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Tensegrity Structures

Part of the Mathematics for Industry Book Series (volume 6)

DOI: 10.1007/978-4-431-54813-3

ISBN: 978-4-431-54812-6

Publisher: Springer Japan - Springer Journals

Mar 18, 2015

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Introduction

Zhang, Jing Yao; Ohsaki, Makoto

Pages: 1 –13

[In this introductory chapter, we first introduce the basic concepts and some applications of tensegrity structures, and then present their design problems which motivates our study in this book. Finally, a brief review of the existing researches on the design problems is given.]
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Equilibrium

Zhang, Jing Yao; Ohsaki, Makoto

Pages: 15 –54

[Tensegrity structures are classified as prestressed pin-jointed structures, and they have distinct properties compared to other pin-jointed structures: (1) they are free-standing, without any support; and (2) they have both tensile and compressive members. Prior to further studies on tensegrity...
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Self-equilibrium Analysis by Symmetry

Zhang, Jing Yao; Ohsaki, Makoto

Pages: 55 –96

[For a tensegrity structure with high level of symmetry, its equilibrium analysis can be significantly simplified by considering the representative nodes only. This makes presentation of analytical conditions possible. In this chapter, we study several classes of symmetric structures, including...
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Stability

Zhang, Jing Yao; Ohsaki, Makoto

Pages: 97 –135

[In this chapter, we present formulations of the stiffness matrices, including the tangent, linear, and geometrical stiffnesses for a prestressed pin-jointed structure. Moreover, three different stability criteria—stability, prestress-stability, and super-stability—are presented for its stability...
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Force Density Method

Zhang, Jing Yao; Ohsaki, Makoto

Pages: 137 –170

[This chapter presents a numerical method for form-finding problem of tensegrity structures, by making use of the idea of force density method originally developed for cable-nets. The basic idea is to find the feasible force densities satisfying the non-degeneracy condition as presented in Chap....
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Prismatic Structures of Dihedral Symmetry

Zhang, Jing Yao; Ohsaki, Makoto

Pages: 171 –203

[This chapter presents the conditions for self-equilibrium and super-stability of prismatic tensegrity structures with dihedral symmetry in an analytical manner. These conditions are derived based on the analytical symmetry-adapted force density matrix given in Appendix D.]
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Star-Shaped Structures of Dihedral Symmetry

Zhang, Jing Yao; Ohsaki, Makoto

Pages: 205 –231

[This chapter presents self-equilibrium as well as super-stability conditions for star-shaped structures that have dihedral symmetry. Star-shaped tensegrity structures have the same dihedral symmetry and similar configurations to the prismatic structures studied in Chap. 6. The star-shaped...
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Regular Truncated Tetrahedral Structures

Zhang, Jing Yao; Ohsaki, Makoto

Pages: 233 –248

[In this chapter, we present the analytical conditions for self-equilibrium and super-stability of the regular truncated tetrahedral tensegrity structures. These structures have tetrahedral symmetry, and their nodes have one-to-one correspondence to the symmetry operations of a tetrahedral group....

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