Abstract
The stress-strain state of an isotropic plane, weakened by a cavity of arbitrary shape, is sought approximately by solving the elastic problem in a large circle with the same cavity. An asymptotic analysis of the problem is carried out with a parameter (the radius of the circle) and, among the variety of stable natural and artificial boundary conditions on the circle, the one is chosen which provides the best approximation of the problem for an infinite body. Asymptotically accurate estimates of the errors in calculating the displacements, stresses and their derivatives are given. Possible extensions of this approach to other bodies, including three-dimensional or two-dimensional wedge-shaped bodies are discussed.
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