Axisymmetric Stress State of Adhesive Joint of a Circular Patch with a Plate Weakened by a Circular Cut-out

Adhesive lap joints are widely used in modern structures. Known analytical mathematical models of the stress state of lap joints describe the joints of straight beams or cylindrical coaxial pipes. It is assumed that the stress state of these structures depends on only one coordinate. The study of the stress state of plates with defects, which are reinforced by patches, in most cases requires the use of at least two-dimensional mathematical models. In this work, it is shown that the axial symmetry of the plate, the cut-out, the patch, and the applied load makes it possible to reduce the problem to a one-dimensional problem in the polar coordinate system. An adhesive lap joint with circular symmetry is considered for the first time. The stress-strain state of the structure is described in an analytical form. Comparison of the results of calculating the stress state of the joint with the results of finite element modelling showed good adequacy of the proposed mathematical model.