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Elasto-Plastic Problem for a Cracked Plate

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Computational Mechanics ’86

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Summary

Elasto-plastic deformation of a center-cracked circular plate has been considered, displacements on its boundary being given. The use is made of the Leonov-Panasyuk-Dugdale’s crack model [1,2]. The problem is reduced to the singular integral equation with a discontinuous right-side. Numerical and approximate analytical solutions have been obtained and compared between themselves. The stable/unstable crack growth was shown to depend on the proximity of the crack to the plate boundary. The relationship between the solution of the problem for the infinite plate and the one presented is established and its practical applications are indicated.

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References

  1. Dugdale, D.C.: Yielding of steel sheets containing slit, J.Mech.Phys.Solids 8 (1960) 100–104.

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  2. Leonov, M.Ya.; Panasyuk, V.V.: Propagation of minute cracks in solids. Prikladnaya Mekh. 16 (1959) 64–70.

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  3. Boiko, A.V.; Karpenko, L.H.: Cracks in a round plate (specimen and calculation method). Eng.Fract.Mech. 20 (1984; 489–499.

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  4. Boiko, A.V.; Karpenko, L.T.: On some numerical methods for the solution of the plane elasticity problem for bodies with cracks by means of singular integral equations. Int. Journ.of Fract. 17 (1981) 381–388.

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  5. Kantorovich, L.V. Functional analysis and applied mathematics. Uspiekhi Matematicheskikh Nauk 3, H6, (1948).

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  6. Gakhov, F.D. Boundary problems. Moscow: Fizmatgiz 1962.

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Author information

Authors and Affiliations

  1. Institute for Problems of Strength, Ukrainian Academy of Sciences, Timiryazevskaya str., 2, 252014, Kiev-14, USSR

    A. V. Boiko

Authors
  1. A. V. Boiko
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Editor information

Editors and Affiliations

  1. Department of Nuclear Engineering, The University of Tokyo, 3-1, Hongo 7-chome, Bunkyo-ku, Tokyo 113, Japan

    Genki Yagawa

  2. Center for the Advancement of Computational Mechanics, School of Civil Engineering, Georgia Institute of Technology, 225, North Avenue, Atlanta, GA, 30332, USA

    Satya N. Atluri

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© 1986 Springer Japan

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Boiko, A.V. (1986). Elasto-Plastic Problem for a Cracked Plate. In: Yagawa, G., Atluri, S.N. (eds) Computational Mechanics ’86. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68042-0_164

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  • DOI: https://doi.org/10.1007/978-4-431-68042-0_164

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-68044-4

  • Online ISBN: 978-4-431-68042-0

  • eBook Packages: Springer Book Archive

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