Читать книгу Rethinking Prototyping - Группа авторов - Страница 71

Natural structures give impressive examples of structurally optimised geometries. Nature has developed a great variety of very lightweight structures, resulting from optimisation procedures running over billions of years. The methods of structural optimisation can be used to clarify the basic characteristic of their load-bearing behaviour and to develop structural geometries with the same efficiency, basically reproducing the process of optimisation in nature. The merging of studies of natural structures with the methods of structural optimisation can produce a new morphology of natural lightweight structures. Lightweight structures must and will play an important role in architecture and engineering when acting responsively in the field of material use.

A good example for an efficient natural structure is the skeleton of the columniform cactus, which reaches up to approximately 6m of height. Its structure can be described as a perforated tube. Developed by the SOM-affiliated engineer Fazlur Khan in the 1960s tube structures are very efficient structural systems for the design of tall slender buildings: The concentration of material along the outline of the structure allows for optimised structural efficiency in comparison to the classical core structure.

For this study, the structural model was set up as a vertical cast-in beam with a hollow tube section. The optimisation objective was to minimise the compliance, i.e. maximize stiffness of the structure with the design constraint of only 15% of the structural volume to be filled with material. The result is an organic geometry with thorough structural background. Fig. 12 shows the antetype, the structural system and the optimisation result.

The tube is now optimised for one dominant wind direction. In combination with an inner tube the tube-in-tube system, also initially developed by Fazlur Khan, the structure serves all wind directions. Wind loadings acting from varying wind directions are carried by two interacting structural systems: The wind loading at the lower part of the structure is assigned mainly to the outer tube, with the geometry not being

optimised for this load case, but working as a tube. The wind loading at the top part of the skyscraper is assigned to the inner tube, which acts as a (much more slender) cantilever, cast-in into the outer tube structure, with an appropriate slenderness of about 1:6 when considering only the top part actually working on its own.

Fig. 12 Skeleton of the columniform cactus; structural model and optimisation result

Fig. 13 Development of the structure into a tube-in-tube skyscraper structure

Another demonstrative example of efficient natural structures can be found at a much smaller scale: the diatoms. As a very good example of long-term optimisation processes in nature, there exists an evolutionary competition between crab and shell: the crab developing stronger pincers, while the diatom shell increasing in strength.

Ernst Haeckel is until today outstanding with his demonstration of the amazing variety of shapes in microscopic structures (Haeckel 1904) - with descriptive variations of structural shapes depending on the overall geometry as well as on the loading conditions of a structure. The division into Centrales with radial geometries and Pennales with bilaterally symmetric shapes leads to an overall classification of diatom geometries (Fig. 14).

Fig. 14 Diatoms, as documented by Ernst Haeckel

When carrying out studies of structural optimisation, geometrical influences have to be taken into account - as it can be seen from a comparative optimisation study of a circular geometry compared to an elongated geometry. The design proposals produced by the optimisation algorithm refer directly to the geometrical conditions of the design space. Fig. 15 shows optimisation studies, with the analysis model composed of one quarter of the circular shell and the interpretation of the design proposal into a structural geometry for a grid shell.

Fig. 15 Development of a diatom structure based on diatom‘s principles

Further development of optimisation studies of the circular shell, based on the design proposal shown in Fig. 15, produces in fact a structure resembling diatom structures. The optimisation study simulates the evolutionary process of nature resulting in a structure optimised for its loading (distributed loading is dominating) and support conditions (constant supports along the bottom edge) and of high aesthetic quality.

Fig. 16 Grid shell derived from the optimisation result (interior views)

Further structural studies including the spongiosa and sandwich-like systems in bone structures, the sea urchin, branching structures, seashells and dragonfly wings. They all conclude that nature is an excellent role model for the holistic design of structures, and that structural optimisation is a useful tool to grasp the inherent logic of natural structures.