Many large-scale tensegrity structures are formed by assembling repeating units; a tensegrity tower formed by stacking tensegrity prisms is one example. Tessellated tensegrity structures tend to feature a repeating topology, but the geometry and self-stress vary across the assembly. In this work we design tensegrity structures by imposing periodic boundary conditions on a single unit cell to enforce repetitive topology, geometry and self-stress. A tessellated tensegrity tower is designed by using a stiffness matrix form-finding technique in combination with nodal position constraints. Since the tessellated tensegrity is not globally in equilibrium, a transition structure is required to balance the tessellated tensegrity tower on one side and to connect to a fixed boundary on the other. The challenge in designing the transition structure is that both coordinates and residual forces are simultaneously predefined at specific nodes. In this paper, we propose an adapted stiffness form-finding method to design the transition structure as an alternative method to the conventional ground structure method.
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