Bistable Shells Research Articles

Snapping of bistable, prestressed cylindrical shells

Bistable shells can reversibly change between two stable configurations with very little energetic input. Understanding what governs the shape and snap-through criteria of these structures is crucial for designing devices that utilize instability for functionality. Bistable cylindrical shells fabricated by stretching and bonding multiple layers of elastic plates will contain residual stress that will impact the shell's shape and the magnitude of stimulus necessary to induce snapping. Using the framework of incompatible elasticity, we first predict the mean curvature of a nearly cylindrical shell formed by arbitrarily prestretching one layer of a bilayer plate with respect to another. Then, beginning with a residually stressed cylinder, we determine the amount of the stimuli needed to trigger the snapping between two configurations through a combination of numerical simulations and theory. We demonstrate the role of prestress on the snap-through criteria, and highlight the important role that the Gaussian curvature in the boundary layer of the shell plays in dictating shell stability.

Modeling and analysis of the ploy region of bistable composite cylindrical shells

Bistable composite cylindrical shells have attracted many attentions thanks to their lightness, simple structure and high packaging efficiency. The ploy region between the two stable states of a bistable cylindrical shell affects the structural properties and overall compactness significantly. An analytical model is proposed assuming that the longitudinal and transverse curvatures are two dominant factors for the two different zones of the ploy region respectively. The model can be used to predict the length and the curvature distributions of the ploy region conveniently. Results obtained from the analytical model agree with numerical and experimental results. The influences of geometric parameters and bending stiffnesses on the ploy region are discussed according to the proposed analytical model.

Harnessing the bistable composite shells to design a tunable phononic band gap structure

By proposing a system composed of an array of bistable composite shells immersed in air, we develop a new class of periodic structure to control the propagation of sound. Through numerical investigation, we find that the acoustic band gap of this system can be switched on and off by triggering the snap through deformation of the bistable composite shells. The shape of cross section and filling fraction of unit cell can be altered by different number of bistable composite shells, and they have strong impact on the position and width of the band gap. The proposed concept paves the way of using the bistable structures to design a new class of metamaterials that can be enable to manipulate sound.

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.

Viscoelastic bistable behaviour of antisymmetric laminated composite shells with time-temperature dependent properties

Due to the bistable characteristics, antisymmetric laminated ([+α/−α]n) composite bistable shells have been used as novel morphing structures in many engineering fields. Previous theoretical analyses were mainly based on the hypothesis that the composite shell is elastic, which leads to unexpected calculation and prediction errors. In this paper, the fiber reinforcements are assumed to be elastic while the matrix is treated as a viscoelastic material. The resulting viscoelastic material properties of the composite shell are obtained through the experimental test and numerical modeling. Based on the classical lamination theory, together with the principle of minimum potential energy and Maxwell viscoelasticity model, a theoretical model is developed to predict the bistable behaviour of those composite shells with viscoelastic material properties. Subsequently, the influences of applied temperature and relaxation time on the second stable configuration of bistable composite shells are analytically investigated. The results are then compared with those obtained from the experiments and numerical modeling. Comprehensive results show that the principal curvature of the shell's second stable state increases as the applied temperature and relaxation time increase. In contrast, the twisting curvature of the second stable shape generally decreases with the relaxation time increasing but increases with the applied temperature rising.

Bistable behaviour and microstructure characterization of carbon fiber/epoxy resin anti-symmetric laminated cylindrical shell after thermal exposure

Bistable behaviour and microstructure characterization of carbon fiber/epoxy resin anti-symmetric cylindrical shells after thermal exposure are investigated by experimental method in this paper. The effect of thermal exposure temperature and duration on the curvatures, load-displacement curves and snap loads of bistable shells are discussed systematically. The results show that both the thermal exposure temperature and duration have a significant influence on the bistable behaviour of those antisymmetric laminated cylindrical shells. Some interesting phenomena after high-temperature exposure are found in snap-through and snap-back processes. The microstructure of the shell before and after thermal exposure is characterized using scanning electron microscope (SEM), which provide an insight into bistable deformation mechanism of those shells after being exposed to elevated temperature.

Thermal Effect on Bistable Behaviour of T700/3234 Anti-symmetric Cylindrical Shells

The temperature effects on the bi-stable characteristics of T700/3234 anti-symmetric carbon-fiber composite structure were studied. Three different layup specimens were prepared through composite molding process.The two points loading method was used in the experiment. The modified experimental testing machine (the experimental testing machine could be used to induce the bistable composite shell to snap between the two stable shapes, and continually capture the data in the experimental process.) was related to tensile testing machine at present. The load-displacement curvatures under the temperature of 20℃, 40℃, 60℃ and 80℃ were given. The snap load was recorded and the photos were taken in the experimental process. After the experiment, the detailed data of curvature and twisting curvature were obtained by image processing technology. The variation law of the coiled-up radius, out-of-plane displacement, maximum snap-through and snap-back loads were analyzed. The effect on the composite structure was also discussed.The result shows that the thermal effect is vital to the bistable snaps process, and corresponding influence trends to the snap through and snap back process are given.

Eversion of bistable shells under magnetic actuation: a model of nonlinear shapes

We model in closed form a proven bistable shell made from a magnetic rubber composite material. In particular, we incorporate a non-axisymmetrical displacement field, and we capture the nonlinear coupling between the actuated shape and the magnetic flux distribution around the shell. We are able to verify the bistable nature of the shell and we explore its eversion during magnetic actuation. We show that axisymmetrical eversion is natural for a perfect shell but that non-axisymmetrical eversion rapidly emerges under very small initial imperfections, as observed in experiments and in a computational analysis. We confirm the non-uniform shapes of shell and we study the stability of eversion by considering how the landscape of total potential and magnetic energies of the system changes during actuation.

On the thermally induced multistability of connected curved composite plates

So far thermally induced bistable flat plates and shells have been studied separately. Combination of these elements together introduces a new set of bistable structures. This paper presents a Rayleigh–Ritz model to study the thermal deformation of connected curved plates. In this work, the initially curved plate model (Eckstein et al., 2014) is extended to account for the continuity of displacements and strains on the connection line. The model is compared with experimental data and finite element for two and three connected curved plate geometries. Effect of different layups other than [0/90] can be examined by this model. As an example, a [−45/45] layup is studied. The accuracy of the presented model is good away from the boundaries but inaccuracies occur close to the edges, i.e. giving reasonable accuracy overall. As a new result, combining different layups and initial curvatures can lead into more than two stable configurations. Compared to previous analytical models which are focused on single flat or curved plates, in this work a more general model is developed that can take into account various initial shapes. Finally, the combined effect of initial shape and temperature variation on the existence of bistability is demonstrated.

Thermal effect and active control on bistable behaviour of anti-symmetric composite shells with temperature-dependent properties

Anti-symmetric cylindrical shells with two stable configurations have been proved to offer novel morphing structures in advanced engineering fields. The bistable behaviour of anti-symmetric composite shells under thermomechanical loading is analysed herein theoretically combined with a finite element modelling. The properties of the composite material in current study are considered to be functions of temperature. The shell is subjected to two different thermal load, i.e. the uniform temperature field and through-thickness thermal gradient. The influence of this two temperature field on the shell’s stable shapes was predicted analytically, which thereafter is determined by finite element results. This provides a feasible approach of controlling the deformation of the bistable shell through adjusting the applied temperature field. For this purpose, a superposition of uniform temperature field and through-thickness thermal gradient is imposed and its influence on the bistable shapes of bistable shells is therefore investigated, which is of great importance to the design and application of morphing structures manufactured from bistable composite shells.

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.

Highly multistable composite surfaces

Novel continuous composite surfaces are presented which possess a high degree of multistability. Inspired by the illustrative behaviour of a multistable analog model, we first show how two identical bistable composite shells with tailored asymmetric bistability may be connected to form a continuous quadstable surface. The concept is then extended to surfaces composed of three and by extension more identical bistable shells connected in series in order to achieve additional stable states. The multistable behaviour of these surfaces is investigated by finite element analysis and verified by experimental work.

双安定性を有する複合材シェルのスナップスルー変形に関する多目的最適化

双安定性を有する複合材シェルのスナップスルー変形に関する多目的最適化

The bistable behaviors of carbon-fiber/epoxy anti-symmetric composite shells

Bistability of cross-ply [0n°/90n°] laminates has already been examined in detail by researchers. Another kind of bistable composite shell manufactured from carbon-fiber/epoxy prepreg with anti-symmetric layup, such as [30°/−30°/0°/30°/−30°], is investigated in this paper using analytical, experimental and numerical methods. A new experimental method named two points loading method is presented to capture the bistable behavior of the manufactured specimens. The coiled-up radius and the snap loads, including snap-through and snap-back load used to induce the bistable composite shell to snap between two stable shapes are measured. The factors affecting the bistable performance of the anti-symmetric composite shell, including structure sizes and layup conditions, are discussed by comparing experimental test results and analytical solutions. Good agreement was found between analytical predictions and measured results. The finite element results are approximately in accord with experimental results. Possible reasons of differences between numerical simulation and experimental results are given.

A Novel Experimental Method and its Numerical Simulation for the Bi-Stable Anti-Symmetric Composite Shell

Based on the discussion of the current research methods about the bi-stable composite shell, a novel experimental method named four points bending loading is presented to provide driving moments to snap an anti-symmetric bi-stable composite shell from one stable state to another. Then, the feasibility of this new method was confirmed using the finite element analysis software ABAQUS. Finally, the future work, which is to construct an experimental platform according the four points bending loading method, is pointed out.

804 双安定性を有する非対称積層複合材シェルの振動特性評価

Asymmetric laminates of fibrous composites have strong elastic and thermal anisotropic properties, resulting in the curved surfaces caused by residual thermal strain during curing process. Specific asymmetric laminates indicate bi-stable states in terms of surface shapes, and these bi-stable states enable large deformation with relatively small energy input. This becomes an advantage when the asymmetric laminate is applied to the aerospace structures such as a morphing airfoil. The present paper first reveals occurrence criteria of bi-stable states for asymmetric laminates. In-plane buckling strengths are employed as an index of occurrence and calculated for plates with different width-to-thickness ratio and lay-up configurations. Then, vibration properties of bi-stable composite shells are evaluated by using both numerical study with the Ritz method based on Donnel-Mushtari theory and the experimental modal analysis technique. The numerical and experimental results show that there are some relations between the buckling strength and the occurrence of bi-stable states within plates having specific lay-up configurations, and asymmetric laminates with bi-stable states indicate different vibration characteristics before and after snap-thorough deformation.

Prestressed Morphing Bistable and Neutrally Stable Shells

This study deals with prestressed shells, which are capable of “morphing” under large deflexions between very different load-free configurations. Prestressing involves plastically curving a flat, thin shell in orthogonal directions either in the opposite or same sense, resulting in two unique types of behavior for isotropic shells. Opposite-sense prestressing produces a bistable, cylindrically curved shell provided the prestress levels are large enough and similar in size: This effect forms the basis of a child’s “flick” bracelet and is well known. On the other hand, same-sense prestressing results in a novel, neutrally stable shell provided the levels are also sufficiently large but identical: The shell has to be made precisely, otherwise, it is monostable and is demonstrated here by means of a thin, helically curved strip. The equilibrium states associated with both effects are quantified theoretically and new expressions are determined for the requisite prestress levels. Furthermore, each stability response is revealed in closed form where it is shown that the neutrally stable case occurs only for isotropic materials, otherwise, bistability follows for orthotropic materials, specifically, those, which have a shear modulus different from the isotropic value. Finally, prestressing and initial shape are considered together and, promisingly, it is predicted that some shells can be neutrally stable and bistable simultaneously.

Analytical models for bistable cylindrical shells

Thin cylindrical shell structures can show interesting bistable behaviour. If made unstressed from isotropic materials they are only stable in the initial configuration, but if made from fibre-reinforced composites they may also have a second, stable configuration. If the layup of the composite is antisymmetric, this alternative stable configuration forms a tight coil; if the layup is symmetric the alternative stable configuration is helical. A simple two-parameter model for these structure is presented that is able to distinguish between these different behaviours.