Geodesic
Transfer of loads from three heterogeneous elastic stringers with finite lengths to an infinite sheet through adhesive layers
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 57 (2023) no. 3, pp. 86-100.

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This paper considers the problem for an elastic infinite plate (sheet), which on parallel finite parts of its upper surface is strengthened by three finite stringers, two of which are located on the same line, having different elastic properties. The stringers are deformed under the action of horizontal forces. The interaction between infinite sheet and stringers takes place through thin elastic adhesive layers having other physical-mechanical properties and geometric configuration. The problem of determining unknown shear stresses acting between the infinite sheet and stringers is reduced to a system of Fredholm integral equations of second kind with respect to unknown functions, which are specified on three finite intervals. It is shown that in the certain domain of the change of the characteristic parameters of the problem this system of integral equations can be solved by the method of successive approximations. Particular cases are considered, the character and behaviour of unknown shear stresses are investigated. Further, for various values of changing characteristic parameters of the problem the multiple numerical results and its analysis are presented.
Keywords: elastic infinite plate, infinite sheet, parallel elastic stringers, contact, adhesive layer, system of integral equations, operator equation 
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A. V. Kerobyan; K. P. Sahakyan. Transfer of loads from three heterogeneous elastic stringers with finite lengths to an infinite sheet through adhesive layers. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 57 (2023) no. 3, pp. 86-100. http://geodesic.mathdoc.fr/item/UZERU_2023_57_3_a2/

[1] A. V. Kerobyan, “On the Problem of an Elastic Infinite Sheet Strengthen with Two Parallel Stringers of Finite Length through Adhesive Layers”, Proceedings of the YSU, Physical and Mathematical Sciences, 54:3 (2020), 153–164 | DOI | Zbl

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

[3] 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”, Proc. of the YSU. Phys. and Math. Sci., 49:2 (2015), 30–39 | DOI | MR

[4] 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 (2002), 14–23 (in Russian)

[5] J.L. Lubkin, L.C. Lewis, “Adhesive Shear Flow for an Axially Loaded, Finite Stringer Bounded to an Infinite Sheet”, Quart. J. of Mech. and Applied Math., 23 (1970), 521 | DOI | Zbl

[6] 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”, Proc. of the Scientific Conference.1 (Dedicated to the 60th Anniversary of the Pedagogical Institute of Gyumri), Vysshaya Shkola, Gyumri, 1994, 73–76 (in Russian)

[7] 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, 753 (2000), 11–16 (in Russian)

[8] 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 (1997), 17–26 (in Russian)

[9] 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) | DOI | MR

[10] A. V. Kerobyan, “Transfer of Loads from a Finite Number of Elastic Overlays with Finite Lengths to an Elastic Strip through Adhesive Shear Layers”, Proc. of the YSU. Phys. and Math. Sci., 53:2 (2019), 109–118 | DOI | Zbl

[11] K. L. Aghayan, “Some Contact Problems for an Elastic Infinite Plate Strengthened by Elastic Overlays”, Proceedings AS USSR, MSB, 5 (1972), 34–45 (in Russian)

[12] R. Muki, E. Sternberg, “On the Diffusion of Load from a Transverse Tension Bar into a Semi-Infinite Elastic Sheet”, Journal of Applied Mechanics, 1968, no. 4, 124–135 | DOI

[13] G.E. Shilov, Mathematical Analysis, Second Special Course, Nauka, Moscow, 1969 (in Russian) | MR | Zbl