Geometric Design of Deploybale Structures with Discrete Joint Size

Abstract

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.

A Systematic Design Methodology for Deployable Structures

“…In [39] it is explained how scaling a lightweight structure as a whole will affect the design of structural parts. The design methodology proposed here for deployable structures is largely based on these concepts, and makes use of the specific geometric and structural behaviour characteristics of deployable structures that are described in other publications of the authors [13,14,22,23,16,17,18,19,21,20,25,26,15,12,24]. The proposed generic design methodology for deployable structures of any shape is illustrated in Figure 3.…”

“…The overall design problem has been broken down into three smaller subproblems that are, in hierarchical order, geometric design, structural design in the deployed configuration under service loads, and structural design during deployment. Geometric design has the highest priority, because only full satisfaction of the geometric constraints discussed in [13,22,23,17,20] guarantees the desired property of deployability. The assignment of higher priority to the design under service loads than that during deployment reflects our basic design philosophy.…”

“…Since these two objectives contradict each other, iterations are necessary until a balanced behaviour is achieved. The authors have been studying the behaviour of these structures during the last few years [13,14,22,23,16,17,18,19,21,20,25,26,15,12,24]. This paper contains their final recommendations on a design methdology that aims at reducing the number of iterations and the required computational effort.…”

Geometric design of triangulated bistable scissor structures taking into account finite hub size

“…Gantes and Connor formulated a systematic approach for the geometric and structural design for bistable deployable structures [8][9][10][11][12][13][14]. Their geometric design approach included the deployability conditions for flat, curved and arbitrarily shaped bistable scissor modules without and with hub size (i.e.…”

A novel concept of convertible roofs with high transformability consisting of planar scissor-hinge structures

“…Their studies proved that a defined geometry can be obtained from the multiplication of different units. In addition to the development of geometric designs for new structures, Escrig's [8,9], Gantes' [10][11][12][13][14] and Langbecker's works [15,16] also aimed at explaining the structural behaviour of the scissor-hinge structures in analytical and numerical ways, and at proposing methods for their combined geometric and structural design. However, the work of these researchers also concentrated on structures that are transformed between two pre-defined geometries, an open and a closed one, without attempting to provide additional geometric flexibility of scissor-hinge structures.…”