Geodesic
Transfer of loads from a finite number of elastic overlays with finite lengths to an elastic strip through adhesive shear layers
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 53 (2019) no. 2, pp. 109-118.

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This article deals with the problem of an elastic infinite strip, which is strengthened along its free boundary by a finite number of finite overlays with different elastic characteristics and small constant thicknesses. The interaction between the strip and the overlays is mediated by adhesive shear layers. The overlays are deformed under the action of horizontal forces. The problem of determination of unknown stresses acting between the strip and overlays are reduced to a system of Fredholm integral equations of the second kind for a finite number of unknown functions defined on different finite intervals. It is shown that in the certain domain of variation of the characteristic parameter of the problem this system of integral equations in Banach space may be solved by the method of successive approximations. Particular cases are discussed and the character and behaviour of unknown shear stresses are investigated.
Keywords: Contact, overlays (stringers), elastic infinite strip, adhesive shear layer, system of integral equations, operator equation. 
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A. V. Kerobyan. Transfer of loads from a finite number of elastic overlays with finite lengths to an elastic strip through adhesive shear layers. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 53 (2019) no. 2, pp. 109-118. http://geodesic.mathdoc.fr/item/UZERU_2019_53_2_a4/

[1] A. V. Kerobyan, K. P. Sahakyan, “Loads Transfer from Finite Number Finite Stringers to an Elastic Half-Plane through Adhesive Shear Layers”, Proceedings of NAS RA. Mechanics, 70:3 (2017), 39–56 (in Russian)

[2] A. V. Kerobyan, “Contact Problem for an Elastic Half-Plane with Finite Number Finite Elastic Overlays in the Presence of Shear Interlayers”, Topical Problems of Continuum Mechanics, Proceedings of IV Inter. Conference (Yer., 2015), 241–245 (in Russian)

[3] A. V. Kerobyan, “Contact Problems for an Elastic Strip and the Infinite Plate with Two Finite Elastic Overlays in the Presence of Shear Interlayers”, Proceedings of NAS RA. Mechanics, 67:1 (2014), 22–34 (in Russian)

[4] A. V. Kerobyan, “About Contact Problems for an Elastic Half-Plane and the Infinite Plate with Two Finite Elastic Overlays in the Presence of Shear Interlayers”, Proceedings of the YSU. Physical and Mathematical Sci., 2015, no. 2, 30–39

[5] E. Kh. Grigoryan, A. V. Kerobyan, S. S. Shahinyan, “The Contact Problem for the Infinite Plate with Two Finite Stringers One from which is Glued, Other is Ideal Conducted”, Proceedings of NAS RA. Mechanics, 55:2 (2002), 14–23 (in Russian)

[6] J. L. Lubkin, L. C. Lewis, “Adhesive Shear Flow for an Axially Loaded, Finite Stringer Bonded to an Infinite Sheet”, Quarterly Journal of Mechanics and Applied Mathematics, XXIII (1970), 521–533

[7] A. V. Kerobyan, V. S. Sarkisyan, “The Solution of the Problem for an Anisotropic Half-Plane on the Boundary of which Finite Length Stringer is Glued”, Proceedings of the Scientific Conference, Dedicated to the 60th Anniversary of the Pedagogical Institute of Gyumri, Vysshaya Shkola, Gyumri, 1994, 73–76 (in Russian)

[8] E. Kh. Grigoryan, “On Solution of Problem for an Elastic Infinite Plate, One the Surface of which Finite Length Stringer is Glued”, Proceedings of NAS RA. Mechanics, 53:4 (2000), 11–16 (in Russian)

[9] V. S. Sarkisyan, A. V. Kerobyan, “On the Solution of the Problem for Anisotropic Half-Plane on the Edge of which a Nonlinear Deformable Stringer of Finite Length is Glued”, Proceedings of NAS RA. Mechanics, 50:3–4 (1997), 17–26 (in Russian)

[10] E. Melan, “Ein Beitrag Zur Theorie Geschweisster Verbindungen”, Ingeniuer-Archiv, 3:2 (1932), 123–129

[11] G. E. Shilov, Mathematical Analysis (Special Course), M., 1961, 442 pp. (in Russian)

[12] Kerobyan A.V., “To the Solution of the Problem for an Elastic Strip with Finite Number Elastic Finite Overlays Trough Adhesive Shear Layers”, The Problems of Dynamic of Interaction of Deformable Media, Proc. of IX Inter. Conf. (Yer., 2018), 186–190 (in Russian)