Mechanics of adhesive joints as a plane problem of the theory of elasticity. Part I: general formulation

The subject of the paper is a formulation of a general model for adhesive joints within the frame of the plane linear theory of elasticity. Adherends can be of varying thickness and made of various anisotropic materials. The adhesive surface can be curvilinear. The shape of the adherends in the joint can be arbitrary. The adhesive joint can be loaded by shear stresses of any distribution on surfaces of adherends as well as by normal and shear stresses of any distribution on edges of adherends. The general case is expressed in a displacements space with a set of four partial differential equations of the second order and in a stresses space by means of a set of six partial differential equations of the second order. In a specific case a set of two partial differential equations of the second order was formulated for shear stresses in the adhesive. The boundary conditions allow for a possibility of sharp edges for adherends.