Mechanics of adhesive joints as a plane problem of the theory of elasticity. Part II: Displacement formulation for orthotropic adherends

The present paper is a continuation of the general formulation discussed in the paper: Mechanics of adhesive joints as a plane problem of the theory of elasticity. Part I: general formulation, Archives of Civil and Mechanical Engineering 10 (2) (2010). Adhesive joints between adherends of varying thickness, made of various orthotropic materials are considered. The adhesive surface can be curved and shapes of the adherends are arbitrary. The joints can be loaded with shear stress distributed arbitrarily on the adherend surfaces as well as by normal and shear stresses of any distribution along the adherend edges. The problem is formulated in terms of displacements in the form of four partial differential equations of the second order. The boundary conditions allow for existence of sharp edges of adherends. Notions of the obtuse sharp edge and the tangent sharp edge are introduced. The presented examples include complete solutions within the framework of the plane theory of elasticity for adhesive joints with adherends of constant thickness and adherends of varying thickness and curved adhesive surface. The influence of sharp edges on the reduction of stress concentration in the adhesive and the adherends is illustrated. The assumptions, notation and equations presented in the general formulation of Part I are used.