Closed-form solutions for two-layer Timoshenko beams with interlayer slip, uplift and rotation compliance

An analytical model for a two-layer Timoshenko beam allowing for interlayer slip, uplift, and relative rotations of the layers’ cross-sections (distortion) is presented and solved in closed form. Each kinematic field at the interface is related to a corresponding traction by means of a linear-elastic law. The proposed model introduces the rotational stiffness at the interface, completely separate from the tangential and normal stiffness, that may restrict the amount of interlayer distortion at the interface. The derived closed-form solutions provide an exact stiffness matrix for any case of boundary and continuity conditions. All solutions are also valid if the effect of the rotational stiffness is excluded. Based on the presented parametric studies it can be concluded that in addition to the known effects of the tangential and normal stiffness of the interface, its rotational stiffness may strongly affect the behaviour of a composite beam. It has been also noticed that for certain combinations of parameters of the interface, a layer that is not directly loaded can bend opposite from the direction of the load. This peculiar effect has been discussed in detail, showing that it is not an artefact of the present model, but a possible physical behaviour that may have practical implications.