The three-dimensional problem of a thin inclusion in a composite elastic wedge

• Published in: Journal of applied mathematics and mechanics Vol. 75; no. 5; pp. 589 - 594
• Main Authors: Aleksandrov, V.M., Pozharskii, D.A.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01-01-2011; Elsevier
• Subjects: Applied sciences; Bonding; Contact stresses; Elastic wedges; Exact sciences and technology; Fractures; Fundamental areas of phenomenology (including applications); Inclusions; Mathematical analysis; Mechanical properties and methods of testing. Rheology. Fracture mechanics. Tribology; Metals. Metallurgy; Physics; Shear; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Three dimensional; Wedges; Fourier transformation; Solid inclusion; Contact stress; Sandwich structure; Mechanical contact; Integral equation; Asymptotic approximation; Rubber; Wedge; Modeling; Elastic contact; Contact surface
• ISSN: 0021-8928; 0021-8928
• DOI: 10.1016/j.jappmathmech.2011.11.013

The three-dimensional problem of a thin rigid elliptic inclusion in the middle of a composite elastic wedge is investigated. The wedge consists of three connected wedge-shaped layers connected by a sliding clamp, in which the layer containing the inclusion is incompressible. The outer faces of the composite wedge are also under sliding-clamp conditions. The inclusion is completely bonded to the elastic medium in the contact region. Using Fourier and Kontorovich–Lebedev transformations, a system of integral equations of the problems are derived for the shear contact stresses. A regular asymptotic method is used to solve this system. Calculations are carried out. The results can be used for calculations on the strength of rubber-metal articles and structures having a corner line.