Shape changing structures will play an important role in future engineering designs since rigid structures are usually only optimal for a small range of service conditions. Hence, a concept for reliable and energy-efficient morphing structures that possess a large strength to self-weight ratio would be widely applicable. We propose a novel concept for morphing structures that is inspired by the nastic movement of plants. The idea is to connect prismatic cells with tailored pentagonal and/or hexagonal cross sections such that the resulting cellular structure morphs into given target shapes for certain cell pressures. An efficient algorithm for computing equilibrium shapes as well as cross-sectional geometries is presented. The potential of this novel concept is demonstrated by several examples that range from a flagellum like propulsion device to a morphing aircraft wing.

Plants such as Dionaea muscipula (Venus Flytrap) can change the shape of their shell-like leaves by actively altering the cell pressures. These leaves are hydraulic actuators that do not require any complex controls and that possess an energy efficiency that is unmatched by natural or artificial muscles (Huber et al 1997 Proc. R. Soc. A 453 2185-205). We extend our previous work (Pagitz et al 2012 Bioinspir. Biomim. 7 016007) on pressure-actuated cellular structures by introducing a concept for shape-changing shell-like structures that can significantly alter their Gaussian curvature. The potential of this concept is demonstrated by a hemispherical shell that can reversibly change the sign of its Gaussian curvature. Furthermore, it is shown that a snap-through behaviour, similar to the one known from Dionaea muscipula, can be achieved by lowering the pressure in a single layer of cells.

a b s t r a c tThis paper presents a novel form-finding algorithm for tensegrity structures that is based on the finite element method. The required data for the form-finding is the topology of the structure, undeformed bar lengths, total cable length, prestress of cables and stiffness of bars. The form-finding is done by modifying the single cable lengths such that the total cable length is preserved and the potential energy of the system is minimized. Two-and three-dimensional examples are presented that demonstrate the excellent performance of the proposed algorithm.

A remarkable property of nastic, shape changing plants is their complete fusion between actuators and structure. This is achieved by combining a large number of cells whose geometry, internal pressures and material properties are optimized for a given set of target shapes and stiffness requirements. An advantage of such a fusion is that cell walls are prestressed by cell pressures which increases, decreases the overall structural stiffness, weight. Inspired by the nastic movement of plants, Pagitz et al. 2012 Bioinspir. Biomim. 7 published a novel concept for pressure actuated cellular structures. This article extends previous work by introducing a modular approach to adaptive structures. An algorithm that breaks down any continuous target shapes into a small number of standardized modules is presented. Furthermore it is shown how cytoskeletons within each cell enhance the properties of adaptive modules. An adaptive passenger seat and an aircrafts leading, trailing edge is used to demonstrate the potential of a modular approach.

This paper presents a computational study of the critical buckling pressure of pumpkin balloons, which consist of a thin, compliant membrane constrained by stiff meridional tendons. The n-fold symmetric shape of a pumpkin balloon with n identical lobes is exploited by adopting a symmetry-adapted coordinate system, which leads to the tangent stiffness matrix in an efficient block-diagonal form; the smallest eigenvalue of a particular block leads to the buckling pressure for the balloon. Two different types of balloon design are considered. Extensive results are obtained for the buckling pressures of a set of 10 m diameter experimental balloons and also for an 80 m diameter flight balloon. The key findings are as follows: the same type of buckling mode, forming four circumferential waves is critical for most of the balloons that have been analysed; balloons with flatter lobes are more stable, and the buckling pressure varies with an inverse power-law of the number of lobes; increasing the Young's modulus, the Poisson's ratio of the membrane, or the diameter of the end fitting has the effect of increasing the buckling pressure; but increasing the axial stiffness of the tendons has the effect of decreasing the buckling pressure.

This paper gives a brief overview of the historical development of scientific balloons and their capabilities. Furthermore, a recent programme by NASA is introduced that aims to develop balloons capable of carrying payloads of several tonnes to above 99% of the Earth's atmosphere for up to 100 days. It is shown that the currently investigated balloons suffer from instabilities that can be minimized using a different design paradigm for the cutting patterns. Finally, a novel balloon design, similar to the topology of radiolarians, is introduced that is potentially superior to existing designs.

Biologically inspired pressure actuated cellular structures can alter their shape through pressure variations. Previous work introduced a computational framework for pressure actuated cellular structures that is limited to two cell rows and central cell corner hinges. This article rigorously extends these results by taking into account an arbitrary number of cell rows, a more complicated cell kinematic that includes hinge eccentricities and varying side lengths as well as rotational and axial cell side springs. The nonlinear effects of arbitrary cell deformations are fully considered. Furthermore, the optimization is considerably improved by using a second-order approach. The presented framework enables the design of compliant pressure actuated cellular structures that can change their form from one shape to another within a set of one-dimensional C 1 continuous functions. Several examples are used to demonstrate the performance of the proposed framework.

a b s t r a c tThis paper is concerned with the optimization of the cutting pattern of n-fold symmetric super-pressure balloons made from identical lobes constrained by stiff meridional tendons. It is shown that the critical buckling pressure of such balloons is maximized if the unstressed surface area of the balloon is minimized under a stress constraint. This approach results in fully stressed balloon designs that in some cases have a smaller unstressed surface area than the corresponding axisymmetric surface that is in equilibrium with zero hoop stress. It is shown that, compared to current designs, the buckling pressures can be increased by up to 300% without increasing the maximum stress in the lobe.