Discontinuous Solutions of Axisymmetric Elasticity Theory for a Piecewise Homogeneous Layered Space with Periodical Interfacial Disk-Shape Defects

By the method of Hankel integral transformation, discontinuous solutions of equations of the axisymmetric elasticity theory are constructed for a piecewise homogeneous uniform layered space obtained by alternately joining two heterogeneous layers of equal thickness and whose junction contains a peri...

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Bibliographic Details
Published in:Mechanics of composite materials 2019-03, Vol.55 (1), p.13-28
Main Authors: Hakobyan, V. N., Hakobyan, L. V., Dashtoyan, L. L.
Format: Article
Language:English
Subjects:
Ceramics
Characterization and Evaluation of Materials
Chemistry and Materials Science
Classical Mechanics
Composite materials
Composites
Cracks
Defects
Elasticity
Glass
Inclusions
Integral transforms
Materials Science
Mathematical analysis
Natural Materials
Operators (mathematics)
Periodicals
Quadratures
Singular integral equations
Solid Mechanics
Thickness
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Summary:By the method of Hankel integral transformation, discontinuous solutions of equations of the axisymmetric elasticity theory are constructed for a piecewise homogeneous uniform layered space obtained by alternately joining two heterogeneous layers of equal thickness and whose junction contains a periodic system of parallel circular disk-shaped defects. On the basis of the solutions found, as examples, the governing systems of integral equations with Weber–Sonin kernels are presented for two cases: with defects in the form of absolutely rigid disk-shape inclusions and circular cracks. Using rotation operators, the governing systems of equations, in both cases, are reduced to a singular integral equation of the second kind, which is solved by the method of mechanical quadratures. Simple formulas for determining the rigid-body displacement of inclusions and crack opening are obtained.
ISSN:0191-5665
1573-8922
DOI:10.1007/s11029-019-09788-y