Certificate of Registration Media number Эл #ФС77-53688 of 17 April 2013. ISSN 2308-6033. DOI 10.18698/2308-6033
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Technique employing the modified SIMP topology optimization method to determine the panel-to-panel support bracket position in a spacecraft body

Published: 24.01.2024

Authors: Borovikov A.A., Tushev O.N.

Published in issue: #1(145)/2024

DOI: 10.18698/2308-6033-2024-1-2331

Category: Aviation and Rocket-Space Engineering | Chapter: Design, construction and production of aircraft

One of the most important requirements to spacecraft design is that of ensuring dynamic compatibility between the spacecraft and the launch vehicle, which consists in limiting the first fundamental tones of the spacecraft’s natural oscillations. Selecting the optimal number and installation positions of the panel-to-panel brackets connecting the spacecraft thermal honeycomb panels appears to be one of the approaches to solving the problem. “Manual” selection of the panel-to-panel brackets position is extremely ineffective and could be rather time consuming; therefore, the authors previously proposed a technique using the SIMP topology optimization method. Its essence lies in simulating the area of possible installation of the panel-to-panel brackets with the hexagonal finite elements and further topology optimization. However, using the SIMP method in standard formulation significantly increases the number of required design variables (at least three per one bracket), and, consequently, the computation time. This paper proposes modification to the SIMP method making it possible to use a minimum number of the design variables (one variable per one bracket). To illustrate efficiency of the developed apparatus, it uses a test problem as an example and compares the results obtained through the standard and modified versions of the SIMP method.

[1] Wijker J.J. Spacecraft Structures. Springer Science & Business Media, 2008, 504 p.
[2] Soyuz CSG User’s Manual. Issue 2.1. Arianspace, May 2018. Available at:
[3] Falcon User’s Guide. September 2021. Available at:
[4] Borovikov A.A., Leonov A.G., Tushev O.N. Metodika opredeleniya raspolozheniya mezhpanelnykh kronshteynov korpusa kosmicheskogo apparata s ispolzovaniem topologicheskoy optimizatsii [Technique employing topology optimization to determine panel-to-panel support bracket positions in a spacecraft body]. Vestnik MGTU im. N.E. Baumana. Ser. Mashinostroenie — Herald of the Bauman Moscow State Technical University, Series Mechanical Engineering, 2019, no. 4, pp. 4–19.
[5] Bendsoe M.P., Sigmund O. Topology optimization. Theory, methods, and application. Springer, 2004, 370 p.
[6] MSC Nastran 2018. Quick reference guide. Available at:
[7] Attetkov A.V., Galkin S.V., Zarubin V.S. Metody optimizatsii [Optimization methods]. 2nd ed., stereotip. Zarubin V.S., Krishchenko A.P., ed. Moscow, BMSTU Publ., 2003, 440 p.
[8] Borodakiy Yu.V., Zagrebaev A.M., Kritsyna N.A., Kulyabichev Yu.P., Shumilov Yu.Yu. Nelineynoe programmirovanie v sovremennykh zadachakh optimizatsii [Nonlinear programming in modern optimization problems]. Moscow, NIYaU MIFI Publ., 2011, 244 p.
[9] Haug E., Arora J. Applied optimal design: Mechanical and structural systems. Wiley, 1979 [In Russ.: Khog E., Arora Ya. Prikladnoe optimalnoe proektirovanie: Mekhanicheskie sistemy i konstruktsii. Moscow, Mir Publ., 1983, 478 p.].
[10] Christensen P.W., Klarbring A. An introduction to structural optimization. Gladwell G.M.L. ed. Sweden, Springer, 2009, 211 p.
[11] Bazaraa M., Shetti C. Nonlinear Programming: Theory and Algorithms. John Wiley & Sons Inc., 1979 [In Russ.: Bazara M., Shetti K. Nelineynoe programmirovanie. Teoriya i algoritmy. Moscow, Mir Publ., 1982, 583 p.].
[12] Zangwill W. Nonlinear Programming: A Unified Approach. Prentice-Hall, 1969 [In Russ.: Zangvill U. Nelineynoe programmirovanie. Edinyi podkhod. Moscow, Sovetskoe Radio Publ., 1973, 312 p.].
[13] Golub J., Van Loan Ch. Matrix Computations. Johns Hopkins University Press, 1996 [in Russ.: Golub Dzh., Van Loun Ch. Matrichnye vychisleniya. Moscow, Mir Publ., 1999, 548 p.].
[14] Biderman V.L. Teoriya mekhanicheskikh kolebaniya [Theory of mechanical oscillations]. Moscow, Vysshaya Shkola Publ., 1980, 408 p.
[15] Parlett B. The symmetric eigenvalue problem. Englewood Cliffs, NJ, Prentice-Hall, 1980 [in Russ.: Parlett B. Simmetrichnaya problema sobstvennykh znacheniy. Chislennye metody. Moscow, Mir Publ., 1983, 384 p.].
[16] MSC Nastran 2018. Dynamic analysis user’s guide. Available at:
[17] Zienkiewicz O. The Finite Element Method in Engineering Science. McGraw-Hill, 1971 [In Russ.: Zenkevich O. Metod konechnykh elementov v tekhnike. Moscow, Mir Publ., 1975, 541 p.].
[18] Gallagher R. Finite Element Analysis: Fundamentals. Pearson College Div., 1975 [In Russ.: Gallager R. Metod konechnykh elementov. Osnovy. Moscow, Mir Publ., 1984, 428 p.].
[19] Liu G.R., Quek S.S. The finite element method: a practical course. Butterworth-Heinemann, 2003, 348 p.