‘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.