Abstract

Tensegrities are prestressable trusses that have been proven to support various load distributions with minimum mass. This article presents a novel efficient method for designing lightweight tensegrities under local and global failure constraints. Local failure includes buckling and material yielding of individual members in the tensegrity. Global failure refers to global buckling of the tensegrity, where it loses stability without undergoing local failure at its individual members. The formulation and numerical approach to determine the critical global buckling forces and mode shapes of tensegrities with arbitrary shape and topology are first provided. Next, the design method considering local and global failure is presented, which starts with the local sizing of the member areas of the given tensegrity for the prevention of local failure. The method then determines the dominant failure mode by comparing the external forces and the critical global buckling force of the locally sized structure. If the critical global buckling force is larger than the external force, the dominant mode is a local failure and the locally sized design is returned as the minimum mass design. Conversely, if global failure is the dominant mode, different global reinforcement approaches are applied to raise the critical buckling force of the structure until it matches the external force, preventing global buckling. These reinforcement approaches include increasing the areas of the members and increasing the prestress in the tensegrity. Representative examples are provided to demonstrate the effectiveness of the design method considering box and T-bar tensegrities.

References

References
1.
Buckminster
,
F. R.
,
1962
, “
Tensile-Integrity Structures
,”
U.S. Patent No. 3,063,521
.
2.
Skelton
,
R. E.
, and
de Oliveira
,
M. C.
,
2009
,
Tensegrity Systems
,
Springer
,
New York
.
3.
Goyal
,
R.
,
Skelton
,
R. E.
, and
Peraza Hernandez
,
E. A.
,
2020
, “
Design of Minimal Mass Load-Bearing Tensegrity Lattices
,”
Mech. Res. Commun.
,
103
, p.
103477
. 10.1016/j.mechrescom.2020.103477
4.
Skelton
,
R. E.
, and
de Oliveira
,
M. C.
,
2010
, “
Optimal Tensegrity Structures in Bending: The Discrete Michell Truss
,”
J. Franklin Inst.
,
347
(
1
), pp.
257
283
. 10.1016/j.jfranklin.2009.10.009
5.
Carpentieri
,
G.
,
Skelton
,
R. E.
, and
Fraternali
,
F.
,
2015
, “
Minimum Mass and Optimal Complexity of Planar Tensegrity Bridges
,”
Int. J. Space Struct.
,
30
(
3–4
), pp.
221
243
. 10.1260/0266-3511.30.3-4.221
6.
SunSpiral
,
V.
,
Gorospe
,
G.
,
Bruce
,
J.
,
Iscen
,
A.
,
Korbel
,
G.
,
Milam
,
S.
,
Agogino
,
A.
, and
Atkinson
,
D.
,
2013
, “
Tensegrity Based Probes for Planetary Exploration: Entry, Descent and Landing (EDL) and Surface Mobility Analysis
,”
Int. J. Planet. Probes
,
7
, p.
13
.
7.
Rimoli
,
J. J.
,
2018
, “
A Reduced-Order Model for the Dynamic and Post-Buckling Behavior of Tensegrity Structures
,”
Mech. Mater.
,
116
, pp.
146
157
.
IUTAM Symposium on Dynamic Instabilities in Solids
. 10.1016/j.mechmat.2017.01.009
8.
Goyal
,
R.
,
Peraza Hernandez
,
E. A.
, and
Skelton
,
R.
,
2019
, “
Analytical Study of Tensegrity Lattices for Mass-Efficient Mechanical Energy Absorption
,”
Int. J. Space Struct.
,
34
(
1–2
), pp.
3
21
. 10.1177/0956059919845330
9.
Zhao
,
L.
, and
Peraza Hernandez
,
E. A.
,
2019
, “
Theoretical Study of Tensegrity Systems With Tunable Energy Dissipation
,”
Extreme Mech. Lett.
,
32
, p.
100567
. 10.1016/j.eml.2019.100567
10.
Silverman
,
R. E.
, and
Peraza Hernandez
,
E. A.
,
2019
, “
Designing Lightweight Tensegrity-Based Structures and Materials of Tailorable Thermal Expansion
,”
International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Anaheim, CA
. https://doi.org/10.1115/DETC2019-97304
11.
Jiang
,
S.
,
Skelton
,
R. E.
, and
Peraza Hernandez
,
E. A.
,
2020
, “
Analytical Equations for the Connectivity Matrices and Node Positions of Minimal and Extended Tensegrity Plates
,”
Int. J. Space Struct.
, p.
0956059920902375
. https://doi.org/10.1177/0956059920902375
12.
Peraza Hernandez
,
E. A.
,
Goyal
,
R.
, and
Skelton
,
R. E.
,
2018
, “
Tensegrity Structures for Mass-Efficient Planetary Landers
,”
Proceedings of IASS Annual Symposia
,
Boston, MA
,
July 16–20
, pp.
1
8
.
13.
Bel Hadj Ali
,
N.
, and
Smith
,
I. F. C.
,
2010
, “
Dynamic Behavior and Vibration Control of a Tensegrity Structure
,”
Int. J. Solids Struct.
,
47
(
9
), pp.
1285
1296
. 10.1016/j.ijsolstr.2010.01.012
14.
Atig
,
M.
,
Ouni
,
M. H. E.
, and
Kahla
,
N. B.
,
2017
, “
Dynamic Stability Analysis of Tensegrity Systems
,”
Eur. J. Environ. Civ. Eng.
,
23
(
6
), pp.
675
692
. 10.1080/19648189.2017.1304275
15.
Xu
,
X.
, and
Luo
,
Y.
,
2010
, “
Multistable Tensegrity Structures
,”
J. Struct. Eng.
,
137
(
1
), pp.
117
123
. 10.1061/(ASCE)ST.1943-541X.0000281
16.
Sumi
,
S.
,
Boehm
,
V.
, and
Zimmermann
,
K.
,
2017
, “
A Multistable Tensegrity Structure With a Gripper Application
,”
Mech. Mach. Theory
,
114
, pp.
204
217
. 10.1016/j.mechmachtheory.2017.04.005
17.
Micheletti
,
A.
,
2013
, “
Bistable Regimes in an Elastic Tensegrity System
,”
Proc. R. Soc. A Math. Phys. Eng. Sci.
,
469
(
2154
), p.
20130052
. 10.1098/rspa.2013.0052
18.
Murakami
,
H.
, and
Nishimura
,
Y.
,
2001
, “
Static and Dynamic Characterization of Some Tensegrity Modules
,”
ASME J. Appl. Mech.
,
68
(
1
), pp.
19
27
. 10.1115/1.1331058
19.
Montuori
,
R.
, and
Skelton
,
R. E.
,
2017
, “
Globally Stable Tensegrity Compressive Structures for Arbitrary Complexity
,”
Compos. Struct.
,
179
, pp.
682
694
. 10.1016/j.compstruct.2017.07.089
20.
Lazopoulos
,
K. A.
,
2005
, “
Stability of an Elastic Tensegrity Structure
,”
Acta Mech.
,
179
(
1–2
), pp.
1
10
. 10.1007/s00707-005-0244-0
21.
De Tommasi
,
D.
,
Marano
,
G. C.
,
Puglisi
,
G.
, and
Trentadue
,
F.
,
2015
, “
Optimal Complexity and Fractal Limits of Self-Similar Tensegrities
,”
Proc. R. Soc. Lond. A Math. Phys. Eng. Sci.
,
471
(
2184
), p.
20150250
. 10.1098/rspa.2015.0250
22.
De Tommasi
,
D.
,
Marano
,
G.
,
Puglisi
,
G.
, and
Trentadue
,
F.
,
2017
, “
Morphological Optimization of Tensegrity-Type Metamaterials
,”
Compos. Part B: Eng.
,
115
, pp.
182
187
.
Composite Lattices and Multiscale Innovative Materials and Structures
. 10.1016/j.compositesb.2016.10.017
23.
Ohsaki
,
M.
, and
Zhang
,
J.
,
2006
, “
Stability Conditions of Prestressed Pin-Jointed Structures
,”
Int. J. of Non-Linear Mech.
,
41
(
10
), pp.
1109
1117
. 10.1016/j.ijnonlinmec.2006.10.009
24.
Zhang
,
J.
, and
Ohsaki
,
M.
,
2007
, “
Stability Conditions for Tensegrity Structures
,”
Int. J. Solids Struct.
,
44
(
11–12
), pp.
3875
3886
. 10.1016/j.ijsolstr.2006.10.027
25.
Ohsaki
,
M.
,
Zhang
,
J.
, and
Elishakoff
,
I.
,
2012
, “
Multiobjective Hybrid Optimization–Antioptimization for Force Design of Tensegrity Structures
,”
ASME J. Appl. Mech.
,
79
(
2
), p.
021015
. 10.1115/1.4005580
26.
Xu
,
X.
,
Wang
,
Y.
,
Luo
,
Y.
, and
Hu
,
D.
,
2018
, “
Topology Optimization of Tensegrity Structures Considering Buckling Constraints
,”
J. Struct. Eng.
,
144
(
10
), p.
04018173
. 10.1061/(ASCE)ST.1943-541X.0002156
27.
Liu
,
K.
, and
Paulino
,
G. H.
,
2019
, “
Tensegrity Topology Optimization by Force Maximization on Arbitrary Ground Structures
,”
Struct. Multidiscip. Optim.
,
59
(
6
), pp.
2041
2062
. 10.1007/s00158-018-2172-3
28.
Kanno
,
Y.
,
2013
, “
Topology Optimization of Tensegrity Structures Under Compliance Constraint: A Mixed Integer Linear Programming Approach
,”
Optim. Eng.
,
14
(
1
), pp.
61
96
. 10.1007/s11081-011-9172-0
29.
Pellegrino
,
S.
, and
Calladine
,
C.
,
1986
, “
Matrix Analysis of Statically and Kinematically Indeterminate Frameworks
,”
Int. J. Solids Struct.
,
22
(
4
), pp.
409
428
. 10.1016/0020-7683(86)90014-4
30.
Guest
,
S.
,
2006
, “
The Stiffness of Prestressed Frameworks: A Unifying Approach
,”
Int. J. Solids Struct.
,
43
(
3–4
), pp.
842
854
. 10.1016/j.ijsolstr.2005.03.008
31.
Argyris
,
J. H.
, and
Scharpf
,
D. W.
,
1972
, “
Large Deflection Analysis of Prestressed Networks
,”
J. Struct. Div.
,
98
(
3
), pp.
633
654
.
32.
Goyal
,
R.
, and
Skelton
,
R. E.
,
2019
, “
Tensegrity System Dynamics With Rigid Bars and Massive Strings
,”
Multibody Syst. Dyn.
,
46
(
3
), pp.
203
228
. 10.1007/s11044-019-09666-4
33.
Gere
,
J. M.
, and
Goodno
,
B. J.
,
2011
,
Mechanics of Materials
,
Cengage Learning
,
Boston, MA
34.
Golub
,
G. H.
, and
Van Loan
,
C. F.
,
1996
,
Matrix Computations
, 3rd ed.,
The Johns Hopkins University Press
,
Boston, MA
.
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