Читать книгу Rethinking Prototyping - Группа авторов - Страница 59

The Downland Gridshell, which is charcaterised for its unique triple-bulb geometry, is our first form-finding example. The task is to find a single-layer grid pattern that complies with the material aspects and satisfies the geometric constraints.

Fig. 4 (a) Pre-stressed beam on a barrel surface; (b) Beam relaxed from a strained geometry

Fig. 5 Strain energy versus time step

The grid, which is composed of 102 initially straight planks, has a uniform square profile and a width of 5cm (Fig.6). Each beam element has an unstrained length of 1m. The connections between the crossing rods are revolute joints, which enable free rotation along the local z-direction. The elasticity and shear modulus of the material are defined as E=107KN/m2 and G=E/2, respectively.

Two geometrical constraints are given. First, the grid nodes on the two longer edges must stay on the curved boundaries. Second, the remaining grid nodes must remain on the triple-bulb surface.

Fig. 6 (a) Initial grid and geometric constraints; (b) Transient state; (c) Equilibrium state under constraint; (d) Bearing structure after constraints are removed and bracing and bearing conditions are added; the enlarged part shows the nodal orientations.