Abstract
This paper presents a geometrically nonlinear analytical model of the flexible cylindrical rim of a deployable precision large space antenna reflectors made of shape-memory polymer composites. A nonlinear boundary-value problem for the rim in the deformed (folded) configuration is formulated and exact analytical solutions in elliptic functions and integrals describing the deformation modes of the rim are obtained. Exact analytical solutions based on the geometrically nonlinear model are obtained and can be used to determine preliminary geometric dimensions and optimal shape of the flexible rim along with the estimation of the accumulated energy.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. Shintate, K. Terada, M. Usui, et al., “Large Deployable Reflector (LDR),” J. Nat. Inst. Inform. Comm. Technol. 50 (3/4), 33–39 (2003).
Y. Murata, H. Hirabayashi, M. C. Natori, et al., “Development of the Large and High Accuracy Deployable Antenna for the VSOP-2 Mission”, www.ursi.org/Proceedings/ProcGA05/pdf/BP.11(01277).pdf.
G. Tibert, “Deployable Tensegrity Structures for Space Applications,” Ph. D. Thesis. (Roy. Inst. Technol., Stockholm, 2002), www2.mech.kth.se/~gunnart/TibertDocThesis.pdf.
A. V. Lopatin and M. A. Rutkovskaya, “Design of Large Space Antenna Composite Rim,” Composite Structures 76, 99–105 (2006).
A. V. Lopatin, Yu. V. Zakharov, K. G. Okhotkin, et al., “Geometrically Nonlinear Model of a Deployable Large Space Antenna Rim with Flexible Composite Elements,” Vestn. Sib. Gos. Aerokosm. Univ., No. 5, 75–80 (2012).
A. Yu. Vlasov, K. A. Pasechnik, and V. A. Martynov, “Design and Technological Aspects of Producing Precision Articles of Complex Shape Using Polymer Composites,” Vestn. Sib. Gos. Aerokosm. Univ. 17 (2), 460–465 (2016).
Yu. B. Zakharov and K. D. Okhotkin, “Nonlinear Bending of Thin Elastic Rods,” Prikl. Mekh. Tekh. Fiz. 43 (5), 124–131 (2002) [J. Appl. Mech. Tech. Phys. 43 (5), 739–744 (2002)].
S. S. Antman, Nonlinear Problems of Elasticity (Springer, New York, 1995).
D. E. Panayotounakos and A. B. Sotiropoulos, “Exact Parametric Analytic Solutions of the Elastic ODEs for Bars Including Effects of the Transverse Deformation,” Intern. J. Non-Linear Mech. 39 (10), 1555–1570 (2004).
M. Batista, “Analytical Treatment of Equilibrium Configurations of Cantilever under Terminal Loads using Jacobi Elliptical Functions,” Intern. J. Solids Structures 51 (13), 2308–2326 (2014).
E. P. Popov, Theory and Design of Flexible Elastic Rods (Nauka, Moscow, 1986) [in Russian].
M. A. Lavrent’ev and A. Yu. Ishlinskii, “Dynamic Buckling of Elastic Systems,” Dokl. Akad. Nauk SSSR 64 (6), 779–782 (1949).
N. F. Morozov, A. K. Belyaev, P. E. Tovstik, and T. P. Tovstik, “Ishlinskii–Lavrent’ev Problem at the Initial Stage of Motion,” Dokl. Akad. Nauk 463 (5), 543–546 (2015).
V. V. Alekhin, B. D. Annin, A. V. Babichev, and S. N. Korobeynikov, “Natural Vibrations and Buckling of Graphene Sheets,” Dokl. Akad. Nauk 453 (1), 37–40 (2013).
L. I. Shkutin, “Numerical Analysis of the Branched Forms of Bending for a Rod,” Prikl. Mekh. Tekh. Fiz. 42 (2), 141–147 (2001) [J. Appl. Mech. Tech. Phys. 42 (2), 310–315 (2001)].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © K.G. Okhotkin, A.Yu. Vlasov, Yu.V. Zakharov, B.D. Annin.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 58, No. 5, pp. 190–200, September–October, 2017.
Rights and permissions
About this article
Cite this article
Okhotkin, K.G., Vlasov, A.Y., Zakharov, Y.V. et al. Analytical modeling of the flexible rim of space antenna reflectors. J Appl Mech Tech Phy 58, 924–932 (2017). https://doi.org/10.1134/S0021894417050194
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894417050194