科研之友
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摘要
Using the method of singular integral equations, we have obtained a solution of the plane problem of the theory of elasticity for a plane with a semiinfinite rounded V-shaped notch under antisymmetric loading. On this basis, we have determined relations between the stress intensity factor at the vertex of a sharp V-shaped notch, the maximal stresses on the boundary contour or stress gradient at the vertex of the corresponding rounded V-shaped notch, and its rounding-off radius. It is shown that such dependences are ambiguous: for the same curvature at the notch vertex, they are significantly different for various shapes of its neighborhood. For finite bodies with V-shaped notches, the obtained solutions are asymptotic dependences for small rounding-off radii of their vertices. Such relations can be used in passing to the limit for determination of the stress intensity factors at the vertices of sharp notches based on the solutions for the corresponding rounded stress concentrators.
