Quasi-static Shape Morphing of Adaptive Columns Toward Funicular Forms

Funicular load-bearing structures achieve exceptional efficiency because their shapes follow the natural trajectories of internal stresses. However, time-varying loads can disrupt funicularity if they have fixed geometries. Recently, the authors found that funicularity may be restored through shape adaptation mediated by a simple, novel feedback control law. In this work, we investigate the limit of slow adaptation - an important special case of the new structural paradigm that is relevant to real-world applications in which external loads also evolve slowly. By considering the quasi-static limit of the coupled Newtonian and shape dynamics, we develop a discrete, chain-like multibody model of a morphing column, which enables detailed examination and visualization of shape dynamics. We show that, despite the lack of Newtonian dynamics, the shape dynamics is rich and nonlinear because of large geometric changes. Illustrative examples of shape adaptation reveal cases of successful convergence to the target shape as well as sustained shape oscillations with repeated snapping. The prominent role of elastic buckling instability in shape convergence is highlighted. Linearized evolution equations are used to verify local convergence to the target shape, and a condition of non-local convergence from almost all initial configurations to the target configuration is also developed.