On junction problem for elastic Timoshenko inclusion and semi-rigid inclusion

  • Khludnev Alexander M., khlud@hydro.nsc.ru Lavrentiev Institute of Hydrodynamics, 15 Lavrentiev Avenue, Novosibirsk 630090, Russia; Novosibirsk State University, 1 Pirogov Street, Novosibirsk, 630090, Russia
  • Popova Tatyana S., ptsokt@mail.ru M. K. Ammosov North-Eastern Federal University, 58 Belinsky Street, Yakutsk 677000, Russia
Keywords: Timoshenko inclusion, semi-rigid inclusion, elastic body, crack, nonlinear boundary conditions


An equilibrium problem for elastic bodies with a thin elastic inclusion and a thin semi-rigid inclusion is investigated. The inclusions are assumed to be delaminated from the elastic bodies, forming therefore a crack between the inclusions and the elastic matrix. Nonlinear boundary conditions are considered at the crack faces to prevent mutual penetration between the crack faces. The inclusions have a joint point. We present both differential formulation in the form of a boundary value problem and a variational formulation in the form of a minimization problem for an energy functional on a convex set of admissible displacements. The unique solvability of the problem is substantiated. Equivalence of differential and variational statements is shown. Passage to the limit is investigated as the rigidity parameter of the elastic inclusion goes to infinity. The limit model is analyzed. Junction boundary conditions are found at the joint point for the considered problem as well as for the limit problem.


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How to Cite
Khludnev, A. and Popova, T. ( ) “On junction problem for elastic Timoshenko inclusion and semi-rigid inclusion”, Mathematical notes of NEFU, 25(1), pp. 73-89. doi: https://doi.org/10.25587/SVFU.2018.1.12770.