Closed-form solutions for modelling the rotational stiffness of continuous and discontinuous compliant interfaces in two-layer Timoshenko beams

Abstract

An analytical model for a two-layer Timoshenko beam with a compliant interface is presented. A family of closed-form solutions is given for several cases of contact conditions at the interface that can include or exclude interlayer slip and relative rotations of the layers’ cross sections (distortion), with particular attention devoted to the latter. Each kinematic field at the interface is related to a corresponding traction by means of a linear-elastic law. The novelty of the proposed model is the rotational stiffness at the interface, completely separate from the tangential stiffness, that can control the amount of interlayer distortion at the interface. The derived closed-form solutions allow an exact stiffness matrix for any case of admissible boundary conditions to be obtained, as well as for continuity conditions in the case where multiple elements with closed-form solutions are mutually connected. The application of the closed-form solutions for continuous interface (adhesive joints) or for discontinuous interface (shear connectors or adhesive defects) is presented. Accuracy and applicability of the closed-form solutions have been assessed in two representative numerical examples allowing to conclude that the rotational stiffness at the interface can strongly affect the behaviour of a two-layer beam.