Читать книгу Rethinking Prototyping - Группа авторов - Страница 14

For the M1, the importance of generating the complete mechanical behaviour was exhibited in defining the final geometry of the entire system. In physical form-finding and spring-based modelling the results are approximations due respectively to their scalar nature and the relative calculations of material behaviour. In this case, the behaviour of the forces in the tensile surfaces resolves the geometry for critical cantilever conditions. Several iterations are explored to define the geometry of the free-spanning edge beam condition, whose position is only realized in the exact equilibrium of bending stiffness in the boundary rod and tensile stress in the upper and lower membrane surfaces as shown in Fig. 9. While this is only a single feature within the textile hybrid system, it can be explored efficiently as the topology generation and form-finding process is automated as a programmed routine within the FE software Sofistik.

Fig. 9 Form-finding of the brow condition for M1, with various membrane pre-stress ratios (Lienhard, 2012)

Element length is a critical consideration not only for the effort of form generation but also for the construction of an architecture that relies upon continuous and integrated structural behaviour. In typical building structures the joining of elements is solved at crossing nodes or points where the momentum curve passes through zero. Though in bending active structures the beam elements pass through the nodes with continuous curvature as defined by bending stress. Adjoining elements at these moments is unfavourable. Rather, the locations of low bending curvature are targeted as the moments for adjoining elements. For the M1 this defined the location of crossing nodes and total length of elements, as shown in Fig. 10, in order to assure positioning the joints at the locations of smallest bending stress and, at the same time, maximizing individual element lengths.

Fig. 10 Topology map of GFRP rods for M1 (Ahlquist and Lienhard, 2012)