International Journal of Space Structures

This paper presents several concepts of deployable space structures with emphasis on their relation to the basic principles of mechanics on which the concepts depend.

The following subjects are treated: the coilable longeron extendible mast and the theory of “Elastica” by Euler and Kirchhoff; the two-dimensionally deployable array and the theory of elastic surfaces (“Plate Elastica”) by Miura and Tanizawa; the variable geometry truss and the theory of truss by Mobius; the tension truss antenna and the theory of truss.

The concept of symmetry is applied to the design of some existing as well as some new deployable space structures. Through the use of axis or plane symmetry, including anti-symmetry, a bay of a deployable structure may be reduced to an equivalent simple kinematic linkage. This axis of symmetry may be in the direction of deployment of the structure so that by providing a fictitious sliding joint along this axis, the problem of the design and analysis of such deployable structures can be simplified to the study of a plane or a face of the given structure. Such axis or plane of symmetry can also be used for the synthesis of new concepts. As an aid to synthesis, platonic solids can also be used for determining the orientation of these symmetric planes. Several examples are considered. A brief discussion on structural symmetry observed in graphs and dual graphs of some deployable structures will also be presented.

This paper describes a new type of deployable masts for use in Space, based on the following elements. A deployable backbone, consisting of rods and/or plates, which can be folded or deployed freely. One or more active cable, following specially chosen routes along the mast, and running over small pulleys. The overall length of an active cable can vary between two extremes: a maximum length when the mast is fully folded; a minimum length when the mast is fully deployed. A set of passive cables joining pairs of points on the backbone. The passive cables are all slack when the backbone is partially folded and become taut when it is fully extended. A final, essential ingredient is structural prestress in the deployed state, so that all of the cables are in a state of pretension and therefore are able to carry any tensile or compressive force changes induced by external loads. An additional effect of this state of prestress is to remove backlash at the joints. Three deployable masts based on this approach are presented in the paper.

Future space applications include very large elements, whose in orbit configuration cannot be launched in a single flight by the existing launchers. Deployable structures present great advantages in this field, as the mass and volume savings that can be achieved are significant.

SENER has carried out, under ESA contract, a study to develop, manufacture and test a deployable Large Truss Structure (LTS), that meets the requirements for the mid-term applications foreseen within the European scenario. This paper presents the design, analysis, manufacturing and test phases of a full scale three-module Engineering Model of the LTS.

The deployable modular mesh antenna is composed of independently fabricated and tested antenna modules to reduce difficulties in ground testing. Each module comprises a metallic mesh shaped by a cable nework and a deployable truss structure. This paper states the basic constitution of each module, especially of the cable network, and results of surface shape adjustment simulations and experiments. Employing the present method, reflector distortions after the fabrication can be adjusted by changing cable lengths without any sensitivity analysis. Numerical simulations and experiments clarify that the attainable surface accuracy of a module is determined mainly by the accuracy of the truss structure.

This paper deals with the numerical simulation of the deployment process of a parabolic space reflector. The described deployable antenna is of the rigid panel type. The numerical simulations cover kinematic, inverse dynamic, quasi-static and dynamic analysis modes. Special phenomena included are hinge friction and the investigation of a deployment failure mode. Different software packages have been applied and their performance has been assessed.

Expandable Structures are a special kind of mechanism that can be used in several different geometries. The geometry of structures based on scissors is introduced to explain concepts necessary to design a wide range of forms like masts, archs, plane spatial structures, cylindrical and spherical bar structures.

The paper presents engineering details of a prototype scissor-link deployable structure and outlines a systematic development approach as an example of the steps involved in realizing a new idea. The arch-like structure consists of multiple pairs of scissor-linked rod elements, which can be deployed instantaneously to form a stable, spatial network and which can be collapsed to a compact bundle of nearly parallel rods. A momentary geometric non-fit during deployment causes large displacement bending or buckling and a self-stabilizing ာclickingိ effect which facilitates full deployment, and leaves the structure with no residual internal stresses after deployment. The paper concludes with recommendations for further experimental work on the subject.

Prefabricated, deployable space frames that exhibit self-standing and stress-free states in both the deployed and collapsed configurations are investigated in this paper. This type of deployable structures shows considerable advantages as compared to previous designs that either required external stabilizing or had members with residual stresses in the deployed configuration.

Following previous developments for flat deployable structures consisting of units with regular-polygon planviews, this study deals with flat structures made of trapezoidals, and curved structures assembled from regular-polygonal units. First, the general geometric constraints and deployability conditions for these units are formulated, and a methodology for using these constraints as geometric design criteria is presented. Furthermore, additional conditions for the assemblage of single units into larger structures are given. Then, structural analysis issues for this type of structures are discussed. The necessity of nonlinear analysis during deployment is emphasized. Finally, the above geometric design procedures are demonstrated with specific examples.

This paper presents further developments in the geometric design of deployable structures that are self-standing and stress-free in both the deployed and collapsed configurations. The basic geometric design philosophy of these structures has been explained in previous publications. Furthermore, guidelines for the geometric design of polygonal and trapezoidal units for flat and curved structures have been proposed. The size of the joints has been assumed to be infinitesimally small.

In reality however, the joints have certain discrete dimensions that have to be taken into account. This paper presents a more realistic geometric design procedure allowing for discrete joint sizes. First, a simple but accurate model is adopted for the joints that treats them as a grid of bars that are hinged to the members of the structure. Then, the geometric constraints and deployability conditions derived earlier are modified to account for joint size. Regular polygonal units for flat and curved structures, and trapezoidal units for flat structures are covered. An example of a medium size model is presented, where adjustments for the joint size had to be made during geometric design. Finally, the influence of joint size in the structural response during deployment is illustrated.

The study deals with the static and kinematic analysis of a column-like structure composed of absolutely rigid hinged plane elements and of linear elastic bars. The elements form congruent space structural units which can be folded separately by using appropriate external loads.

The analysis shows that a chain of these units can work as a deployable column only if the cyclic symmetry of the structure is not disturbed by imperfections. The equilibrium paths for packaging or deploying the imperfect structure are not stable, thus the geometry of the column cannot be controlled by an axial force only.

Any polyhedral structure composed of identical regular polygons can be turned into an expandable structure by replacing the polygons by pairs of polygons which can rotate about a common central hinge, and connecting a vertex of an upper polygon with the vertex of a lower polygon of an adjacent pair. Most of these structures will collapse in the fully expanded position by losing their rigidity near the final stage, and hence, become deployable. A triangular element which enables one to assemble and dismantle such structures is presented here, together with a series of examples of experimental shapes.

Tensegrity grids are internally prestressed cable networks, in which the cables are prestressed against a disjointed system of bars. These structures are inherently collapsible and deployable in the nonprestressed state. In double-layer tensegirity grids, the bars are relatively short, producing a compact packing in the collapsed state. In the deployed prestressed state, geometrically rigid as well as geometrically flexible configurations are feasible. Flat or curved surfaces can be generated. Deployability and prestress are achieved through the extension of bars, shortening of cables or a combination of both techniques. A description of the system and some analytical results and deployable models are presented.