Читать книгу Rethinking Prototyping - Группа авторов - Страница 61

Hybgrid, which was proposed by Truco and Felipe [8], is an innovative double-layer structural type that is composed of uniform flexible chord members and can generate various geometries by controlling the strut lengths between the chords (Fig. 8). Currently, the only available form-finding for Hybgrid is based on physical models. Thus, the testing of our method constitutes a significant benchmark.

The grid is composed of three chords: the upper chord, the middle chord and the lower chord. Every chord is composed of 40 beam elements; each contains an unstressed length of 12.88cm. The connections between the chords consist of revolute joints. Each chord has a uniform rectangular profile that exhibits a width of 80mm and a thickness of 4mm. The elasticity and shear modulus are defined as E=107KN/m2 and G=E/2, respectively.

Fig.7 Comparison of the grid patterns of the irregular grid and the regular grid, which are presented by the orange colour and the purple colour respectively. Both grid patterns are smooth, but the irregular grid has less in-plane bending curvatures.

Fig. 8 (a) Initial geometry; (b) Transient state; (c) Transient state; (d) Equilibrium state under constraint; (e) Bearing structure after boundaries are removed and struts and supporting conditions are added.

Fig.9. (a) Initial grid; (b) Transient state; (c) Transient state; (d) Equilibrium state under constraint; (e) Bearing structure after constraints are removed and struts and supporting conditions are added; (f) The enlarged part shows the nodal orientations.

The upper chord nodes that will be subsequently connected with struts after form-finding are constrained by the upper curve, only movable on the curve. Similarly, the lower chord nodes that will be subsequently connected with struts are constrained by the lower curve. The two constraint curves, which contain an interval of 0.375m between the curves, are equivalent. The constraint curve is defined by two arcs with a curvature of 4.4m.