On the solution regularity of an equilibrium problem for the Timoshenko plate having an inclined crack

  • Lazarev Nyurgun P., nyurgun@ngs.ru M. K. Ammosov North-Eastern Federal University, Institute of Mathematics, 48 Kulakovsky Street, Yakutsk 677891, Russia
  • Itou Hiromichi, h-itou@rs.tus.ac.jp Tokyo University of Science, Department of Mathematics, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
  • Sivtsev Petr V., sivkapetr@mail.ru M. K. Ammosov North-Eastern Federal University, 42 Kulakovsky Street, Yakutsk 677000, Russia
  • Tikhonova Irina M., IrinaMikh3007@mail.ru M. K. Ammosov North-Eastern Federal University, 42 Kulakovsky Street, Yakutsk 677000, Russia
Keywords: variational inequality, the Timoshenko plate, crack, nonpenetration condition, solution regularity

Abstract

The equilibrium problem for an transversely isotropic elastic plate (Timoshenko model) with an inclined crack is studied. It is supposed that the crack does not touch the external boundary. For initial state, we assume that opposite crack faces are in contact with each other on a frictionless crack surface. Herewith, the crack is described with the use of a surface satisfying certain assumptions. On the crack curve defining the crack in the middle plane, we impose a nonlinear boundary condition as an inequality describing the nonpenetration of the opposite crack faces. It is assumed that on the exterior boundary of the cracked elastic plate the homogeneous Dirichlet boundary conditions are prescribed. We establish additional smoothness of the solution in comparison with that given in the variational statement. We prove that the solution functions are infinitely smooth under additional assumptions on the function of external loads and the functions of displacements near the curve describing the inclined crack.

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How to Cite
Lazarev, N., Itou, H., Sivtsev, P. and Tikhonova, I. ( ) “On the solution regularity of an equilibrium problem for the Timoshenko plate having an inclined crack”, Mathematical notes of NEFU, 25(1), pp. 38-49. doi: https://doi.org/10.25587/SVFU.2018.1.12767.
Section
Mathematics