PROBLEM OF BENDING OF A PLATE WITH FILLED SLIT - Shatskyi, I. P.; Kurtash, I. S. (Computer Science and Applied Mathematics, 2017)
The problem of bending of an elastic plate weakened by narrow rectilinear through slit filled with lowmodulus material is considered within framework the classical Kirchhoff’s theory. It is supposed that the filler and plate are in perfect mechanical contact. For the inclusion of narrow width the hypothesis of elastic Winkler’s layer is accepted. The boundary problem for the biharmonic equation with complicated boundary conditions on the cut is formulated. The analytical solution of singular integrodifferential equation of the problem is built in case of the elliptical form of slit and uniform bending load. The jump of the normal rotation angle on the cut, the stress intensity factor for crack tips and the stresses in the filler are obtained. Special attention is paid to the issue of limited equilibrium of composition. The two mechanisms of fracture are considered: cracking of the plate near the peak of a slit and breach of filler integrity. The first of them is described by the criterion of the linear mechanics of fracture and the second one is described by the classical theory of strength. The considered model of the filled slit allows analytically to evaluating the results of the renovation of defective lamellar structures under bending conditions. The key parameters that determine the reinforcement efficiency are relative stiffness and relative strength of the filler. For a given strength value there is a rigidity value for which the composition is equable according to the criteria of the boundary state of the plate and inclusion. In this case the ultimate bending load reaches the maximum.