Skip to main content
SpringerLink
Log in

Continuum Approaches in the Mechanics of Curved Composites and Associated Problems for Structural Members

  • Published:
International Applied Mechanics Aims and scope

Abstract

A review is made of studies on the mechanics of curved composites carried out using continuum approaches. The relevant theory, problem formulations, and solution methods are considered and some typical results on the influence of structural distortion on the mechanical behavior of composites are analyzed. Subjects for near-term studies are proposed

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. S. D. Akbarov and M. H. Asadov, “Quasihomogeneous state in multilayered composites with an arbitrary plane structural curvature,” Izv. AGPU im. N. Tusi, No. 1/2, 94–103 (1995).

    Google Scholar 

  2. S. D. Akbarov and A. N. Guz, “Continuum theory in the mechanics of composite materials with small-scale structural distortion,” Sov. Appl. Mech., August, 107-117 (1991).

  3. S. D. Akbarov and A. N. Guz, “Mechanics of composite materials with distorted structure (review). Continuum theory, fiber composites,” Sov. Appl. Mech., November, 429-443 (1991).

  4. S. D. Akbarov and A. N. Guz, Mechanics of Curved Composites, Kluwer Acad. Publ., Dordrecht-Boston-London (2000).

    Google Scholar 

  5. S. D. Akbarov, A. N. Guz, É. A. Movsumov, and S. M. Mustafaev, Mechanics of Materials with Distorted Structures, Vol. 4 of the 12-volume series Mechanics of Composites [in Russian], Naukova Dumka, Kiev (1995).

    Google Scholar 

  6. S. D. Akbarov, A. N. Guz, and A. D. Zamanov, “Natural vibrations of composite materials with small-scale curvatures in structure,” Int. Appl. Mech., 28, No. 12, 794–800 (1993).

    Google Scholar 

  7. S. D. Akbarov, A. N. Guz, and N. Yahnioglu, “Mechanics of composite materials with curved structures and elements of constructions (review),” Int. Appl. Mech., 34, No. 11, 1067–1079 (1999).

    Google Scholar 

  8. S. D. Akbarov and G. M. Guliev, Quasihomogeneous States in Structure [in Russian], Manuscript No. 511-B91-90 dep. at VINITI 01.02.91.

  9. S. D. Akbarov and N. Yahnioglu, “Stress distribution in a strip fabricated from a composite material with small-scale curved structure,” Int. Appl. Mech., 32, No. 9, 684–690 (1997).

    Google Scholar 

  10. S. D. Akbarov and N. Yahnioglu, “On the finite element analysis of the influence of a local structural damage in a multilayered thick plate material on the stress distribution,” in: C. A. Brebbia and A. Carpinteri (eds.), Damage and Fracture Mechanics, Computational Mech. Pub., Sauthampton-Boston (1998), pp. 187–196.

    Google Scholar 

  11. S. D. Akbarov and N. Yahnioglu, “The influence of a local structural damage in a multilayered thick plate material on the stress distribution,” Int. App. Mech., 34, No. 9, 873–878 (1998).

    Google Scholar 

  12. S. D. Akbarov and S. Selim, “Stability of a strip made of a multilayered composite with a curved structure,” Int. Appl. Mech., 37, No. 6, 831–839 (2001).

    Google Scholar 

  13. S. D. Akbarov and I. Genc-Demiriz, “Natural vibration of a thick plate fabricated from a spatially curved composite,” in: D. Hui (ed.), Proc. ICCE/8, August 5-11 (2001), pp. 11–12.

  14. M. H. Asadov, “On the quasihomogeneous state in multilayered composites with spatially curved structures in pure shear,” Izv. AGPU im. N. Tusi, No. 1/2, 89–93 (1995).

    Google Scholar 

  15. Z. P. Bazhant, “Influence of the curvature of reinforced fibers on the elastic modulus and strength of composite materials,” Mekh. Polim., No. 2, 314–321 (1968).

    Google Scholar 

  16. V. V. Bolotin, “A theory of reinforced layered material with random distortions,” Mekh. Polim., No. 1, 11–19 (1966).

    Google Scholar 

  17. V. V. Bolotin, “Layered elastic and viscoelastic materials with initial random distortions,” Mekh. Tverd. Tela, No. 3, 59–65 (1966).

    Google Scholar 

  18. V. V. Bolotin and Yu. N. Novichkov, Mechanics of Multilayered Structures [in Russian], Mashinostroenie, Moscow (1980).

    Google Scholar 

  19. T. W. Chou, R. L. McCullough, and R. B. Pipes, “Composites,” J. Sci. Amer., No. 10, 193–203 (1986).

    Google Scholar 

  20. R. M. Christensen, Mechanics of Composite Materials, Willey, New York (1979).

    Google Scholar 

  21. H. T. Corten, “Fracture of reinforcing plastics,” in: L. J. Broutman and R. H. Krock (eds.), Modern Composite Materials, Addison-Wesley, Reading, Massachusetts (1967), pp. 27–100.

    Google Scholar 

  22. M. M. Schwartz (ed.), Composite Materials Handbook, 2nd ed, McGraw-Hill, New York (1992).

    Google Scholar 

  23. Z.-N. Feng, H. G. Alien, and S. S. May, “Micromechanical analysis of a woven composite,” in: Proc. ECCM-8, Vol. 4 (1998), pp. 619–625.

    Google Scholar 

  24. V. K. Ganesh and N. K. Naik, “Failure behavior of plane weave fabric laminates under on-axis uniaxial tensile loading: Ill-effect of fabric geometry,” J. Comp. Mater., 30, 1823–1856 (1996).

    Google Scholar 

  25. I. Genf-Demiriz and S. D. Akbarov, “Stress analysis for a thick rectangular plate from a composite material with a periodic spatially curved structure under forced vibrations,” in: Abstracts of Papers Read at 12th Int. Conf. on the Mechanics of Composite Materials, Riga (2002), p. 51.

  26. A. N. Guz, “On the continuum theory of composite materials with small-scale structural curvature,” Dokl. Akad. Nauk USSR, 268, No. 2, 307–313 (1983).

    Google Scholar 

  27. A. N. Guz, “Mechanics of composite materials with a small-scale structural flexure,” Sov. Appl. Mech., November, 383–393 (1983).

  28. A. N. Guz, “Quasi-uniform states in composites with a small-scale curvatures in the structure,” Sov. Appl. Mech., December, 479–490 (1983).

  29. A. N. Guz, “On the vibration theory of composite materials with small-scale structural curvature,” Dokl. Akad. Nauk USSR, 270, No. 5, 1078–1081 (1983).

    Google Scholar 

  30. A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer-Verlag, Berlin (1999).

    Google Scholar 

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

    Google Scholar 

  32. A. N. Guz, N. A. Shul'ga, V. T. Tomashevskii et al., Technological Stresses and Strains in Materials, Vol. 6 of the 12-volume series Mechanics of Composites [in Russian], A.S.K., Kiev (1997).

    Google Scholar 

  33. A. N. Guz, V. T. Tomashevskii, N. A. Slul'ga, and V. S. Yakovlev, Technological Stresses and Strains in Composite Materials [in Russian], Vyshcha Shkola, Kiev (1988).

    Google Scholar 

  34. Y. Kahramaner, I. Taylan, I. Genc-Demiriz, and S. Selim, “Investigation of the stress distribution in a thick plate fabricated from a curved composite,” in: D. Hui (ed.), Proc. ICCE/8, August 5-11 (2001), pp. 413–414.

  35. A. L. Kalmkarov, B. A. Kudryavtsev, and V. Z. Parton, “A problem on a periodically curved composite layer,” Prikl. Mat. Mekh., 51, No. 1, 68–75 (1987).

    Google Scholar 

  36. A. Kromm, “Verallgemeinerte Theorie der Plattenstatik,” Ing. Arch., 21, 266–286 (1953).

    Google Scholar 

  37. A. Kromm, “Ñber die randquerkrafte biegestutzte platten,” ZAMM, 35, 231–242 (1955).

    Google Scholar 

  38. Z. Kutug, “Natural vibration of the beam-strip fabricated from a composite material with small-scale curvings in the structure,” Mech. Comp. Mater., 36, No. 4, 502–512 (1996).

    Google Scholar 

  39. Z. Kutug, Natural Vibration and Buckling of the Composite Beam-Plates Fabricated from Composite Material with Locally and Periodically Curved Structure, Ph. D. Thesis, The Yildiz Technical University, Turkey, Istanbul (1997).

    Google Scholar 

  40. S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  41. B. P. Makarov and V.P. Nikolayev, “Influence of the curvature of reinforcing elements on the mechanical and thermal properties of composite materials,” Mekh. Polim., No. 6, 1036–1039 (1971).

    Google Scholar 

  42. E. H. Mansfied and D. Purslow, “The influence of fiber waviness on the moduli of unidirectional fiber reinforced composites,” Aeronoutical Research Council Current Paper, No. 1339 (1974).

  43. A. V. Nosarev, “Influence of fiber curvature on the elastic properties of unidirectionally reinforced plastics,” Mekh. Polim., No. 5, 858–863 (1967).

    Google Scholar 

  44. E. Reissner, “The effect of transverse shear deformation on the bending of elastic plates,” J. Appl. Mech., No. 12, 67–77 (1945).

    Google Scholar 

  45. D. G. Swift, “Elastic moduli of fibrous composites containing misaligned fibers,” J. Phys. D: Appl. Phys., 8, 223–240 (1975).

    Google Scholar 

  46. Yu. M. Tamopolskii and A. V. Rose, A Special Design Feature of Parts Fabricated from Reinforced Plastics, Zinatne, Riga (1969).

    Google Scholar 

  47. Yu. M. Tamopolskii, I. G. Jigun, and V. A. Polyakov, Spatially-Reinforced Composite Materials: Handbook, Mashinostroenie, Moscow (1987).

    Google Scholar 

  48. E. Tekin Tarim and S. D. Akbarov, “Three-dimensional stress analysis for a thick plate fabricated from a composite material with a spatial locally curved structure,” Abstracts of Papers Read at 12th Int. Conf. on the Mechanics of Composite Materials, Riga (2002).

  49. Ph. Vandeurzen, J. Ivens, and I. Verpoest, “A three-dimensional micromechanical analysis of woven fabric composites: I. Geometric analysis,” Comp. Sci. Technol., 56, 1303–1315 (1996).

    Google Scholar 

  50. J. M. Whitney, “Geometrical effects of filament twist on the modulus and strength of graphite fiber,” Reinforced Composites, Textile Res. J., 36, 765–770 (1966).

    Google Scholar 

  51. T. J. Whitney and T.-W. Chou, “Modeling of 3-D angle-interlock textile structural composites,” J. Comp. Mater., 23, 890–911 (1989).

    Google Scholar 

  52. N. Yahnioglu, FEM Analyses of the Boundary-Value Problems Corresponding to the Statics of Elements of Constructions Fabricated from Composite Materials with Curved Structure, Ph. D. Thesis, The Yildiz Technical University, Turkey, Istanbul (1996).

    Google Scholar 

  53. N. Yahnioglu, “Three-dimensional analysis of stress fields in a plate fabricated from composite materials with small-scale structural curving,” Mech. Comp. Mater., 33, No. 3, 340–348 (1997).

    Google Scholar 

  54. N. Yahnioglu and S. Selim, “Bending of a composite material strip with curved structure in the geometrically nonlinear statement,” Mech. Comp. Mater., 36, No. 6, 459–464 (2000).

    Google Scholar 

  55. J. M. Yang, C. L. Ma, and T.-W. Chou, “Fiber inclination model of three-dimensional textile structural composites,” J. Comp. Mater., 20, 472–484 (1986).

    Google Scholar 

  56. A. D. Zamanov, “On the stress distribution in the thick plate fabricated from the composite material with curved structures under forced vibration,” Mech. Comp. Mater., 35, No. 4, 447–454 (1999).

    Google Scholar 

  57. A. D. Zamanov, “Natural vibration of a rectangular plate of composite material with periodically bent structures,” Int. Appl. Mech., 35, No. 10, 1035–1039 (1999).

    Google Scholar 

  58. A. D. Zamanov, “Stress distribution in a rigidly clamped composite plate with locally curved structures under forced vibration,” Int. Appl. Mech., 37, No. 9, 1189–1195 (2001).

    Google Scholar 

  59. A. D. Z amanov, “The effect of structural curvings on the stress distribution in a rigidly fixed composite plate under forced vibration,” Mekh. Comp. Mater., 38, No. 1, 41–46 (2002).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Yildiz Technical University, Istanbul, Turkey

    S. D. Akbarov

  2. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev

    A. N. Guz

Authors
  1. S. D. Akbarov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. N. Guz
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Akbarov, S.D., Guz, A.N. Continuum Approaches in the Mechanics of Curved Composites and Associated Problems for Structural Members. International Applied Mechanics 38, 1285–1308 (2002). https://doi.org/10.1023/A:1022668417687

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022668417687

Keywords

Search

Navigation