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Flexibility-based pre-stress design of tensegrity structures
KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.ORCID iD: 0000-0002-5819-4544
KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.ORCID iD: 0000-0001-6802-8331
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Tensegritiy structures have been subjects of research for many years, but very few of them have been built. One major disadvantage of tensegrities compare to regular truss structures is their low stiffness. This papers aims to have a new look at the stiffness problem of tensegrity structures. Here, it is assumed that the form-finding step has been completed and the axial stiffness of the elements is known. We introduce a tool for stiffness characterization of a given tensegrity structure for different pre-stress magnitudes. Since the pre-stress has a critical influence on the stability of the structure with a role to prevent or postpone slackening, the magnitude of pre-stress of the structure exposed to large external loads and disturbances are found. Finite elements are utilized in the solution for the non-linear static analysis. The method is based on geometrical interpretation of flexibility of unconstrained nodes. Suggested concept, flexibility analysis, shows promising properties in finding flexible nodes, weak directions of structure, detection of cable elements with higher risk of going slack and better knowledge of influence of various external loads. The authors believe results of this research could help the researchers and designer of better understanding the behavior of tensegrity structures.

 

National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-34036OAI: oai:DiVA.org:kth-34036DiVA: diva2:418849
Available from: 2011-05-24 Created: 2011-05-24 Last updated: 2012-09-04Bibliographically approved
In thesis
1. Stiffness modification of tensegrity structures
Open this publication in new window or tab >>Stiffness modification of tensegrity structures
2011 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Although the concept of tensegrity structures was invented in the beginning of the twentieth century, the applications of these structures are limited, partially due to their low stiffness. The stiffness of tensegrities comes from topology, configuration, pre-stress and initial axial element stiffnesses.

 The first part of the present work is concerned with finding the magnitude of pre-stress. Its role in stiffness of tensegrity structures is to postpone the slackening of cables. A high pre-stress could result in instability of the structure due to buckling and yielding of compressive and tension elements, respectively. Tensegrity structures are subjected to various external loads such as self-weight, wind or snow loads which in turn could act in different directions and be of different magnitudes. Flexibility analysis is used to find the critical load combinations. The magnitude of pre-stress, in order to sustain large external loads, is obtained through flexibility figures, and flexibility ellipsoids are employed to ensure enough stiffness of the structure when disturbances are applied to a loaded structure.

 It has been seen that the most flexible direction is very much sensitive to the pre-stress magnitude and neither analytical methods nor flexibility ellipsoids are able to find the most flexible directions. The flexibility figures from a non-linear analysis are here utilized to find the weak directions.

 In the second part of the present work, a strategy is developed to compare tensegrity booms of triangular prism and Snelson types with a truss boom. It is found that tensegrity structures are less stiff than a truss boom when a transversal load is applied. An optimization approach is employed to find the placement of the actuators and their minimum length variations. The results show that the bending stiffness can be significantly improved, but still an active tensegrity boom is less stiff than a truss boom. Genetic algorithm shows high accuracy of searching non-structural space.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. viii, 24 p.
Series
Trita-MEK, ISSN 0348-467X ; 2011:02
Keyword
tensegrity, boom, finite element analysis, genetic algorithm, flexibility analysis, active structure
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-34039 (URN)
Presentation
2011-05-26, 10:15
Opponent
Supervisors
Note
QC 20110524Available from: 2011-05-24 Created: 2011-05-24 Last updated: 2011-05-24Bibliographically approved
2. Stiffness and vibration properties of slender tensegrity structures
Open this publication in new window or tab >>Stiffness and vibration properties of slender tensegrity structures
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The stiffness and frequency properties of tensegrity structures are functions of the pre-stress, topology, configuration, and axial stiffness of the elements. The tensegrity structures considered are tensegrity booms, tensegrity grids, and tensegrity power lines.

A study has been carried out on the pre-stress design. It includes (i) finding the most flexible directions for different pre-stress levels, (ii) finding the pre-stress pattern which maximizes the first natural frequency.

To find the optimum cross-section areas of the elements for triangular prism and Snelson tensegrity booms, an optimization approach is utilized. A constant mass criterion is considered and the genetic algorithm (GA) is used as the optimization method.

The stiffness of the triangular prism and Snelson tensegrity booms are modified by introducing actuators. An optimization approach by means of a GA is employed to find the placement of the actuators and their minimum length variations. The results show that the bending stiffness improves significantly, but still an active tensegrity boom is less stiff than a passive truss boom. The GA shows high accuracy in searching the non-structural space.

The tensegrity concept is employed to design a novel transmission power line .A tensegrity prism module is selected as the building block. A complete parametric study is performed to investigate the influence of several parameters such as number of modules and their dimensions on the stiffness and frequency of the structure. A general approach is suggested to design the structure considering wind and ice loads. The designed structure has more than 50 times reduction of the electromagnetic field and acceptable deflections under several loading combinations.

A study on the first natural frequencies of Snelson, prisms, Micheletti, Marcus and X-frame based tensegrity booms has been carried out. The result shows that the differences in the first natural frequencies of the truss and tensegrity booms are significant and not due to the number of mechanisms or pre-stress levels. The tensegritybooms of the type Snelson with 2 bars and prism with 3 bars have higher frequencies among tensegrity booms.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. vii, 25 p.
Keyword
Tensegrity booms, Tensegrity grids, Tensegrity power lines, Finite element analysis, Genetic algorithm, Flexibility analysis, Form-finding, Pre-stress design, Optimization
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-101769 (URN)978-91-7501-461-6 (ISBN)
Public defence
2012-09-20, Sal F3, Lindstedtsvägen 26, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20120904

Available from: 2012-09-04 Created: 2012-09-03 Last updated: 2012-09-04Bibliographically approved

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Eriksson, AndersTibert, Gunnar

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