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State of stress of an anisotropic plate with a closed rod pressed into a curvilinear hole in it

Abstract

A method is proposed for solving the problem of elastic equilibrium in the case of an anisotropic plate with a closed rod pressed into a curvilinear hole in it (or stretched over an anisotropic disk). This method is based on representing the boundary conditions in the form of contour integrals of an arbitrary function holomorphic within the region of that plate. The normal magnitude of the jump of the displacement vector at the contact line is given as the function of the arc. Friction at the contact line is assumed negligible. The stress-strain state of the rod (ring) is described by the equations in the theory of thin curvilinear beams.

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Literature cited

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    T. L. Martynovich, "Pressing a closed rod through a curvilinear hole in an anisotropic plate," Visn. Lvivsk. Univ., Ser. Mekh.-Mat., No. 3, 47–55 (1967).

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    M. K. Zvarich and T. L. Martynovich, "An anisotropic disk compressed by an isotropic ring of smaller radius," Prikl. Mekh.,6, No. 5, 66–72 (1970).

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    M. K. Zvarich and T. L. Martynovich, "Press fitting of an isotropic ring into an anisotropic disk," Mekh. Polim., No. 3, 569 (1974).

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    S. G. Lekhnitskii, Anisotropic Plates [in Russian], Moscow (1957).

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Additional information

I. V. Franko L'vov State University. Translated from Mekhanika Polimerov, No. 2, pp. 304–309, March–April, 1976.

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Martynovich, T.L., Zvarich, M.K. & Shchukin, V.S. State of stress of an anisotropic plate with a closed rod pressed into a curvilinear hole in it. Polymer Mechanics 12, 262–267 (1976). https://doi.org/10.1007/BF00856463

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Keywords

  • Boundary Condition
  • Arbitrary Function
  • Displacement Vector
  • Contact Line
  • Contour Integral