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Vol 33 Iss. 3
Pages:
62-89
Download volume:
RUS
Article

Bending of a homogeneous layer under the action of its own weight

Authors:
А. F. Zakharevich
Date submitted:
1954-02-20
Date accepted:
1955-02-23
Date published:
1956-03-13

Abstract

Let us consider a homogeneous isotropic prismatic layer of rectangular cross-section under the action of its own weight. Let the layer extend infinitely in the direction perpendicular to the cross-section. Two sides of the cross section are embedded and the other two sides are free (Fig. 1). In this case, the layer will be under plane strain conditions. Let us place the origin at the center of gravity of the layer cross-section and denote: layer height 2c, layer width 2l, weight per unit volume of material g, elastic constants E, n, G.

Область исследования:
(Archived) Articles
Keywords:
-
Funding:

None

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References

  1. Grinsberg G.A. On the method proposed by P.F. Papkovich for solving the plane problem of elasticity theory for a rectangular region and the problem of bending of a rectangular thin plate with two fixed edges, and on some of its generalizations. PMM, vol. XVII, 1953. (in Russian)
  2. Grinsberg G.A., Poplavsky R.P. On the bending of a semicircular thin plate with a fixed arc edge and a free diameter. Inzhenernyy sbornik, vol. XVIII, 1954. (in Russian)
  3. Gurevich S.G. Solution of the plane problem for a rectangular region loaded along the edges by normal forces and its application to the calculation of flange connections. Sbornik Prochnost' elementov parovykh turbin. Mashgiz, 1951. (in Russian)
  4. Erzhanov Zh.S. On the theory of movement of rocks of mine deposits. Issledovaniya po voprosam gornogo i marksheyderskogo dela, collection XXII, Ugletekhizdat, 1950. (in Russian)
  5. Kitover I.A. On the use of special systems of biharmonic functions for solving some problems of elasticity theory. PMM, vol. XVI, issue 6, 1952. (in Russian)
  6. Kitover I.A. Bending of deep beams. Inzhenernyy sbornik, vol. XIV, 1953. (in Russian)
  7. Lurie A.I. On the theory of thick plates. PMM, 1942, vol. IV, issue 2. (in Russian)
  8. Lurie A.I. Stress states in an elastic cylinder loaded along the lateral surface.Inzhenernyy sbornik, vol. XVII, 1953. (in Russian)
  9. Papkovich P.F. On one form of solution of the plane problem of elasticity theory for a rectangular strip. Doklady AN SSSR, 1940, vol. XXVII, No. 4. (in Russian)
  10. Papkovich P.F. Structural mechanics of the ship, part II. Gos. izd-vo sudostroitel'noy promyshlennosti, 1941. (in Russian)
  11. Prokopov V.K. Bending of a circular plate by an axisymmetric load. PMM, vol. XIV, issue 5, 1950. (in Russian)
  12. Prokopov V.K. The problem of constrained bending of a rectangular strip. Inzhenernyy sbornik, vol. XI, 1952. (in Russian)
  13. Prokopov V.K. On a plane problem of elasticity theory for a rectangular region. PMM, vol. XVI, issue 1, 1952. (in Russian)
  14. Fadle I. Die Selbstspannung—Eigenwertfunktionen der quadratischen Scheibe, Ing. Archiv, IV Bd. XI, 1940.

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