Modeling the Bistability of Laminated Composite Toroidal Slit Tubes

Abstract

The bistability of a toroidal slit tube is modeled using the Rayleigh-Ritz method. Approximate explicit expressions for the original stable deployed geometry, and the deformed stowed geometry are used to derive forms for the bending and stretching strain energy. The surface of a torus has varying Gaussian curvature, requiring a new approach to the modeling and analysis of the stable configurations. A comparative study with established straight-BRC models was conducted from which the doubly curved-BRC model presented here predicts second stable state coil radii with 96.25% agreement.

Curved Bistable Composite Slit Tubes with Positive Gaussian Curvature

“…Now consider the point P located at X 0 (s = 0) on the torus with azimuthal and cross-sectional This is a symmetric problem allowing a single function, X 0 of a single independent variable, s to be used. The initial slit tube cross-section, T 0 (s) is modeled as [26],…”

“…Equations 3 & 4 use cosine and polynomial trial functions for X(s), respectively. They are developed from previous models [26] and necessary in order to describe non-uniformly curved cross-sections, which are non-circular, by using even/symmetrical trial functions.…”

“…Furthermore, exploration of the design space is required in order to study the effects of multiple design parameters. This work builds on the recently developed 'toroidal BRC model' [26] by conducting a detailed study of curved bistable slit tubes that have: (i) initial, positive longitudinal curvature; (ii) cross-sections subtending more and less than 180 o ; (iii) nonuniformly curved cross-section shape; (iv) variable laminate properties; and (v) been manufactured for experimental verification. Curved tubes, either positively or negatively curved are defined by their azimuthal, or longitudinal curvature, and slit location.…”

Neutrally stable double-curved shells by inflection point propagation

“…A characteristic property of this group of shell structures is the existence of a second stable, though non-zero energy, configuration, from hereon referred to as the 'inverted state'. Bi-stable behavior of similar compliant shells, both with and without Gaussian curvature, is discussed in the context of laminated composites (Galletly and Guest, 2004;Knott and Viquerat, 2016, 2018. In this research, so-called 'slit tubes' form either positive-or negative barrel-shaped coils at their second equilibrium configuration when a positive-or negative longitudinal curvature is applied respectively.…”