Contact Problem on the Interaction of Two Lap Plates, Absolutely Rigid in Tension and Flexible in Bending, with a Thin Circular Sector

Abstract

Using the Fourier method, a solution is constructed for the boundary-value problem of elasticity theory for a circular sector whose radial sides are reinforced by two lap plates absolutely rigid in tension and flexible in bending. On the arc part of its contour, external conditions are given. The stress singularity in the vicinity of top of the circular sector and the behavior of coefficients of the singularity are investigated. It is established that stresses in this vicinity have a singularity of the type r −1+e (e > 0; e → 0 at α → π or α → 2π), whose coefficients, in the general case of loading of the arc part of the sector, differ from zero, which is inadmissible from the viewpoint of the mechanics of brittle fracture. However, an appropriate selection of external conditions on the arc part of sector allows one to equate these coefficients to zero.