Multistable Shells Research Articles

Aerodynamic Performance of a Nanostructure-Induced Multistable Shell

Multistable shells that have the ability to hold more than one stable configuration are promising for adaptive structures, especially for airfoil. In contrast to existing studies on bistable shells, which are well demonstrated by the Venus flytrap plant with the ability to feed itself, this work experimentally studies the aerodynamic response of various stable configurations of a nanostructure-induced multistable shell. This multistable shell is manufactured by using nanotechnology and surface mechanical attrition treatment (SMAT) to locally process nine circular zones in an original flat plate. The aerodynamic responses of eight stable configurations of the developed multistable shell, including four twisted configurations and four untwisted configurations with different cambers, are visually captured and quantitively measured in a wind tunnel. The results clearly demonstrate the feasibility of utilizing different controllable configurations to adjust the aerodynamic performance of the multistable shell.

Multistable shells with designable configurations based on localized nanocrystallization processes

Highly multistable shells of designable configurations are proposed for morphing surfaces, which are manufactured by using nanocrystallization process, i.e. surface mechanical attrition treatment (SMAT). Through a localized treatment, the nanostructuring process can bring bistable properties for localized regions, whose configurations were determined by their shapes and sizes. With coupled deformations among multiple nanostructured regions, the processed shell can hold different stable configurations with localized bistable regions capping toward different sides. The stable configurations are determined by the shapes and sizes of the localized bistable regions and their in-plane distributions. Furthermore, the stable configurations of the multistable shells can be further mechanically modified by plastic bending. To guide the design and investigation of the multistable behavior, finite element analysis and experimental work have been conducted to correlate the stable configurations to design parameters, including shapes and sizes of the localized nanostructuring regions, their pattern distributions, applied mechanical processes as well as boundary conditions.

Bistability of orthotropic shells with clamped boundary conditions: An analysis by the polar method

Multistable shells have been recently proposed as an effective solution to design morphing structures. We describe a class of shallow shells which are bistable after one of their sides, initially curved, is clamped along a flat line. Supposing the shell being assembled as a composite laminate, we show how the anisotropy of the material can influence the multistable behaviour and the robustness of stable configurations. Specifically, we focus on orthotropic laminated shells using the polar method for a complete representation of the anisotropic elastic properties. Two experimental prototypes have been produced and tested to validate our analytical and numerical results.

Bistable metallic materials produced by nanocrystallization process

Through a localized nanocrystallization process using surface mechanical attrition treatment (SMAT), a new method is proposed to build bistable and multistable metallic shells. The impacts from randomly fast-moving balls during the nanocrystallization process accumulate plastic deformations, which induce nanotwins and mesh grains into nanoscales significantly increasing elastic behavior range of the treated shells. The in-plane self-equilibrium residual stress field, which is induced from the stretching plastic deformations in the treated region under the constraint of the untreated region, renders nanostructured shells bistable characteristics. An effective numerical modelling is carried out to analyze the bistable behavior and predict their stable configurations. A flat plate with multiple nanostructured regions is manufactured and numerically studied, which is capable of holding multiple stable configurations. In addition, the developed bistable and multistable shells can be further mechanically processed to modify their stable configurations.

Effects of boundary conditions on bistable behaviour in axisymmetrical shallow shells.

Multistable shells are thin-walled structures that have more than one stable state of self-stress. We consider isotropic axisymmetrical shallow shells of arbitrary polynomial shapes using a Föppl-von Kármán analytical model. By employing a Rayleigh-Ritz approach, we identify stable shapes from local minima in the strain energy formulation, and we formally characterize the level of influence of the boundary conditions on the critical geometry for achieving bistable inversion-an effect not directly answered in the literature. Systematic insight is afforded by connecting the boundary to ground through sets of extensional and rotational linear springs. For typical cap-like shells, it is shown that bistability is generally enhanced when the extensional spring stiffness increases and when the rotational spring stiffness decreases, i.e. when boundary movements in-plane are resisted but when their rotations are not; however, for certain other shapes and large in-plane stiffness values, bistability can be enhanced by resisting but not entirely preventing edge rotations. Our predictions are furnished as detailed regime maps of the critical geometry, which are accurately correlated against finite-element analysis. Furthermore, the suitabilities of single degree-of-freedom models, for which solutions are achieved in closed form, are evaluated and compared to our more accurate predictions.

Basic criteria to design and produce multistable shells

A shell can have multiple stable equilibria either if its initial curvature is sufficiently high or if a suitably strong pre-stress is applied. Under the hypotheses of a thin and shallow shell, we derive closed form results for the critical values of curvatures and pre-stresses leading to bistability and tristability. These analytical expressions allow to easily provide guidelines to build shells with different stability properties.

Multistable grid and honeycomb shells

The manufacturing of multistable shells has been dominated by the use of pre-stressed and composite materials. Here we advocate the use of common materials through a simple design that requires no pre-stressing and has an initially developable geometry. A rudimentary demonstrator is constructed and serves as the starting point for further study. An existing homogenisation model for a lattice structure is combined with an analytical strain energy model from the literature to show the mechanical properties needed to construct an initially developable, bistable grid shell. The concept is also tested in a commercial finite element package, where a number of parametric studies are performed. Both the demonstrator and the FE model confirm the validity of the design while a series of parametric studies helps establish the limits of this behaviour with respect to local and global geometry of grid shell and honeycomb structures.

Magnetic actuation and transition shapes of a bistable spherical cap

Multistable shells have been proposed for a variety of applications; however, their actuation is almost exclusively addressed through embedded piezoelectric patches. Additional actuation techniques are needed for applications requiring high strains or where remote actuation is desirable. Part of the reason for the lack of research in this area is the absence of appropriate models describing the detailed deformation and energetics of such shells. This work presents a bistable spherical cap made of iron carbonyl-infused polydimethylsiloxane. The magnetizable structure can be actuated remotely through permanent magnets while the transition is recorded with a high-speed camera. Moreover, the experiment is reproduced in a finite element (FE) dynamic model for comparison with the physical observations. High-speed footage of the physical cap inversion together with the FE modeling gives valuable insight on preferable intermediate geometries. Both methods return similar values for the magnetic field strength required for the snap-through. High-strain multistable spherical cap transformation is demonstrated, based on informed material selection. We discover that non-axisymmetric transition shapes are preferred in intermediate geometries by bistable spherical caps. We develop the methods for design and analysis of such actuators, including the feasibility of remote actuation methods for multistable shells.