Landolf Rhode-Barbarigos

Design of tensegrity structures using parametric analysis and stochastic search

Tensegrity structures are lightweight structures composed of cables in tension and struts in compression. Since tensegrity systems exhibit geometrically nonlinear behavior, finding optimal structural designs is difficult. This paper focuses on the use of stochastic search for the design of tensegrity systems. A pedestrian bridge made of square hollow-rope tensegrity ring modules is studied. Two design methods are compared in this paper. Both methods aim to find the minimal cost solution. The first method approximates current practice in design offices. More specifically, parametric analysis that is similar to a gradient-based optimization is used to identify good designs. Parametric studies are executed for each system parameter in order to identify its influence on response. The second method uses a stochastic search strategy called probabilistic global search Lausanne. Both methods provide feasible configurations that meet civil engineering criteria of safety and serviceability. Parametric studies also help in defining search parameters such as appropriate penalty costs to enforce constraints while optimizing using stochastic search. Traditional design methods are useful to gain an understanding of structural behavior. However, due to the many local minima in the solution space, stochastic search strategies find better solutions than parametric studies.

Design Aspects of a Deployable Tensegrity-Hollow-rope Footbridge

Tensegrity structures are composed of cables and struts in a prestressed self-equilibrium. Although tensegrity first appeared in the 1950s, it is seldom used in civil engineering. This paper focuses on the design aspects of a deployable tensegrity-hollow-rope footbridge. Deployment is usually not a critical design case for traditional deployable structures. However, for tensegrity systems deployment may be critical due to the actuation required. In this paper, deployment is investigated in a general design framework. The influence of clustered (continuous) cables and spring elements in statics and dynamics is studied. Finally, actuation schemes are explored to identify cases where deployment becomes a critical design case. For this configuration, deployment is a critical design case when the structure has spring elements and continuous cables.

Form finding and analysis of inflatable dams using dynamic relaxation

Inflatable dams are flexible membrane structures inflated by air and/or water. Due to their ease of construction, rapid deployability and low cost, these systems have great potential for hazard mitigation applications in the context of global warming. However, designing inflatable dams is a challenging task as the dams initial equilibrium shape has to be determined by either experimental or numerical form-finding methods. Furthermore, the dams shape and the applied loading are coupled since changes in the form of the structure induce also changes in the loading profile. In this paper, dynamic relaxation, a well-established form-finding and analysis technique, is employed for the cross-sectional analysis of inflatable dams. Using this technique and the proposed extensions, the structural behavior of inflatable dams can be analyzed under constant and varying internal pressure as well as different loading and support conditions. The results are in agreement with published results in literature. Therefore, the presented method provides an alternative computationally advantageous tool for the design of inflatable dams.

Dynamic relaxation study and experimental verification of dielectric-elastomer minimum-energy structures

The shape of a dielectric elastomer minimum energy structure (DEMES) depends on the equilibrium between a pre-stretched membrane and an inextensible frame. The authors show that an extended dynamic relaxation method, a technique employed for the form-finding and analysis of pre-stressed structures, can be used to simulate DEMES equilibrium shapes. Physical models show excellent agreement with the shape of computed models. Dynamic relaxation, with its low computational cost, is a powerful form-finding technique that efficiently predicts the equilibrium shape as well as the elastic energy of DEMES.

Conceptual Design of a Single-Crease Origami-Arc Inspired Movable Footbridge Structure

Origami, the craft of folding paper, has been a source of inspiration for developable foldable systems in various engineering disciplines. Origami-inspired segmented plate systems result in lightweight and stiff structures that change shape by folding. With curved-crease origami, a three-dimensional change in shape can arise from a single fold mechanism. In this paper, the curved-crease mechanism of a single-crease arc is investigated as the driver for the conceptual design of a movable footbridge. The folding mechanism is investigated using particle-spring models and small-scale physical models. The structural feasibility of a 40 m radius curved-crease origami-inspired movable footbridge is investigated using finite element analysis. Static analysis and sizing according to US footbridge design code are presented for the critical configurations of the footbridge. Results show that the footbridge can meet typical civil engineering design criteria and illustrate the potential of curved-crease folding mechanisms to inspire the development of movable structures.

Generation of planar tensegrity structures through cellular multiplication

Abstract Tensegrity structures are frameworks in a stable self-equilibrated prestress state that have been applied in various fields in science and engineering. Research into tensegrity structures has resulted in reliable techniques for their form finding and analysis. However, most techniques address topology and form separately. This paper presents a bio-inspired approach for the combined topology identification and form finding of planar tensegrity structures. Tensegrity structures are generated using tensegrity cells (elementary stable self-stressed units that have been proven to compose any tensegrity structure) according to two multiplication mechanisms: cellular adhesion and fusion. Changes in the dimension of the self-stress space of the structure are found to depend on the number of adhesion and fusion steps conducted as well as on the interaction among the cells composing the system. A methodology for defining a basis of the self-stress space is also provided. Through the definition of the equilibrium shape, the number of nodes and members as well as the number of self-stress states, the cellular multiplication method can integrate design considerations, providing great flexibility and control over the tensegrity structure designed and opening the door to the development of a whole new realm of planar tensegrity systems with controllable characteristics.

Comments on the Paper: “Debunking “Tensegrity” — A Personal Perspective” by Ariel Hanaor:

247 Tensegrity was introduced in the 1950s and since then many researchers from various fields have focused on the topic. There are still a lot of questions that need to be answered. Therefore, the role of “devil’s advocate” taken by the author is important for discussions and I appreciate his willingness to take this role, as well as the position of the editor who included this article in the special issue on tensegrity.