A new approach to optimizing the waffle shell sections of the launch vehicle is proposed. The waffle cantilever cylindrical shells are considered under the action of the axial force that is lower than the critical load. The nonuniformity load coefficient is calculated based on the analysis of the static stress-strain state using the finite element method. Considering the calculation data and analytical relations that are successfully applied in the design of launch vehicles, the optimal parameters are chosen. For this purpose, the structural surface is conventionally divided into the main zones with the nonuniformity coefficients exceeding a certain predetermined value, and the weight reduction zones. Since the main zones are characterized by significant stresses, they are enhanced via the increase in finning and shell thickness. Low stresses are observed within the zone of weight reduction, therefore finning and shell thickness can be reduced, as well as the structure can be lighter. In this case, both the cross-sectional dimensions of finning and shell thickness are subjected to variation. The results of the optimization of the tail section of the Antares launch vehicle are presented. It has been established that the weight of the weight-reduced tail section is 188 kg less than the weight of the original structure, which is 18% of the total weight.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. T. Lizin and V. A. Pyatkin, Design of Thin-Walled Structures [in Russian], Mashinostroenie, Moscow (1994).
I. Ya. Amiro and I. Ya. Zarutskii, Theory of Ribbed Shells [in Russian], Naukova Dumka, Kiev (1980).
I. Ya. Amiro, O. A. Grachev, V. A. Zarutskii, et al., Stability of Ribbed Shells of Rotation [in Russian], Naukova Dumka, Kiev (1987).
L. I. Balabukh, N. A. Alfutov, and B. I. Usyukin, Structural Mechanics of Rockets [in Russian], Vyschaya Shkola, Moscow (1984).
V. I. Mossakovskii, A. G. Makarenko, and P. I. Nikitin, Strength of Rocket Structures [in Russian], Vyschaya Shkola, Moscow (1990).
A. V. Karmishin, V. A. Lyaskovets, V. I. Myachenkov, and A. N. Frolov, Statics and Dynamics of Thin-Walled Shell Structures [in Russian], Mashinostroenie, Moscow (1975).
V. I. Myachenkov, Calculations of Machinebuilding Structures by Finite Element Method. Handbook [in Russian], Mashinostroenie, Moscow (1989).
V. P. Pechnikov, R. V. Zakharov, and R. V. Tarasova, “Design of waffle shells of rocket fuel tanks considering plastic strains,” Inzh. Sb. Ser. Nauka Innov., 11, 1–14 (2007).
A. V. Kondrat’ev, “Design of main nose fairings of launch vehicles made of polymer composite materials under the simultaneous thermal and mechanical exposure,” Vopr. Proekt. Proizv. Konstr. Letat. Apparat., 4, 11–22 (2019).
V. S. Gudramovich, É. L. Gart, D. V. Klimenko, et al., “Finite element analysis of elastoplastic stress-strain state of compartments of the rocket structures with notches,” Tekh. Mekh., 4, 52–61 (2011).
M. Sadeghifar, M. Bagheri, and A. A. Jafari, “Buckling analysis of stringer-stiffened laminated cylindrical shells with nonuniform eccentricity,” Arch. Appl. Mech., 81, No. 7, 875–886 (2011).
C. Cinquini, G. Guerlement, and D. Lamblin, “Shell-stiffener interaction. Application to simply supported cylindrical shells under uniform pressure,” Int. J. Solids Struct., 21, No. 5, 447–465 (1985).
S.-W. Yen, “Buckling of cylindrical shells with spiral stiffeners under uniform compression and torsion,” Comput. Struct., 11, No. 6, 587–595 (1980).
V. Birman, “Divergence instability of reinforced composite circular cylindrical shells,” Int. J. Solids Struct., 26, Nos. 5–6, 571–580 (1990).
Z. Ji and K. Yeh, “General solution for nonlinear buckling of nonhomogeneous axial symmetric ring and stringer stiffened cylindrical shells,” Comput. Struct., 34, No. 4, 585–591 (1990).
S. Sridharan, M. Zeggane, and J. H. Starnes, Jr, “Mode interaction analysis of stiffened shells using “locally buckled” elements,” Int. J. Solids Struct., 31, No. 17, 2347–2366 (1994).
J. Subbiah J. and R. Natarajan, “Stability analysis of ring stiffened shells of revolution,” Comput. Struct., 14, Nos. 5–6, 479–490 (1981).
R. B. Rickards, Finite Element Method in the Theory of Shells and Plates [in Russian], Zinatne, Riga (1988).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Problemy Prochnosti, No. 2, pp. 62 – 71, March – April, 2019.
Rights and permissions
About this article
Cite this article
Degtyarev, M.A., Shapoval, A.V., Gusev, V.V. et al. Structural Optimization of Waffle Shell Sections in Launch Vehicles. Strength Mater 51, 223–230 (2019). https://doi.org/10.1007/s11223-019-00068-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11223-019-00068-7