Asymptotic solution of three-dimensional problems of the theory of elasticity of extended plane separation cracks
A solution of three-dimensional elasticity theory problems for separation cracks occupying a plane domain with one characteristic dimension much smaller than the other is constructed by the method of matched asymptotic expansions (cracks that are extended along a certain plane curve). The appropriate terms of the expansion of the solution in a small parameter characterizing the extent of the crack are constructed using an integro- differential equation in the displacement of points of the crack surface. For cracks that are extended along a line, the representation of the integro-differential equation in terms of a two-dimensional Fourier transform is used, which substantially simplifies the calculation. In the general case, the expansion is executed directly in the equation written in x-space. The asymptotic expansion constructed is valid in the middle part of the crack, outside of certain small neighbourhoods of the ends of the curve along which the crack is drawn. The accuracy of the solution obtained is analysed, and formulas are presented for the crack aperture and the distribution of the stress intensity factors for specific kinds of cracks.
three-dimensional elasticity theory problems
integro-differential equation in the displacement of points of
distribution of the stress intensity factors
integro-differential equation in the displacement of points of the crack surface
scientific article; zbMATH DE number 3938800