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The state of strain in a semi-infinite plate with edge slots

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An approximate method is given for determining the stress distribution in a semi-infinite plate weakened by several closely spaced edge slots with complicated shapes. The method is based on representing the displacement vector as the superposition of four types of singular solution in the planar theory of elasticity for a half-plane, with the solutions continuously distributed over rectilinear segments at the plate boundary, which are completely contained within the slots. Numerical results are given for two slots in a half-plate under tension when one of the slots is a half-ellipse and the other is a half-circle and when both slots are of the same shape and are formed by two quarter circles joined by a segment of the common tangent.

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Literature cited

  1. 1.

    A. Love, The Mathematical Theory of Elasticity [Russian translation], Moscow (1935).

  2. 2.

    G. Neuber, Stress Concentration [Russian translation], Moscow-Leningrad (1947).

  3. 3.

    A. S. Ovsyannikov and V. A. Starikov, “The singular-solution superposition method in deriving the state of strain for a semi-infinite plate having an edge slot,” Prikl. Mekh.,22, No. 6, 119–121 (1986).

  4. 4.

    R. Peterson, Stress Concentration Coefficients [Russian translation], Moscow (1977).

  5. 5.

    G. N. Savin, Stress Distributions around Holes [in Russian], Kiev (1968).

  6. 6.

    M. Abramowicz and I. Stigan (eds.), Handbook on Special Functions with Formulas, Graphs, and Tables [Russian translation], Moscow (1979).

  7. 7.

    M. Seika, “Stresses in a semi-infinite plate containing a U-type notch under uniform tension,” Ing.-Arch.,27, No. 5, 285–294 (1960).

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Additional information

Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 20, pp. 112–116, 1989.

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Ovsyannikov, A.S., Starikov, V.A. The state of strain in a semi-infinite plate with edge slots. J Math Sci 60, 1332–1335 (1992). https://doi.org/10.1007/BF01097698

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  • Stress Distribution
  • Displacement Vector
  • Quarter Circle
  • Approximate Method
  • Plate Boundary