Designing Equistrong Shaped, Branching or Delaminated Elastic Composite Members

This paper examines the analogy with regard to bending flexibility of shaped beams with a constant cross section area and branching or delaminated treetop-like composite structures with a constant sum of cross sections of the branches (Leonardo’s rule). In the ideal case, shaping or branching provides threefold bend flexibility growth while retaining the strength i.e., threefold increase of the accumulated elastic energy for a fixed applied load and the same mass of the elastic member. It is shown that the use of glass fiber reinforced plastic in shaped elastic beams makes it possible to reduce their mass by approximately 15 times compared to the steel analog. The limitations of using a linearized bend equation for equistrong shaped heavy beams under distributed or concentrated load are described. Shaped or branching composite elastic members can be efficiently used in space-based constructions due to their low mass and low energy consumption of the polymer composite member manufacturing, therefore allowing production directly in orbit.

References

[1] Sho 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.

[2] Malakhov A.V., Polilov A.N. Construction of trajectories of the fibers which bypass a hole and their comparison with the structure of wood in the vicinity of a knot. Journal of Machinery Manufacture and Reliability, 2013, vol. 42, no. 4, pp. 306–311.

[3] Malakhov A.V., Polilov A.N. Design of composite structures reinforced curvilinear fibres using FEM. Composites Part A: Applied Science and Manufacturing, 2016, vol. 87, pp. 23–28.

[4] Malakhov A.V., Polilov A.N. Design algorithm of rational fiber trajectories in arbitrarily loaded composite plate. Journal of Machinery Manufacture and Reliability, 2017, vol. 46, no. 5, pp. 479–487.

[5] Wegst U.G.K., Ashby M.F. The structural efficiency of orthotropic stalks, stems and tubes. Journal of Material Science, 2007, vol. 42, pp. 9005–9014.

[6] Plitov I.S., Polilov A.N. Rational dimensions of segments of bamboo stems and composite tubes subjected to compression, flexure, and torsion. Journal of Machinery Manufacture and Reliability, 2015, vol. 44, no. 3, pp. 239–248.

[7] 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.

[8] Eloy C. Leonardo’s rule, self-similarity and wind-induced stresses in trees. Available at: https://arxiv.org/pdf/1105.2591v2.pdf (accessed 15 December 2017).

[9] Minamino R., Tateno M. Tree branching: Leonardo da Vinci’s rule versus biomechanical models. Plos one, April 2014, vol. 9, no. 4, e 9535. Available at: http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0093535 (accessed 15 December 2017).

[10] 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.

[11] Cherepanov G.P. Ravnoprochnyi tiazhelyi brus: reshenie problemy Galileia [Equistrong heavy beam: solving the problem of Galileo Galilei]. Fizicheskaia mezomekhanika [Physical mesomechanics journal]. 2016, vol. 19, no. 1, pp. 84–88.

[12] Polilov A.N. Eksperimental’naia mekhanika kompozitov [Experimental mechanics of composites]. Moscow, Bauman Press, 2015. 375 p.

[13] Polilov A.N. Etiudy po mekhanike kompozitov [Etudes on mechanics of composites]. Moscow, Fizmatlit publ., 2015. 320 p.

[14] Polilov A.N., Tatus’ N.A. Biomekhanika prochnosti voloknistykh kompozitov [Biomechanics of strength of fibrous composites]. Moscow, Fizmatlit publ., 2015. 326 p.