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