On the problem of an elastic infinite sheet strengthen with two parallel stringers of finite length through adhesive layers

In this article the problem for an elastic infinite sheet (plate), which on two parallel finite parts of its upper surface is strengthened by two parallel finite stringers having different elastic properties is considered. The parallel stringers are arranged (located) asymmetrically with respect to horizontal axis of the sheet and are deformed under the action of horizontal forces. The interaction between infinite sheet and stringers through thin, elastic adhesive layers is realized. The determination problem of unknown shear stresses acting between the infinite sheet and stringers are reduced to a system of Fredholm integral equations of second kind with respect to unknown functions, which are specified on two parallel finite intervals. It is shown that in the certain domain of the change of characteristic parameters of problem this system of integral equations in Banach space can be solved by the method of successive approximations. The particular cases are observed, the character and behaviour of unknown shear stresses are investigated.