Effect of Gravity on the Scale of Compliant Shells

Abstract

Thin shells are found across scales ranging from biological blood cells to engineered large-span roof structures. The engineering design of thin shells used as mechanisms has occasionally been inspired by biomimetic concept generators. The research goal of this paper is to establish the physical limits of scalability of shells. Sixty-four instances of shells across length scales have been organized into five categories: engineering stiff and compliant, plant compliant, avian egg stiff, and micro-scale compliant shells. Based on their thickness and characteristic dimensions, the mechanical behavior of these 64 shells can be characterized as 3D solids, thick or thin shells, or membranes. Two non-dimensional indicators, the Föppl–von Kármán number and a novel indicator, namely the gravity impact number, are adopted to establish the scalability limits of these five categories. The results show that these shells exhibit similar mechanical behavior across scales. As a result, micro-scale shell geometries found in biology, can be upscaled to engineered shell geometries. However, as the characteristic shell dimension increases, gravity (and its associated loading) becomes a hindrance to the adoption of thin shells as compliant mechanisms at the larger scales-the physical limit of compliance in the scaling of thin shells is found to be around 0.1 m.

Organismal Design and Biomimetics: A Problem of Scale

“…In mechanics, static and kinematic mechanical notions must be taken into consideration for the identification of the key parameters. As seen for a giant sequoia, with respect to a smaller tree (see Section 2), the main variable to consider in the scaling up process is the self-weight, and thus the impact of gravity [68]. Accordingly, the general key parameters to consider in scaling constructions are: mass, geometry, material properties, and applied forces (gravitational or other forces, e.g., seismic).…”

“…The Stuttgart pavilion (2015-2016) effectively demonstrates the scaling of different structural echinoid details: (1) division into modules, (2) material differentiation, (3) double layer modules, and (4) modules interconnected by finger-joints and collagen fibres (Figure 1). Charpentier and Adriaenssens [68] carried out an interesting study on thin shell structures from biology to engineering and across their different scales to establish their scalability limits. They considered 64 thin shell structures related to five categories: (1) engineering stiff and (2) compliance, (3) plant compliance, (4) avian egg stiff, and (5) microscale compliant shells.…”

“…The results demonstrated that all the considered shells exhibited a similar mechanical behaviour across the different scales. Thus, microscaled biological shell geometries can be generally upscaled to macroscaled engineered shell geometries; however, compliant thin shells are identified as prone to self-weight deformation at a large scale due to the effect of gravity; therefore, Charpentier and Adriaenssens [68] carried out an interesting study on thin shell structures from biology to engineering and across their different scales to establish their scalability limits. They considered 64 thin shell structures related to five categories: (1) engineering stiff and (2) compliance, (3) plant compliance, (4) avian egg stiff, and (5) microscale compliant shells.…”