Abstract:
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, axial deformation, Tymoshenko effect, Cosserat effect.
The work was supported by the Russian Foundation for Basic Research (grant no. 19-01-00511) and by the Ministry of Education and Science of the Russian Federation (contract no. 02.G25.31.0147).
Received: 13.03.2019 Received in revised form: 04.04.2019 Accepted: 20.06.2019
Bibliographic databases:
Document Type:
Article
UDC:
539.37
Language: English
Citation:
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”, J. Sib. Fed. Univ. Math. Phys., 12:5 (2019), 533–542
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\paper Strong bending of a beam from a fibrous composite, differently resistant to tension and compression
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2019
\vol 12
\issue 5
\pages 533--542
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\crossref{https://doi.org/10.17516/1997-1397-2019-12-5-533-542}
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Linking options:
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This publication is cited in the following 6 articles:
I. E. Petrakov, “Kontaktnaya zadacha izgiba mnogosloinoi kompozitnoi plastiny s uchetom razlichnykh modulei uprugosti pri rastyazhenii i szhatii”, Sib. zhurn. industr. matem., 25:4 (2022), 153–163
I. Petrakov, APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 13th International Hybrid Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS'21, 2522, APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 13th International Hybrid Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS'21, 2022, 080004
I. E. Petrakov, “Contact Bending Problem for a Multilayer Composite Plate with Allowance for Different Moduli of Elasticity in Tension and Compression”, J. Appl. Ind. Math., 16:4 (2022), 751
I. E. Petrakov, V. M. Sadovskii, O. V. Sadovskaya, “Analysis of bending of composite plates with account for the difference in resistance to tension and compression”, J. Appl. Mech. Tech. Phys., 62:5 (2021), 851–860
V. M. Sadovskii, O. V. Sadovskaya, I. E. Petrakov, “On the theory of constitutive equations for composites with different resistance in compression and tension”, Compos. Struct., 268 (2021), 113921
I. E. Petrakov, V. M. Sadovskii, “Mathematical modeling of plane stress state of a multilayer fibrous composite, differently resistant to tension and compression”, Application of Mathematics in Technical and Natural Sciences (Amitans 2020), AIP Conf. Proc., 2302, ed. M. Todorov, Amer. Inst. Phys., 2020, 090003
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