Form-finding and analysis of bending-active systems using dynamic relaxation

A common challenge for architects and engineers in the development of structurally efficient systems is the generation of good structural forms for a specific set of boundary conditions, a process known as form-finding. Dynamic relaxation is a wellestablished explicit numerical analysis method used for the form-finding and analysis of highly non-linear structures. With the incorporation of bending and clustered elements, the method can be extended for the analysis of complex curved and bending-active structural systems. Bending-active structures employ elastic deformation to generate complex curved shapes. With low computational cost, dynamic relaxation has large potential as a design and analysis technique of novel large span structural systems such as spline stressed membranes and small scale robotics, bio-mechanics and architectural applications made of novel materials such as electro- active polymers (EAP)

ENAC Poster 2010: Active and deployable structures: a tensegrity pedestrian bridge

Research concept: Imagine structures that could function like living systems changing their properties in response to changes in their environment… Research objective: Design a tensegrity pedestrian bridge that can change shape and properties using the same active control system

Analysis of clustered tensegrity structures using a modified dynamic relaxation algorithm

Tensegrities are spatial, reticulated and lightweight structures that are increasingly investigated as structural solutions for active and deployable structures. Tensegrity systems are composed only of axially loaded elements and this provides opportunities for actuation and deployment through changing element lengths. In cable-based actuation strategies, the deficiency of having to control too many cable elements can be overcome by connecting several cables. However, clustering active cables significantly changes the mechanics of classical tensegrity structures. Challenges emerge for structural analysis, control and actuation. In this paper, a modified dynamic relaxation (DR) algorithm is presented for static analysis and form-finding. The method is extended to accommodate clustered tensegrity structures. The applicability of the modified DR to this type of structure is demonstrated. Furthermore, the performance of the proposed method is compared with that of a transient stiffness method. Results obtained from two numerical examples show that the values predicted by the DR method are in a good agreement with those generated by the transient stiffness method. Finally it is shown that the DR method scales up to larger structures more efficiently. (C) 2010 Elsevier Ltd. All rights reserved

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

Deployment aspects of a tensegrity-ring pedestrian bridge

Tensegrity structures are spatial systems that are composed of tension and compression components in a self-equilibrated prestress stable state. Although tensegrity systems were first introduced in 1950s, few examples have been used for civil engineering purposes. In this paper, tensegrity-ring modules are used for a deployable pedestrian bridge. Ring modules belong to a special family of tensegrity systems composed of a single strut circuit. Assembled in a “hollow-rope” structure, ring modules were shown to be a viable system for a tensegrity pedestrian bridge. Furthermore, ring modules are deployable systems that can change shape by adjusting cable lengths (cable actuation). This paper focuses on the deployment of a tensegrity-ring pedestrian bridge. A geometric study of the deployment for a single module identified the solution space that allows deployment without strut jamming. The optimal deployment path is identified amongst hundreds of possible solutions. Moreover, the number of actuators required and their placement in the module are determined by the deployment path that is applied. Cable-based actuation often has the drawback of having to control too many cable elements. Therefore, a deployment path that minimizes the number of actuated cables was found. The number of actuated cables is further reduced by employing continuous cables. A first generation prototype made of aluminium struts and steel cables was used to verify experimentally both findings. The structural response during unfolding and folding is studied numerically using a modified dynamic relaxation algorithm. A well-known dynamic-relaxation algorithm is extended to accommodate clustered tensegrity structures (tensegrity systems with continuous cables). The deployment-analysis algorithm applies cable-length changes first, to create mechanisms allowing deployment and then, to find new equilibrium configurations. Deployment is thus carried out through an equilibrium manifold. The deployment-actuation step size is identified as a critical parameter for successful deployment. Large deployment steps lead to instable configurations while small steps are computationally expensive. Due to mechanism-based deployment, the total energy in the structural system remains nearly constant during deployment. Elastic potential energy due to cable tension is the highest energy identified while kinetic energy and the work of torque friction on strut-to-strut joints are relatively low. Finally, internal forces increase during deployment but remain low compared with service self-stress values showing that deployment is not a critical phase for the design of the bridge

Designing tensegrity modules for pedestrian bridges

Tensegrity systems are spatial structures composed of tensile and compression components in a self-equilibrated state of prestress. The tensegrity concept has already been studied by researchers in various fields over the past decades. A family of tensegrity modules that can offer promising solutions for civil engineering applications such as tensegrity domes, towers and bridges is analyzed. Research into tensegrity systems has resulted in reliable techniques for form finding and structural analysis. However, the tensegrity concept is not yet part of mainstream structural design. This paper presents a design study of a tensegrity-based pedestrian bridge. The structural performance of the bridge using three tensegrity modules is evaluated through parametric studies. Design requirements for pedestrian bridges and results of parametric studies are used to define a design procedure that optimizes section sizes for this type of structure. A structural efficiency indicator is proposed and used to compare proposals for feasible bridge configurations. Design results illustrate that the hollow-rope tensegrity bridge can efficiently meet typical design criteria

Deployment of a Pentagonal Hollow-Rope Tensegrity Module

Tensegrity structures are spatial reticulated structures composed of cables and struts. Tensegrity systems are good candidates for adaptive and deployable structures and thus have applications in various engineering fields. A “hollow-rope” tensegrity system composed of tensegrity-ring modules has been demonstrated by the authors to be a viable system for a pedestrian bridge. This paper focuses on the deployment of pentagonal ring modules. A geometric study is performed to identify the deployment-path space allowing deployment without strut contact. Two actuation schemes are explored for deployment: the first scheme employs only actuated cables, while the second combines actuated cables with spring elements. In both schemes, continuous cables are used to reduce the number of actuators required. Finally, the structural response of the module during deployment is studied numerically using a modified dynamic relaxation algorithm

Design optimization and dynamic analysis of a tensegrity-based footbridge

Tensegrity structures are spatial structural systems composed of struts and cables with pin-jointed connections. Their stability is provided by the self-stress state in tensioned and compressed members. Although much progress has been made in advancing research into the tensegrity concept, a rapid survey of current activities in engineering practice shows that much of its potential has yet to be accomplished. A design optimization study for a tensegrity-based footbridge is presented in order to further advance the tensegrity concept in modern structural engineering. In the absence of specific design guidelines, design requirements for a tensegrity footbridge are stated. A genetic algorithm based optimization scheme is used to find a cost-effective design solution. The dynamic performance of the tensegrity footbridge is studied through parametric studies. Design results illustrate that the proposed tensegrity-based footbridge meets typical static and dynamic design criteria

Deployment analysis of a pentagonal tensegrity-ring module

Ring modules are tensegrity systems that include a single strut circuit and recently, they have been shown to be viable systems for pedestrian bridges. Furthermore, their shape can be controlled using cable actuation. This paper focuses on the deployment of a pentagonal tensegrity-ring module. A geometric study is conducted to identify the deployment-solution space without strut contact. Deployment paths and actuation requirements are explored. The structural response of the module during deployment is analyzed using a modified dynamic relaxation method

Structures actives déployables

"Structures actives déployables