Differentiation of the energy functionals for equilibrium problems of the Kirchhoff-Love plates with nonpenetration conditions for known configurations of plate edges

  • Lazarev Nyurgun P., nyurgun@ngs.ru Ammosov North-Eastern Federal University, 48 Kulakovsky Street, Yakutsk 677980, Russia; Lavrentyev Institute of Hydrodynamics SB RAS, 15 Lavrentiev Avenue, Novosibirsk 630090, Russia
  • Grigoryev Mark P., mp.grigorev@s-vfu.ru North-Eastern Federal University, 48 Kulakovsky Street, Yakutsk 677980, Russia
Keywords: variational inequality, crack, nonpenetration condition, energy functional derivative

Abstract

Equilibrium problems for elastic plates with a rectilinear crack are studied. It is assumed that under the action of certain given loads, plates have deformations with a certain predetermined configuration of edges near the crack. On the crack curve, we impose a nonlinear boundary condition as an inequality describing the nonpenetration of the opposite crack faces. Assuming that the parameter δ describes the crack perturbation, the derivative of the energy functional with respect to δ is found. The results are obtained for new mathematical models with new nonlinear boundary conditions describing special character of the mechanical contact interaction of the plate edges.

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How to Cite
Lazarev, N. and Grigoryev, M. (2020) “Differentiation of the energy functionals for equilibrium problems of the Kirchhoff-Love plates with nonpenetration conditions for known configurations of plate edges”, Mathematical notes of NEFU, 26(4), pp. 51-62. doi: https://doi.org/10.25587/SVFU.2019.18.67.005.
Section
Mathematics