Flexible and Deployable Structure

Investigation of highly flexible, deployable structures : review, modelling, control, experiments and application

By Noémi Friedman
The Budapest University of Technology and Economics
1 March 2012

Investigation of highly flexible, deployable structures : review, modelling, control, experiments and application

Flexible and Deployable StructureObserving nature, several transformable structures can be found, like the extensible worm, deployable leaves and wing of insects, expanding virus capsid, not to mention the movable structure of our own, human body. For centuries several small-scale man-constructed deployable structures have been constructed too, such as umbrellas, chairs, fans etc. For the last four-five decades, advanced man-made structures have appeared mainly for spatial engineering applications like for booms, solar arrays, antennas, reflectors, as the volume and the weight of a structure to be transported to space is crucial. On earth, until recent times, only smaller structures like tents, yurts and shelters had been constructed for architectural purposes. Confirming to the novel conceptions of the 21th century and due to available numerical and robotics technologies, advanced transformable structures are already applied in civil engineering and architecture. Structures used for off-shore industry and light deployable structures used for modern architecture can be mentioned among these.

Flexible and Deployable StructureThese structures are designed to undergo very large displacements and remain fully operational. Often the structures of that kind can integrate a multibody system or which facilitates a construction phase before being integrated in a structural assembly. Modeling of the component of 3D frame-type flexible structures of this kind is nowadays under control thanks to the geometrically exact beam model; capable of representing large displacements and rotations, and solving the pertinent instability problems.

Flexible and Deployable StructureWith the help of these tools, the deployable structures undergoing instability phenomenon were investigated. First the analytical and numerical resolutions of some basic snap-through type lattice structures were carried out, starting with the static and dynamic analysis of a shallow truss and followed by the deployment analysis of the basic unit of the snap-through type structure of Zeigler which was scrutinized by Gantes. The behavior of these structures has been already examined before by several researchers, but it was a good start to familiarize with structures undergoing large displacements and instability phenomenon.

Flexible and Deployable StructureFinally a specific system, namely the deployable antiprismatic lattice structure has been chosen for investigation, because its mechanical behavior has not yet been thoroughly analyzed. This cylindrical structure, derived from the well known yoshimura origami pattern and proposed by Hegedűs, is characterized by its pop-up deployment due to the energy accumulated from lengthening some bars during packing. Zero deployment-load corresponds both to the fully deployed and the compact configuration, the latter being an unstable equilibrium state corresponding to the maximal internal energy. It is true that the antiprismatic pop-up system has been proposed almost two decades ago, but due to the lack of popularity no practical application has been offered yet. The main goal of the dissertation was to investigate the general behavior of the specific system to blaze a trail towards the architectural application of this system by providing designing tools, profound analysis of packing behavior, ideas of applications.

Flexible and Deployable StructureThe first step is already a challenge, to fully master the construction phases of a flexible, deployable structure which takes any structural component from initial (unstressed state) to a `deformed` yet equilibrium state. Naturally, the popping up of the structure requires a thorough dynamical analysis and vibration control. However, the packing of the structure ―even by smoothly controlling boundary displacements ― may also cause inertial effect that cannot be ignored due to intermediate snapping of the structure.

Flexible and Deployable StructureThe history of transformable structures goes back to centuries before. Though possibly everybody is familiar with the light deployable nomad Indian tepees that could be transported by animals, only very few know that a part of the auditorium of the Roman Colosseum (Amfiteatro Flavio) built in the first century had a convertible textile roof. The structure of the umbrella is an ancient structure as well, but its principle is used in modern adaptive architecture.

Flexible and Deployable StructureMore and more recent architectural designs try to apply transformable systems only for achieving the variability of a shell or an envelope of the permanent structure. Though the motion of the building might not be as spellbound as those where whole massive structural parts are in motion, but can offer a nice solution for integrating structural efficiency and the adaptation to external excitation. This was the case with the adaptive sun shading system of the Audencia Provincial, Madrid designed by Hoberman. The hexagonal shading cells can completely cover the roof, but disappear when retracted into the structural profiles of the structure. The algorithm that controls the movement combines historic solar gain data with real-time sensing of light levels. Hoberman designed several adaptive shading systems in accordance with his new patented technology using thin plates sliding on each other to enhance the architectural design of Foster + Partner’s buildings. Another example is the convertible shell design of the Aldar Central Market in Abu Dhabi.

Flexible and Deployable StructureA large number of structures that can be opened and closed are based on the well-known concept of the lazy tong system. The minimum component of this system is the socalled scissor-like element. The SLE consists of two bars connected to each other with a revolute joint. By the parallel connection of SLEs the simplest 2D deployable structure, the lazy tong is constructed. Connecting at least three of SLEs through complete pin joints a ring is formed, providing a secondary unit of this frame structure. By the further connection of secondary units almost all kind of 3D-shapes can be formed folding into bundle. Adding tension components like wire or membrane to its developed form, it becomes a 3D-truss and gets effective strength, thus towers, bridges, domes and space structures can be rapidly constructed.

Flexible and Deployable StructureBy piling up pyramid type structural units vertically a basic pantographic structure is formed: a three-dimensional mast The only internal degree of freedom of the deployable mast developed in the former Deployable Structures Laboratory is controlled by a single, continuous cable which runs over pulleys connected to the joints of the pantograph. One end of this cable is connected to a drum driven by an electric motor, and its route through the structure is in a manner that winding the cable onto the drum causes the structure to deploy. A series of short (initially loose) cables linking neighboring joints of the pantograph become taut when the pantograph is fully deployed, and in this configuration, the continuous cable imparts a global state of pre-stress onto the whole structure.
Flexible and Deployable Structure

While pantograph structures discussed above all need additional stabilizing elements like cables or other locking devices, it is possible to design deployable structures that are self-stable in the erected configuration without any additional member with the application of a special geometric configuration. This can be achieved by adding inner SLEs to the initial secondary units shown in Fig. 2.17. These units are shown in Fig. 2.22. The inner SLEs deform while unfolding due to geometric incompatibilities resulting a self-locking, self-stabilizing mechanism that locks the structure in its opened configuration. The first dome structure of this type was introduced by T. Zeigler in 1974. Several pop-up displays and pavilions are constructed in accordance with his patents.

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