Tian Analysis of the effectiveness of composite structures for space structures capable of storing elastic energy

Аuthors

Polilov A. N.^1*, Tatus N. A.¹, Xiaoyong T. ^2**

1. Mechanical Engineering Research Institute of the Russian Academy of Sciences, 4, M. Khariton'evskii per., Moscow, 101990, Russia
2. State Key Laboratory of Manufacturing Systems Engineering, Xi'an Jiaotong University, Xi'an, China

*e-mail: polilovan@mail.ru
**e-mail: leoxyt@hotmail.com

Abstract

The study confirms that the mass of profiled composite sheet elastic elements with a constant cross-sectional area can be reduced by a factor of three thanks to their optimized geometry while maintaining the same amount of stored elastic energy. A similar effect can be achieved in a branched structure 3D printed using continuous fibers, while maintaining the total cross-sectional area of the branches, meaning an equal number of fibers in each section. In nature, this requirement for equal total branch area is known as Leonardo da Vinci's rule, and when applied to fiber composites, it means the absence of cut fibers, which is important for ensuring high strength. Branching can offer additional advantages over a profiled beam of constant cross-section, as it avoids significant fiber misorientation and maintains dimensions by assembling the "branches" into a bundle. This paper examines beams of circular, rectangular, and square cross-sections, demonstrating methods for increasing elastic energy storage and the effectiveness of branching in such structures. Achieving specified values of stored elastic energy for composite branched structures with branches of varying cross-sections is demonstrated. It is shown that for beams under various types of loads, the mass reduction of any uniformly stressed beam depends only on the type of applied load. The low energy consumption of 3D printing or pultrusion allows for the production of composite elastic elements directly in orbit. The absence of size restrictions allows for the full realization of the properties of composite structures as elastic energy accumulators. Experimental and technological studies have confirmed the effectiveness of printing profiled and branched elastic elements compared to traditional composite technologies.

Keywords:

composite material, additive technology, 3D printer, uninterrupted fibers, low-modulus and high-strength GFRP – glass-fiber-reinforced-plastic, stored elastic energy, equistrong leaf spring, branchy and shaped structure, Leonardo’s rule, space structure

References

1. Rabotnov Yu.N. Mekhanika deformiruemogo tverdogo tela [Mechanics of Solids].  izd. Moscow, Nauka, 1988, 712 p. (in Russion)
2. Vasil'ev V.V. et al. Kompozicionnye materialy: Spravochnik [Composite Materials: Handbook]. Moscow, Mashinostroenie, 1990, 512 p. (in Russion)
3. Alfutov N.A., Zinov'ev P.A., Popov V.G. Raschet mnogoslojnyh plastin i obolochek iz kompozicionnyh materialov. Seriya "Biblioteka raschetchika" [Calculation of multi-layered plates and shells of composite materials. Series "Calculator Library"]. Moscow, Mashinostroenie, 1984, 264 p. (in Russion)
4. Gordon J.E. The New Science of Strong Materials Or Why You Don't Fall through the Floor. Princeton University Press, 2018, 328 p. - ISBN 9780691180984. 
5. Malinin N.N. Nadyozhnost', prochnost', krasota [Reliability, strength, beauty]. Moscow, Academia, 2016, 288 p. (in Russion)
6. Polilov A.N. Eksperimental'naya mekhanika kompozitov (2-e izdanie) [Experimental Mechanics of Composites (2nd edition)]. Moscow, Bauman MSTU, 2016, 376 p. (in Russion)
7. Gibson R. F. Principles of composite material mechanics. Third Edition. CRC Press Content, 2011, 683 p. 
8. Raskutin A.E., Sokolov I.I. Ugleplastiki i stekloplastiki novogo pokoleniya [New generation of carbon and fiberglass] Trudy VIAM. 2013, no. 4, pp. 9-15.
9. Bazhenov S.L., Berlin A.A., Kul'kov A.A., Oshmyan V.G. Polimernye kompozicionnye materialy. Prochnost' i tekhnologiya [Polymer composite materials. Strength and technology]. Dolgoprudnyj, Intellekt, 2010, 352 p. (in Russion)
10. Parhilovskij I.G. Avtomobil'nye listovye ressory [Automobile leaf springs]. Moscow, Mashinostroenie, 1978, 232 p. (in Russion)
11. Osipenko M.A. A contact problem for bending of two-leaf spring with the leaves curved along the circular arc. PNRPU Mechanics Bulletin. 2013, no. 1, pp. 142-152.
12. Ruslancev A.N., Dumanskij A.M., Alimov M.A. Model' napryazhenno-deformirovannogo sostoyaniya krivolinejnoj sloistoj kompozitnoj balki [The stressed-deformed state model of curvilinear composite beam]. Trudy MAI. 2017, no. 96, pp. 1-15.
13. Borovkov A.I., Mamchits D.V., Nemov A.S. and Novokshenov A.D. Problems of Modeling and Optimization of Variable-Hardness Panels and Structures Made of Layered Composites. Mechanics of Solids, 2018, vol. 53, no. 1, pp. 93–100.
14. Polilov A.N., Tatus N.A. Designing branching or shaped composite elements by analogy with the structure of treetops. Journal of Machinery Manufacture and Reliability. 2017, vol. 46, no. 4, pp. 385-393.
15. Сho H.R., Rowlands R.E. Optimizing fiber direction in perforated orthotropic media to reduce stress concentration. Journal of Composite Materials. 2009, vol. 43, no. 10, pp. 1177 - 1198.
16. Spickenheuer A., Schulz M., Gliesche K., Heinrich G. Using tailored fibre placement technology for stress adapted design of composite structures. Plast. Rubber Compos. Macromol. Eng. 2008, vol. 37, no. 5, pp. 227-232.
17. Wegst U.G.K., Ashby M.F. The structural efficiency of orthotropic stalks, stems and tubes. J. Mater. Sci. 2007, vol. 42, pp. 9005-9014.
18. Schulgasser K., Witztum A. On the strength of herbaceous vascular plant stems. Annals of Botany. 1997, vol. 80, pp. 35-44. 
19. Osipenko M.A., Niashin Iu.I. Ob optimizatsii uprugogo elementa proteza stopy. Rossiiskii zhurnal biomekhaniki. 2011, vol. 15, no. 2, pp. 16-23. 
20. Polilov A.N., Tatus N.A. Biomekhanika prochnosti voloknistykh kompozitov [Strength biomechanics of fibrous composites]. Moscow, FIZMATLIT, 2018, 328 p., ISBN 978-5-9221-1760-9. (in Russion)
21. Eloy C. Leonardo’s rule, self-similarity and wind-induced stresses in trees. arXiv: 1105.2591v2 [physics. Bio-ph]. 15 Nov. 2011.
22. Minamino R., Tateno M. Tree branching: Leonardo da Vinci’s rule versus biomechanical models. Open Access available online. Plos one/www.Plosone. Org, April 2014, vol. 9, issue 4, e 9535. 
23. Eloy C., Fournier M., Lacointe A., Moulia B. Wind loads and competition for light sculpt trees into self-similar structures. Nat. Commun., 2017. 8, 1014.
24. Polilov A.N., Tatus N.A., Shabalin V.V. Peculiarities of constructing elastic elements in the form of shaped composite beams. Journal of Machinery Manufacture and Reliability. 2011, vol. 40, no. 6, pp. 532-537.
25. Polilov A.N., Tatus N.A., Plitov I.S. Estimating the effect of misorientation of fibers on stiffness and strength of profiled composite elements. Journal of Machinery Manufacture and Reliability. 2013, vol. 42, no. 5, pp. 390-397.
26. Cherepanov G.P. Equistrong heavy beam: solving the problem of Galileo Galilei. Fizicheskaia mezomekhanika. 2016, vol. 19, no. 1. pp. 84-88.
27. Vlasov D.D., Polilov A.N., Sklemina O.Yu., Tatus’ N.A. Nelineinije zadachi izgiba (ot balki Galileja do kompozitnoi paneli)[Non-linear bending problems (From Galilio’s beam to composite panel]. Moscow.  Izd-vo АСВ. 2024. 452 с. ISBN 978-54323-0522-0. (in Russion)
28. Daulbaev C.B., Dmitriev T.P., Sultanov F.R., Mansurov Z.A., Aliev E.T. Obtaining Three-Dimensional Nanosize Objects on a "3D Printer + Electrospinning" Machine. Journal of Engineering Physics and Thermophysics. 2017, vol. 90, no. 5, pp. 1115-1118.
29. Grigor'ev S.N., Krasnovskij A.N. Napravleniya razvitiya tekhnologij izgotovleniya izdelij iz polimernyh kompozicionnyh materialov sposobom namotki [Directions of development of manufacturing techniques of products from polymeric composite materials in the way of winding]. Vestnik MGTU Stankin. 2011, no. 3, pp. 95-98.
30. Veshkin E.A. Osobennosti bezavtoklavnogo formovaniya nizkoporistyh PKM. Trudy VIAM. 2016, no. 2 (38), pp. 7-13.

Download