PSI - Issue 28

Andrey Fedorov et al. / Procedia Structural Integrity 28 (2020) 2245–2252

2252

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Andrey Fedorov / Structural Integrity Procedia 00 (2020) 000–000

5. Conclusion

The algorithm for the numerical analysis of the stress behavior near singular points of elastic bodies was con sidered. The algorithm is based on extracting from the finite element solution the power law dependence of stresses near singular points of the considered region, where singular solutions are possible. The algorithm is verified for two-dimensional and three-dimensional problems of elasticity theory by comparing the stress singularity exponents founded by the proposed numerical method and those obtained from known analytical and numerical solutions. The proposed algorithm is applicable for variants, in which the stress behavior in the vicinity of singular points is described by one singular term of power-law dependence. It was used to study the stress behavior near the vertex of a single crack, the plane of which is perpendicular to the surface of an elastic half-space. In cases where the stress state in the vicinity of singular points is determined by several singular terms, this algorithm is not applicable. For such cases, the estimation of stresses in the vicinity of the singular points was based on the construction of the appropriate stress distribution pattern with approaching the singular points by the finite element method. The study of stress behavior in the vicinity of the common vertex of several radial spatial cracks in an isotropic material is carried out. The con figurations of two, three and four radial spatial cracks were investigated. The results of numerical studies have shown that at equal distances from the common vertex, the highest stress level is achieved for configurations, in which all the angles between radial cracks are equal, i.e. for symmetrical configurations.

Acknowledgements

This work was performed as part of a government-sponsored program (the state registration number of the topic is AAAA-A19-19012290100-8).

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