Plate N Sheet V4 Full Crack

The stability of an elastic-brittle rectangular plate with three discontinuous cracks is studied. The system of boundary-value equations is reduced to a system of singular integrals and integro-algebraic equations and this system is solved by the method of mechanical quadratures. The region of stability of the plate is determined. The governing equations are also solved numerically for a very thin plate with three discontinuous cracks.

The propagation of a surface crack in a gasket is analyzed. The gasket is modeled as an elastic plate of finite thickness with a linear strip of thickness h which is fixed on one side of the plate. The cracks are started by a displacement of the strip. The wave equations are solved for a crack of length 2a, for a crack of length 4a, and for two cracks of length 4a along the strip. Asymptotic analysis is performed for cracks of lengths greater than the strip width. The results are verified by numerical calculations of the waves on the gasket. The linearization method is applied to the problem of stability of a closed crack in a circular cylinder of diameter 50 times the height. The condition of stability of the cylinder is obtained.

The influence of the basal friction on the stress-intensity factor KI of a three-dimensional crack having a periodic dependence on the horizontal coordinate in the direction of the crack is studied. The stress intensity factor is defined as the ratio of the applied stress to the strength of the material. The problem is reduced to a system of singular integrals and integro-algebraic equations and this system is solved by the method of mechanical quadratures. The stress-intensity factor is calculated as a function of the frequency of the vertical load which is applied to the plane surface of the crack. The analysis is performed for a single crack in an elastic-brittle material and for a pair of cracks in an elastic-brittle material.

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