Shaping of bistable sheets by isometric surface bonding

Abstract

Classical shape-changing bistable sheets exhibit extreme and rapid morphing behavior (snap-through) from one stable developable surface to another. Despite this attractive morphing mechanism, its development and applications are limited owing to its limitation in that only specific morphologies are possible. In this study, we investigated a method in shaping bistable sheets with non-developable surfaces by harnessing the geometrical and mechanical characteristics of the plate and shell. As a result, bi-stability of saddle-shaped sheets was achieved by employing two plane-symmetric orthotropic laminae. The laminated sheet's shape adaptation was examined based on Gauss's Theorema Egregium and the energy barrier during shape conversion estimated using classical plate theory. In order to verify the design method, the equilibrium configuration and energy level of the laminated thin plate are analyzed by using Rayleigh-Ritz method analytically (MATLAB, computer programing software) and Finite Element Method numerically (ABAQUS, commercial finite element analysis software). The considered orthotropic sheets are fabricated using 3D printer, verified the theoretically analyzed bi-stable sheet. Eventually, we developed a fundamental approach to addressing the limitations of bistable structures, making a significant contribution to research in this field.

Keywords

• Bistable
• Orthotropic laminae
• Cross-ply
• Antisymmetric cross-ply
• 3D printer