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Influence of the Interaction Between Fibers Periodically Located in a Composite Material on the Distribution of Stresses in It

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Mechanics of Composite Materials Aims and scope

Within the framework of a piecewise homogeneous body model, with the use of exact equations of the threedimensional geometrically nonlinear elasticity theory, the stress distributions in a unidirectional fibrous composite containing a row of periodically curved fibers is investigated. The midlines of the fibers are located in different parallel planes, and the curvatures of these lines are periodic and cophasal. The body is loaded at infinity by uniformly distributed normal forces in the direction of fiber location, and the stress distribution in it is investigated. The self-balanced normal and shear stresses arising as a result of fiber curvature are analyzed, and the effects of interaction between the fibers and of geometrical nonlinearity on their distribution are studied. The corresponding numerical results are presented and discussed.

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References

  1. Yu. M. Tarnopolsky, I. G. Jigun, and V. A. Polyakov, Spatially-Reinforced Composite Materials: Handbook, Mashinostroyenia, Moscow, (in Russian) (1987).

  2. A. N. Guz, Failure Mechanics of Composite Materials in Compression, Kiev: Naukova Dumka, 630 p. (in Russian.) (1990).

  3. A. Kelly, Composite Materials: impediments do wider use and some suggestions to overcome these. Proc. Book ECCM-8, 3-6 June, Napoles-Italy, Vol. I, pp15-18, (1998).

  4. S. D. Akbarov and A. N. Guz, Mechanics of Curved Composites, Kluwer Academic Publishers, 464 p (2000).

  5. A. N. Guz, “On one two-level model in the mesomechanics of compression fracture of cracked composites,” Int. Appl. Mech., 39, No. 3, 274-285 (2003).

    Article  Google Scholar 

  6. H. T. Corten, in L. J. Broutman and R.H. Krock (eds.) Fracture of Reinforced Plastics. Modern Composite Materials, pp. 27-100, Addison-Wesley, Reading, MA, (1967).

  7. Yu. M. Tarnopolsky and A.V. Rose, Special Feature of Design of Parts Fabricated From Reinforced Plastics, Zinatne, Riga, (1969).

  8. M. Yu. Kashtalyan, “On deformation of ceramic cracked matrix cross-ply composites laminates,” Int. Appl. Mech. 41, No.1, 37-47 (2005).

  9. S. D. Akbarov, Stability Loss and Buckling Delamination: Three-Dimensional Linearized Approach for Elastic and Viscoelastic Composites, Springer, 548 p. (2012)

  10. S. D. Akbarov and A. N. Guz, “Method of solving problems in the mechanics of fiber composites with curved structures,” Soviet Appl. Mech., March, 777-785 (1985).

  11. S. D. Akbarov and A. N. Guz, “Mechanics of curved composites (piecewise homogenous body model),” Int. Appl. Mech., 38, No.12, 1415-1439 (2002).

  12. R. Kosker and S. D. Akbarov, “Influence of the interaction between two neighbouring periodically curved fibers on the stress distribution in a composite material,” Mech. Compos. Mater., 39, No. 2, 165-176 (2003).

    Article  Google Scholar 

  13. S. D. Akbarov and R. Kosker, “On a stress analysis in the infinite elastic body with two neighbouring curved fibers,” Composites: Part B: Eng., 34, No 2,143-150 (2003).

  14. S. D. Akbarov, “Three-dimensional stability loss problems of the viscoelastic composite materials and structural members,” Int. Appl. Mech., 43, No. 10, 3-27 (2007).

    Article  Google Scholar 

  15. S. D. Akbarov, R. Kosker, and Y. Ucan, “Stress distribution in an elastic body with a periodically curved row of fibers,”. Mech. Compos. Mater. 40, No. 3, 191-202 (2004).

    Article  Google Scholar 

  16. S. D. Akbarov, R. Kosker, and Y. Ucan, “Stress distribution in a composite material with the row of anti-phase periodically curved fibers,” Int. Appl. Mech., 42, No. 4, 486-493 (2006).

    Article  Google Scholar 

  17. S. D. Akbarov, R. Kosker, and Y.Ucan,” The effect of the geometrical non-linearity on the stress distribution in the infinite elastic body with a periodically curved row of fibers,” CMC: Computers, Materials, & Continua, 17, No. 2, 77-102 (2010).

  18. A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer, 555 p (1999).

  19. A. N. Guz, “Constructing the three-dimensional theory of stability of deformable bodies”, Int. Appl. Mech., 37, No. 1, 1-37 (2001).

    Article  Google Scholar 

  20. S. D. Akbarov and A. N. Guz, “Mechanics of curved composites and some related problems for structural members,” Mech. of Advanced Mater. and Struct., 11, 445-515 (2004).

    Article  Google Scholar 

  21. G. N. Watson, A Treatise on the Theory of Bessel functions, Cambridge University Press, England, 753, (1944).

  22. L.V. Kantarovich and V. I. Krilov, Approximate Methods in Advanced Calculus, Moscow: Fizmatgiz, 708 p (in Russian) (1962).

  23. A. N. Guz and V. N. Chekhov, “Problems of folding in the earth’s stratified crust,” Int. Appl. Mech., 43, No. 2, 127-159 (2007).

    Article  Google Scholar 

  24. R. Kosker and S. D. Akbarov, “Stress distribution caused by out of plane co-phase periodical curving of two neighboring fibers in a composite material,” Conf. on Damage in Composite Materials: Non-Destructive Testing and Simulation (CDCM06), 18-19 September, Germany, p. 167 (2006)

  25. S. D. Akbarov and A. N. Guz, “Stress state of a fiber composite with curved structures with a low fiber concentration,” Soviet Appl. Mech. December, 560-565 (1985).

  26. M. S. Babaev; A. N.Guz and M. A. Cherevko, “Stability of a series of fibers in an elastic matrix at small subcritical deformations,” Soviet Appl. Mech., 21, No 5, 443-450 (1985).

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Authors and Affiliations

  1. Yildiz Technical University, Faculty of Chemistry and Metallurgy, Department of Mathematical Engineering, Davutpasa Campus No:127, Esenler, 34210, Istanbul, Turkey

    R. Kosker & Y. Ucan

  2. Institute of Mathematics and Mechanics of National Academy of Sciences of Azerbaijan, Baku, Azerbaijan

    S. D. Akbarov

  3. Yildiz Technical University, Faculty of Mechanical Engineering, Department of Mechanical Engineering, Yildiz Campus, 34349, Besiktas, Istanbul, Turkey

    S. D. Akbarov

Authors
  1. S. D. Akbarov
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  2. R. Kosker
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  3. Y. Ucan
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Corresponding author

Correspondence to R. Kosker.

Additional information

Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 52, No. 2, pp. 349-366, March-April, 2016.

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Akbarov, S.D., Kosker, R. & Ucan, Y. Influence of the Interaction Between Fibers Periodically Located in a Composite Material on the Distribution of Stresses in It. Mech Compos Mater 52, 243–256 (2016). https://doi.org/10.1007/s11029-016-9577-0

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  • DOI: https://doi.org/10.1007/s11029-016-9577-0

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