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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     author = {Boris D. Annin and Vladimir M. Sadovskii and Igor E. Petrakov and Anton Yu. Vlasov},
     title = {Strong bending of a beam from a fibrous composite, differently resistant to tension and compression},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     number = {5},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2019_12_5_a0/}
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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/