Coupled Sizing, Shape and Topology Optimisation of Bistable Deployable Structures

Bistable scissor structures, consisting of beams connected by hinges, are transportable and can be transformed from a compact to a deployed configuration. Geometric incompatibilities can be introduced during transformation to obtain a bistable structural response which enforces some instantaneous structural stability in the deployed state. The design of bistable scissor structures requires assessing both the non-linear transformation behaviour, as well as the service state, since a proper structural design has to provide stiffness in the deployed state as well as flexibility during transformation. These contradicting requirements were formulated previously in Arnouts et al. [1] as a multi-objective shape and sizing optimisation (SSO). The originality of this contribution is the elaboration of a design methodology coupling a novel topology optimisation (TO) to SSO and demonstrating its performance for the design of a bistable deployable wall. In this novel step, the number of bistable deployable modules (BDM) of the structure is optimised at low computational cost by finding the location of BDM, yielding mixed structures composed of BDM and non-bistable modules (NBDM) of lower weight and complexity than structures entirely built from BDM. TO is incorporated and assessed in the design methodology prior or subsequent to the SSO step. It is shown that the mixed structures combining BDM and NBDM resulting from the new coupled TO-SSO approach outperform pure BDM based structures.

Sustained representation of perspectival shape

Arguably the most foundational principle in perception research is that our experience of the world goes beyond the retinal image; we perceive the distal environment itself, not the proximal stimulation it causes. Shape may be the paradigm case of such “unconscious inference”: When a coin is rotated in depth, we infer the circular object it truly is, discarding the perspectival ellipse projected on our eyes. But is this really the fate of such perspectival shapes? Or does a tilted coin retain an elliptical appearance even when we know it’s circular? This question has generated heated debate from Locke and Hume to the present; but whereas extant arguments rely primarily on introspection, this problem is also open to empirical test. If tilted coins bear a representational similarity to elliptical objects, then a circular coin should, when rotated, impair search for a distal ellipse. Here, nine experiments demonstrate that this is so, suggesting that perspectival shapes persist in the mind far longer than traditionally assumed. Subjects saw search arrays of three-dimensional “coins,” and simply had to locate a distally elliptical coin. Surprisingly, rotated circular coins slowed search for elliptical targets, even when subjects clearly knew the rotated coins were circular. This pattern arose with static and dynamic cues, couldn’t be explained by strategic responding or unfamiliarity, generalized across shape classes, and occurred even with sustained viewing. Finally, these effects extended beyond artificial displays to real-world objects viewed in naturalistic, full-cue conditions. We conclude that objects have a remarkably persistent dual character: their objective shape “out there,” and their perspectival shape “from here.”

The Effects of Three-Dimensional Context on Shape Perception

Humans have a unique ability to perceive shape in different ways. Although we naturally estimate objective (physical) shape in our daily interactions with the world, we are also capable of estimating projective (retinal) shape, especially when attempting to accurately draw objects and scenes. In four experiments, we demonstrated robust effects of 3D context on shape perception. Using a binocular stereo paradigm, we presented rectangular surfaces of varying widths alone or embedded in a polyhedron. We investigated how context, judgment type, and angle affected width estimates. We found that the presence of even a small amount of 3D context aids objective judgments but hinders projective judgments, whereas a lack of context had the opposite effect. Context facilitated objective shape assessments by improving estimates of surface orientation. These results demonstrate that the typical presence of 3D context aids shape perception (shape constancy) while simultaneously making the projective judgments necessary for realistic drawing more difficult.