‘Morphing’ bistable orthotropic elliptical shallow shells

Abstract

This study is concerned with the equilibrium shapes of orthotropic, elliptical plates and shells deforming elastically without initial stresses. The aim is to explore potential bistable configurations and their dependencies on material parameters and initial shape for elucidating novel morphing structures. A strain energy formulation gives way to a compact set of governing equations of deformation, which can be solved in closed form for some isotropic and orthotropic conditions. It is shown that bistability depends on the change in Gaussian curvature of the shell, in particular, for initially untwisted shells, isotropy precludes bistability, where there is negative initial Gaussian curvature, but orthotropic materials yield bistability irrespective of the sign of the initial Gaussian curvature. This improved range of performance stems from increasing the independent shear modulus, which imparts sufficient torsional rigidity to stabilize against perturbations in the deformed state. It is also shown that the range of bistable configurations for initially twisted shells generally diminishes as the degree of twist increases.

Tristability of thin orthotropic shells with uniform initial curvature

“…This paper extends the approaches and the results of Guest & Pellegrino (2006) and Seffen (2007) to show that orthotropic shallow shells with uniform initial curvature may be tristable and discusses the range of initial curvatures and material parameters leading to tristability. Section 2 presents the basic equations of the shell model in the framework of the uniform curvature assumption used by Forterre et al (2005), Guest & Pellegrino (2006) and Seffen (2007).…”

“…Section 2 presents the basic equations of the shell model in the framework of the uniform curvature assumption used by Forterre et al (2005), Guest & Pellegrino (2006) and Seffen (2007). Focusing on the role played by the shell extensibility and the Gaussian curvature, it discusses both the extensible and inextensible variants and comments on the respective conditions of applicability.…”

“…Those studies are limited to the numerical and/or experimental analysis of specific structures, showing a reasonable agreement among experimental results, numerical computations and semi-analytical approaches. Guest & Pellegrino (2006) and Seffen (2007) provided a deeper insight into the phenomenon of multistability of shallow shells by recalling the crucial role of geometry and the interplay between extension and curvature (e.g. Love 1906;Mansfield 1989).…”

“…shells with zero Gaussian curvature). Seffen (2007) adopted an extensible uniform curvature model to investigate the range of initial curvatures for which orthotropic shells are bistable. He showed that even isotropic shells may be bistable, but in numerical investigations he was unable to find more than two stable equilibria.…”

Multi-stable composite twisting structure for morphing applications

“…In a general approach, multi-stability is achieved by designing a structure that has multiple total potential energy minima. When using fibre-reinforced plastic (FRP), this can occur owing to several phenomena: the combination of residual stresses induced during the cure cycle and geometric nonlinearity in a non-symmetric laminated FRP lay-up (Hyer 1981(Hyer , 1982Dano & Hyer 1998;Potter & Weaver 2004), Gaussian curvature effects (Seffen 2007), fibre pre-stress (Daynes et al 2008(Daynes et al , 2010a or plastic deformation (Guest & Pellegrino 2006). This paper is concerned with a class of bistable structures able to achieve overall large deformations in length while the strains everywhere remain small and below the elastic limit.…”