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.
Highlights
IntroductionWhether stiff or flexible, are curved solids with two large dimensions and a third one that is very small (thickness)
Thin shells, whether stiff or flexible, are curved solids with two large dimensions and a third one that is very small
In order to characterize the influence of gravity forces on a shell, we introduce a new non-dimensional number called the gravity impact number (Gi ), which is the ratio of the elastogravity length scale [20,21] to the characteristic dimension of the shell
Summary
Whether stiff or flexible, are curved solids with two large dimensions and a third one that is very small (thickness). In contrast to plates whose initial configuration is planar, shells are controlled by geometry and defined by their curvature. Shells built for stiffness are designed to maximize the material efficiency and reduce the overall weight-to-span ratio. By choosing an appropriate geometry for the given boundary conditions and given load case, a stiff shell experiences mostly membrane forces that can be resisted by using little material. Shells built for flexibility use geometry and inextensibility of materials to convert bending stresses into tuned, reversible large displacements. The use of shells as mechanisms is part of the broader, growing trend in compliant mechanisms to deform a large portion of a structure to produce movements (distributed compliance) [1,2,3,4,5,6] instead of lumped compliant hinges or common rigid body hinges
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
