste Leichtbaulösungen zur strukturellen Versteifung von flächigen Bauteilen erzielt werden können.
[Wel09] Weller, H., Weller, H. G. und Fournier, A.: Voronoi, Delaunay, and Block-Structured Mesh Reﬁnement for Solution of the Shallow-Water Equations on the Sphere. Monthly Weather Review 137, S. 4208–4224, 2009.