Multi-Body Rope Approach for Grid Shells: Form-finding and Imperfection Sensitivity

Over the last years, different methods, physical and mathematical, were used to find the optimal shape, minimizing the internal stresses, of shallow grid shells. As far as their original organic shape is concerned, the design of grid shell structures inspired architects and structural engineers in more than one way. Throughout history, the resolution of the problem related to the structural form-finding buried its roots on the activity of researchers and innovators. In the present paper an original approach for the form-finding is obtained by dynamic numerical simulation of hanging net, subjected to gravity load, over the time domain. In particular, the proposed method for the definition of the form is based on a multi-body rope approach (MRA) with masses connected by inextensible ropes characterized by a certain slack coefficient (sc) and by the degree of the constraint conditions. These parameters played a fundamental role in the definition of the shallowness ratio of the grid, and therefore in the effect of the instability of the reversed shape (grid shell) under loading. Moreover, in the case of shells with a very large number of nodes, a combined procedure based on non-uniform rational basis-splines (NURBS) formulation is proposed for the form-finding. Finally, step-by-step nonlinear analyses for the grid shells obtained by MRA were performed by a displacement control scheme, applying vertical incremental displacement to the nodes. Three circular grid shells were generated and analysed considering the effects of geometrical imperfections on the coupled instabilities varying the shallowness ratio.