Geodesic
Strong bending of a beam from a fibrous composite, differently resistant to tension and compression
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 5, pp. 533-542.

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For the analysis of bending of a thin rod made of fiber composite, the generalized Euler elastic equation is used, taking into account different resistance of the material to tension and compression, the influence of transverse shear, elongation of the axis and independent rotations of the reinforcing elements relative to the matrix. Based on Newton's method, a computational algorithm has been developed for solving the static bending problem. A method for determining phenomenological parameters of the composite has been implemented, including photographing the bending state of the rod under the action of a system of forces and couple forces, digital processing of the photography and solving the inverse coefficient problem. The method was validated by comparing the results of computations with a laboratory physical experiment. It is shown that the moduli of elasticity in tension and compression of carbon fiber composite used in the experiment, essentially differ, and that the use of equal moduli in determining bending stiffness results in a significant error in the deflection calculations.
Keywords: fiber reinforced composite, bending state, different resistance to tension and compression, Tymoshenko effect
Mots-clés : axial deformation, Cosserat effect. 
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Boris D. Annin; Vladimir M. Sadovskii; Igor E. Petrakov; Anton Yu. Vlasov. Strong bending of a beam from a fibrous composite, differently resistant to tension and compression. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 5, pp. 533-542. http://geodesic.mathdoc.fr/item/JSFU_2019_12_5_a0/

[1] Y.N. Rabotnov, Mechanics of a deformable solid, Nauka, M., 1988 (in Russian)

[2] R.M. Christensen, Mechanics of composite materials, Dover Publications, New York, 2005

[3] B.E. Pobedrya, Mechanics of composite materials, Izdatelstvovo Mosk. un-ta, M., 1984 (in Russian) | Zbl

[4] A.S. Kravchuk, V.P. Mayboroda, Y.S. Urzhumtsev, Mechanics of polymer and composite materials: experimental and numerical methods, Nauka, M., 1985 (in Russian) | MR

[5] N.M. Matchenko, L.A. Tolokonnikov, “Relations between stresses and strains for multi-modular elastic media”, Izv. AN SSSR. Ser. “Mekhanika tverdogo tela”, 1968, no. 6, 108–110 (in Russian)

[6] A.I. Oleinikov, “Evaluation of stiffness and strength of laminated composites”, Kompozity i nanostruktury, 9:2 (2017), 77–79 (in Russian)

[7] O.V. Sadovskaya, V.M. Sadovskii, Mathematical modeling in mechanics of granular materials, Advanced Structured Materials, 21, Springer, Heidelberg–New York–Dordrecht–London, 2012 | DOI | MR | Zbl

[8] E.P. Popov, Theory and calculation of flexible elastic rods, Nauka, M., 1986 (in Russian)

[9] V.M. Sadovskii, “Thermodynamically consistent equations of the couple stress elasticity”, Dal'nevostochnyj matematicheskij zhurnal, 16:2 (2016), 209–222 (in Russian) | MR | Zbl

[10] R.A. Kayumov, S.A. Lukankin, V.N. Pajmushin, S.A. Holmogorov, “Identification of the mechanical characteristics of fiber-reinforced composites”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 157:4 (2015), 112–132 (in Russian) | MR