Abstract:
The article considers the problem for an elastic infinite plate (sheet), which along of two parallel lines of its upper surface is strengthened by systems of finite number finite-length stringers having different elastic properties. The interaction between infinite sheet and stringers take place through thin, uniform, elastic adhesive layers having other physical-mechanical properties and geometric configuration. The stringers are deformed under the action of horizontal concentrated forces, which are applied at one end points of stringers. The problem of determining unknown contact forces acting between infinite sheet and stringers is reduced to the system of Fredholm integral equations of second kind with respect to arbitrary finite number of unknown functions, which are specified along of two parallel lines on different finite intervals. Further, are determined of the change regions of the problem characteristic parameters, for which this system of integral equations allows the exact solution and which can be solved by the method of successive approximations. Some particular cases are considered and the character and behavior of unknown shear contact forces near the end points of the stringers are investigated. For these cases numerical results depanding on the multiparameters of the problem are investigated in the previous article (A.V. Kerobyan, K.P. Sahakyan, Proc. YSU. Phys. Math. Sci. 57 (3) (2023), 86–100).
Keywords:infinite sheet, plate, parallel finite stringers, adhesive layer, adhesive contact, system of integral equations, operator equation
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