The Nonuniform in Width Stressed State of the Lap Adhesive Joint

The bearing capacity of construction is usually determined by the strength of the joints, where the stress state is irregular. Most existing mathematical joint models are one-dimensional, and imply a uniform stress distribution in width. However, there are constructions for which classical models are not applicable. To calculate the stress state of such joints, it is necessary to take into account the nonuniformity of stresses not only in the length, but also in the width of the joint. To solve such problems, a simplified two dimensional model of the lap adhesive joint of rectangular plates has been proposed. The simplification is that we consider the movement of the layers only along the applied load. Stresses are assumed to be distributed uniformely over the thickness of the layers, and the adhesive layer works only on shear. These simplifications made it possible to obtain an analytical solution to the problem. The stressed state problem for the adhesive joint of two rectangular plates, one of which is rigidly fixed along one of the sides, and the second plate is loaded with an nonuniform normal load at one of the butts, is solved. The problem is reduced to a system of second-order partial differential equations relatively to the longitudinal displacements of the joined layers. The solution is built using the variables separation method, and is a functional series consisting of eigenfunctions. The boundary conditions on the side are satisfied exactly. Satisfying the boundary conditions at the butts leads to a system of linear equations for the unknown coefficients of the functional series. The convergence of the obtained solution is proved. The model problem is solved and the numerical results are compared with the results of calculations performed using the finite element method. It is shown that the proposed approach is accurate enough for design problems.