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

• Published in: Mechanics of composite materials Vol. 55; no. 1; pp. 13 - 28
• Main Authors: Hakobyan, V. N., Hakobyan, L. V., Dashtoyan, L. L.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2019; Springer; Springer Nature B.V
• 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; periodical mixed boundary-value problems; disk-shape crack; circular rigid inclusion
• ISSN: 0191-5665; 1573-8922
• DOI: 10.1007/s11029-019-09788-y

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.