The design space of plane elastic curves

Computational Design of Laser-Cut Bending-Active Structures

“…9, the method converges to a minimum energy curve and optimal stiffnesses within the prescribed bounds, even though the distance to target is not close to zero (1.2% error). Note our examples with an extra load extend the set of equilibrium curves considered in [5]. In particular the heart, where the line spanned by the 2 inflection points (dotted line) does intersect the equilibrium curve in 2 further points (see Fig.…”

“…In particular the heart, where the line spanned by the 2 inflection points (dotted line) does intersect the equilibrium curve in 2 further points (see Fig. 5 in [5]).…”

“…More recently, Liu et al [24] explored the design of axis-symmetric structures formed by tapered ribbons. Their theoretical results were extended and generalized by Hafner and Bickel [5] who investigated the design space of planar elastic rods for form-finding applications. This latter work shares similarities with ours but also notable differences: on the fabrication side, bending control of the optimized strips is achieved by playing with their width, while we modify their inner meso-scale geometric structure; on the numerical side, this previous study is focused on clamped-clamped ribbons whose deformed shape is primarily determined by geometric boundary conditions, while we are also interested in structures able to carry external loading.…”

“…It is important to know from the beginning if a given target curve is feasible. Similar to [5], we say that a target shape is "feasible" if there is a solution to the constrained minimisation problem for which the distance to the target curve is close to 0. In our case however, feasibility does not imply fabricability, meaning that the structure will not break during bending.…”

“…While this can be achieved by playing with the width of the strips (see e.g. the recent work by Hafner and Bickel [5]) or their thickness (at the expense of a more involved fabrication process), we do not want to alter the outer shape of our ribbons. Instead, drawing inspiration from the design of living hinges and from kerfing techniques used in lute-making, we propose to modulate the curvature of our structures by patterning their interior according to a parameterized rectangular motif that is regularly laser-cut.…”