The: Stressed state of a box-like shell reinforced by a pair of symmetric inclusions parallel to the edge of the shell

Abstract

The problem of the stressed state of an infinite box-like shell of rectangular profile is solved. The shell is reinforced by two absolutely rigid thin inclusions placed on opposite sides and parallel to the shell edges. This problem can be reduced [1] to that concerned with the joint plane and bent state of a plate with defects, the role of the latter being played by the shell edges and the inclusions. On applying a semi-infinite cosine Fourier transform the problem can be reduced to a system of two integral equations with respect to the jumps of the generalized transverse force and shear stresses, which has no solutions in terms of integrable functions [2–4]. The solution is sought in the space of functions having non-integrable singularities by applying regularization methods for divergent integrals [4]. Diagrams of the dependence of inclusion settling on the length of inclusions and the geometric dimensions of the cross-sections of the shell are constructed.