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Materials Science

, Volume 31, Issue 3, pp 350–362 | Cite as

Two-dimensional problems of the theory of elasticity for reinforced cracked plates

  • M. P. Savruk
  • V. S. Kravets'
Article

Abstract

By using the method of singular integral equations, we develop a general approach to the solution of static problems of the two-dimensional theory of elasticity for thin-walled structural elements with curvilinear cracks reinforced by elastic patches. We analyze two basic types of fastening patches to plates, namely, continuous fastening (via the adhesive layer) and discrete fastening (riveting). It is assumed that both the cracked plate and reinforcing patches are characterized by the generalized two-dimensional stressed state. We constructed integral equations for an infinite plate with curvilinear crack reinforced by linear or two-dimensional elastic patches. We also present a brief survey of the literature devoted to the solution of problems of the indicated type.

Keywords

Stressed State Integral Equation Static Problem Basic Type Adhesive Layer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    A. Sorensen,Some Design Considerations for Tear Resistant Airplane Structures, Preprint of the Institute of the Aeronautical Sci., No. 618, New York (1956).Google Scholar
  2. 2.
    T. Swift, “Fracture analysis of adhesively bonded cracked panels,”J. Engineer. Mater. Technol.,100, 10–15 (1978).Google Scholar
  3. 3.
    T. P. Rich, M. M. Ghassem, and D. J. Cartwright, “Fracture diagrams for cracked stiffened panels,”Eng. Fract. Mech.,21, No. 5 (1985).Google Scholar
  4. 4.
    A. I. Kalandiya,Mathematical Methods of the Two-Dimension Theory of Elasticity [in Russian], Nauka, Moscow (1973).Google Scholar
  5. 5.
    V. Z. Parton and E. M. Morozov,Mechanics of Elastoplastic Fracture [in Russian], Nauka, Moscow (1974).Google Scholar
  6. 6.
    É. I. Grigolyuk and V. M. Tolkachev,Contact Problems in the Theory of Plates and Shells [in Russian], Mashinostroenie, Moscow (1980).Google Scholar
  7. 7.
    G. P. Cherepanov,Fracture Mechanics of Composite Materials [in Russian], Nauka, Moscow (1983).Google Scholar
  8. 8.
    F. Vogt, “The load distribution in bolted or riveted joints in light-alloy structures,” RAE Report No. SME 3300, Oct. 1944. Royal Aircraft Establishment, Farnborough, or NACA TM 1135.Google Scholar
  9. 9.
    B. Budiansky and Tai Tl. Wu, “Transfer of load to a sheet from a rivet-attached stiffener,”J. Math. and Phys.,40, No. 2, 142–162 (1961).Google Scholar
  10. 10.
    J. L. Lubkin and L. C. Lewis, “Adhesive shear flow for an axially-loaded finite stringer bonded to an infinite sheet,”Quart. J. Mech. Appl. Math.,33, No. 4, 521–533 (1970).Google Scholar
  11. 11.
    W. Barrois, “Stresses and displacements due to load transfer by fasteners in structural assemblies,”Eng. Fract. Mech.,10, No. 1, 115–176 (1978).Google Scholar
  12. 12.
    V. N. Maksimenko and L. A. Fil'shtinskii, “Transfer of load from a stiffening rib to an anisotropic shell in the case where they are separated by an adhesive layer,”Prikl. Mekh.,14, No. 8, 64–69 (1978).Google Scholar
  13. 13.
    R. Greif and J. L. Sanders, “The effect of a stringer on the stress in a cracked sheet,”J. Appl. Mech.,32, No. 1, 59–66 (1965).Google Scholar
  14. 14.
    K. L. Agayan, “One contact problem for an infinite cracked plate reinforced by elastic patches,”Izv. Akad. Nauk Arm. SSR. Ser. Mekh.,29, No. 4, 3–15 (1976).Google Scholar
  15. 15.
    G. T. Zhorzholiani, “Stretching of a plate strengthened by a stiffening rib,”Tr. Tbil. Mat. Inst.,73, 82–87 (1983).Google Scholar
  16. 16.
    O. S. Yahsi and F. Erdogan, “A note on the cracked plates reinforced by a line stiffener,”Eng. Fract. Mech.,18, No. 6, 1211–1215 (1983).Google Scholar
  17. 17.
    P. S. Theocaris and D. Bardzokas, “Reinforcement of a cracked plate by a loaded strip-inclusion,”Ing.-Arch.,55, No. 1, 45–56 (1985).Google Scholar
  18. 18.
    H. Terada and T. Nakajima, “Analysis of stress intensity factor of a crack approaching welding bead,”Int.-Fract.,27, No. 2, 83–90 (1985).Google Scholar
  19. 19.
    C.-C. Chu, “Arbitrary oriented cracks in a reinforced sheet,”Trans. ASME., J. Appl. Mech.,52, No. 3, 13–18 (1985).Google Scholar
  20. 20.
    J. P. Romauldi, J. T. Frasier, and G. R. Irwin, “Crack-extension-force near a riveted stiffener,” NRL, Memorandum Report No. 4956 (1957).Google Scholar
  21. 21.
    J. M. Bloom and J. L. Sanders, “The effect of riveted stringer on the stress in a cracked sheet,”Trans. ASME., J. Appl. Mech.,33, No. 3, 561–570 (1966).Google Scholar
  22. 22.
    G. P. Cherepanov and V. M. Mirsalimov, “Influence of stiffening ribs on the process of crack propagation,”Izv. Akad. Nauk Azerb. SSR. Ser. Fiz.-Tekhn. Mat. Nauk, No. 1, 7–11 (1969).Google Scholar
  23. 23.
    C. C. Poe, “Stress-intensity factors for a cracked sheet with riveted and uniformly spaced stringers,” NASA TR R-358 (1971).Google Scholar
  24. 24.
    T. Swift, “The effects of fastener flexibility and stiffener geometry on the stress intensity in stiffened cracked sheet,” in:Prospects of Fracture Mechanics, Leyden (1974), pp. 419–436.Google Scholar
  25. 25.
    E. G. Pereslavtsev, “Evaluation of the stress intensity factors at the crack tips for a reinforced sheet with a series of cracks lying along a line,”Tr. TsAGI, Issue 1988 (1979).Google Scholar
  26. 26.
    S. V. Shkaraev, “Stresses in the neighborhood of a crack near the edge of a reinforced plate,”Fiz.-Khim. Mekh. Mater.,21, No. 6. 93–94 (1985).Google Scholar
  27. 27.
    K. Arin, “A note on the effect of lateral bending stiffness of stringers attached to a plate with a crack,”Eng. Fract. Mech.,7, No. 1, 173–179 (1975).Google Scholar
  28. 28.
    G. Dowrick and D. J. Cartwright, “Biaxial stress effects in a reinforced cracked sheet,”J. Strain. Anal. Eng. Des.,19, No. 1, 61–69 (1984).Google Scholar
  29. 29.
    G. Dowrick, D. J. Cartwright, and D. P. Rooke, “The effects of repair patches on the stress distribution in a cracked sheet.” in:Proceedings of the Second International Conference on Numerical Methods in Fracture Mechanics (Swansea, 1980), Swansea (1980), pp. 763–775.Google Scholar
  30. 30.
    M. Creager and A. F. Liu, “The effect of reinforcements on the slow stable tear and catastrophic failure of thin metal sheet.” AIAA Paper (1971), pp. 71–113.Google Scholar
  31. 31.
    N. I. Muskhelishvili,Some Fundamental Problems of the Mathematical Theory of Elasticity [in Russian], Nauka, Moscow (1966).Google Scholar
  32. 32.
    V. V. Panasyuk, M. P. Savruk, and A. P. Datsyshin,Distribution of Stresses Near Cracks in Plates and Shells [in Russian], Naukova Dumka, Kiev (1976).Google Scholar
  33. 33.
    M. P. Savruk,Two-Dimensional Problems of Elasticity Theory for Cracked Bodies [in Russian], Naukova Dumka, Kiev (1981).Google Scholar
  34. 34.
    M. P. Savruk and V. S. Kravets', “Reinforcement of a thin cracked plate by a system of parallel stringers,”Fiz.-Khim. Mekh. Mater.,30, No. 1, 96–105 (1994).Google Scholar
  35. 35.
    G. S. Ivanyts'ka, V. S. Kravets', and O. I. Sements', “Reinforcement of a cracked plate by a system of parallel stringers,” in:Fracture Mechanics: Successes and Problem. Collection of Abstracts, ICF-8 (Kiev, 1993), L'viv, 1993, Part 1, p. 83.Google Scholar
  36. 36.
    J. L. Sanders, “Effect of a stringer on the stress concentration due to a crack in a thin sheet,” NASA Techn. Report, R-13 (1959), pp. 1–10.Google Scholar
  37. 37.
    K. Arin and F. Erdogan, “A plate with a crack stiffened by a partially debonded stringer,”Eng. Fract. Mech.,6, No. 1, 133–140 (1974).Google Scholar
  38. 38.
    R. Chandra, M. V. Murthy, T. S. Ramamurthy, and A. K. Rao, “Analytical estimation of stress intensity factors in patched cracked plates,”Eng. Fract. Mech.,21, No. 3, 479–494 (1985).Google Scholar
  39. 39.
    R. Sethuraman and S. K. Maiti, “Determination of mixed mode stress intensity factors for a crack-stiffened panel,”Eng. Fract. Mech.,33, No. 3, 355–369 (1989).Google Scholar
  40. 40.
    V. N. Maksimenko and V. N. Pavshok, “Influence of glued patches on the intensity of stresses at the crack tips in an anisotropic plate,”Prikl. Mekh.,25, No. 5, 69–75 (1989).Google Scholar
  41. 41.
    M. M. Ratwani and D. P. Wilhelm, “Influence of biaxial loading on analysis of cracked stiffened panels,”Eng. Fract. Mech.,11, No. 3, 585–593 (1979).Google Scholar
  42. 42.
    V. I. Grishin and T. K. Begeev, “Stress intensity factors in a plate with central transverse crack reinforced by patches made of composite materials,”Mekh. Kompoz. Mater., No. 4, 696–700 (1986).Google Scholar
  43. 43.
    F. Erdogan and K. A. Arin, “A sandwich plate with debonding crack,”Eng. Fract. Mech.,4, No. 3, 449–458 (1972).Google Scholar
  44. 44.
    M. M. Ratvani, “Investigation of stresses in glue-layered structures weakened by cracks,”Raket. Tekhn. Kosmonavt.,17, No. 9, 77–85 (1979).Google Scholar
  45. 45.
    R. Chandra and K. Guruprasad, “Numerical estimation of stress intensity factors in patched cracked plates,”Eng. Fract. Mech.,27, No. 5, 559–569 (1987).Google Scholar
  46. 46.
    A. Young, D. J. Cartwright, and D. P. Rooke, “The boundary element method for analyzing repair patches on cracked finite sheets,”Aeron. J.,92, No. 920, 416–421 (1988).Google Scholar
  47. 47.
    K. Arin and R. A. Barnes, “A circular plate attached to another cracked plate through circumferential welding,” in:Proceedings of the Internat. Conf. on Fracture Mechanics and Technology, Vol. 2, Hong Kong (1977), pp. 1213–1226.Google Scholar
  48. 48.
    Yi-Heng Chen, “A finite notched plate stiffened by a smaller circular disk,”Int. J. Engineer. Sci.,26, No. 2, 127–133 (1988).Google Scholar
  49. 49.
    Yi-Heng Chen and H.-G. Hanh, “Interaction of a stiffener with a crack in an anisotropic sheet,”Eng. Fract. Mech.,33, No. 6, 887–895 (1989).Google Scholar
  50. 50.
    M. P. Savruk and V. S. Kravets', “Stress state of a cracked plate reinforced by a patch,”Fiz.-Khim. Mekh. Mater.,27, No. 4, 33–40 (1991).Google Scholar
  51. 51.
    M. P. Savruk and V. S. Kravets', “Effect of reinforcing patches on the distribution of stresses in plates with cracks,”Prikl. Mekh.,29, No. 3, 48–55 (1993).Google Scholar
  52. 52.
    S. V. Shkaraev, “Experimental-theoretical method for the determination of stress intensity factors,”Fiz.-Khim. Mekh. Mater.,25, No. 4, 97–101 (1989).Google Scholar
  53. 53.
    H. Vlieger, “The residual strength characteristics of stiffened panels containing fatigue cracks,”Eng. Fract. Mech.,5, No. 2, 447–477 (1973).Google Scholar
  54. 54.
    R. Jones and R. J. Calliman, “Finite element analysis of patched cracks,”J. Struct. Mech.,7, No. 2, 107–130 (1979).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • M. P. Savruk
  • V. S. Kravets'

There are no affiliations available

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