Abstract

This paper studies the dynamic deployment of cylindrical thin-shell structures with open cross section, attached to a rigid base. The structures are elastically folded and then released. Previous experiments have shown that the total energy decreases while a fold moves back and forth along the structure, which was explained in terms of energy losses related to the fold “bouncing” against the boundary. This paper uses a rigorous numerical simulation, based on an in-house isogeometric shell finite element code that simultaneously eliminates shear locking and hourglassing without any intrinsic energy dissipation, to show that the total energy of the system is conserved during deployment. The discrepancy with the previous results is explained by showing that energy transfers from low-frequency, “rigid body” modes, to higher frequency modes.

References

1.
Miura
,
K.
, and
Pellegrino
,
S.
,
2020
,
Forms and Concepts for Lightweight Structures
,
Cambridge University Press
,
Cambridge
.
2.
Seffen
,
K.
, and
Pellegrino
,
S.
,
1999
, “
Deployment Dynamics of Tape Springs
,”
Proc. R. Soc. Lond. Ser. A: Math. Phys. Eng. Sci.
,
455
(
1983
), pp.
1003
1048
.
3.
Hoffait
,
S.
,
Brüls
,
O.
,
Granville
,
D.
,
Cugnon
,
F.
, and
Kerschen
,
G.
,
2010
, “
Dynamic Analysis of the Self-locking Phenomenon in Tape-Spring Hinges
,”
Acta Astronautica
,
66
(
7–8
), pp.
1125
1132
.
4.
Wilson
,
L. L.
,
2017
, “
Analysis of Packaging and Deployment of Ultralight Space Structures
,” PhD thesis,
California Institute of Technology
,
Pasadena, CA
.
5.
Mallikarachchi
,
H.
, and
Pellegrino
,
S.
,
2014
, “
Deployment Dynamics of Ultrathin Composite Booms With Tape-Spring Hinges
,”
J. Spacecraft Rockets
,
51
(
2
), pp.
604
613
.
6.
Dewalque
,
F.
,
Rochus
,
P.
, and
Brüls
,
O.
,
2015
, “
Importance of Structural Damping in the Dynamic Analysis of Compliant Deployable Structures
,”
Acta Astronautica
,
111
, pp.
323
333
.
7.
Guinot
,
F.
,
Bourgeois
,
S.
,
Cochelin
,
B.
, and
Blanchard
,
L.
,
2012
, “
A Planar Rod Model With Flexible Thin-Walled Cross-Sections. Application to the Folding of Tape Springs
,”
Int. J. Solids Struct.
,
49
(
1
), pp.
73
86
.
8.
Picault
,
E.
,
Marone-Hitz
,
P.
,
Bourgeois
,
S.
,
Cochelin
,
B.
, and
Guinot
,
F.
,
2014
, “
A Planar Rod Model With Flexible Cross-Section for the Folding and the Dynamic Deployment of Tape Springs: Improvements and Comparisons With Experiments
,”
Int. J. Solids Struct.
,
51
(
18
), pp.
3226
3238
.
9.
Stolarski
,
H.
, and
Belytschko
,
T.
,
1983
, “
Shear and Membrane Locking in Curved C0 Elements
,”
Comput. Methods Appl. Mech. Eng.
,
41
(
3
), pp.
279
296
.
10.
Belytschko
,
T.
,
Ong
,
J.
,
Liu
,
W.
, and
Kennedy
,
J.
,
1984
, “
Hourglass Control in Linear and Nonlinear Problems
,”
Comput. Methods Appl. Mech. Eng.
,
43
(
3
), pp.
251
276
.
11.
Hughes
,
T. J.
,
Cottrell
,
J. A.
, and
Bazilevs
,
Y.
,
2005
, “
Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry and Mesh Refinement
,”
Comput. Methods Appl. Mech. Eng.
,
194
(
39–41
), pp.
4135
4195
.
12.
Hokkanen
,
J.
, and
Pedroso
,
D.
,
2020
, “
Quadrature Rules for Isogeometric Shell Formulations: Study Using a Real-World Application About Metal Forming
,”
Comput. Methods Appl. Mech. Eng.
,
363
, p.
112904
.
13.
Kiendl
,
J.
,
Bletzinger
,
K.-U.
,
Linhard
,
J.
, and
Wüchner
,
R.
,
2009
, “
Isogeometric Shell Analysis With Kirchhoff–Love Elements
,”
Comput. Methods Appl. Mech. Eng.
,
198
(
49–52
), pp.
3902
3914
.
14.
Cook
,
R. D.
,
Malkus
,
D. S.
,
Plesha
,
M. E.
, and
Witt
,
R. J.
,
2002
,
Concepts and Applications of Finite Element Analysis
, 4th ed.,
John Wiley and Sons Ltd.
,
Singapore
.
15.
Echter
,
R.
,
Oesterle
,
B.
, and
Bischoff
,
M.
,
2013
, “
A Hierarchic Family of Isogeometric Shell Finite Elements
,”
Comput. Methods Appl. Mech. Eng.
,
254
, pp.
170
180
.
16.
Stolarski
,
H.
, and
Belytschko
,
T.
,
1982
, “
Membrane Locking and Reduced Integration for Curved Elements
,”
ASME J. Appl. Mech.
,
49
, pp.
172
176
.
17.
Jacquotte
,
O.-P.
, and
Oden
,
J. T.
,
1984
, “
Analysis of Hourglass Instabilities and Control in Underintegrated Finite Element Methods
,”
Comput. Methods Appl. Mech. Eng.
,
44
(
3
), pp.
339
363
.
18.
Adam
,
C.
,
Bouabdallah
,
S.
,
Zarroug
,
M.
, and
Maitournam
,
H.
,
2015
, “
Improved Numerical Integration for Locking Treatment in Isogeometric Structural Elements. Part II: Plates and Shells
,”
Comput. Methods Appl. Mech. Eng.
,
284
, pp.
106
137
.
19.
Fujiwara
,
K.
,
Okamoto
,
Y.
,
Kameari
,
A.
, and
Ahagon
,
A.
,
2005
, “
The Newton–Raphson Method Accelerated by Using a Line Search-Comparison Between Energy Functional and Residual Minimization
,”
IEEE Trans. Magn.
,
41
(
5
), pp.
1724
1727
.
20.
Newmark
,
N. M.
,
1959
, “
A Method of Computation for Structural Dynamics
,”
J. Eng. Mech. Div.
,
85
(
3
), pp.
67
94
.
21.
Reinsch
,
C. H.
,
1967
, “
Smoothing by Spline Functions
,”
Numer. Math.
,
10
(
3
), pp.
177
183
.
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