Multiply Loaded Timoshenko Beam on a Stressed Orthotropic Half-Plane via a Thin Elastic Layer

The problem of bonded contact between a uniform finite Timoshenko beam and an orthotropic half-plane via a thin elastic layer is considered in this paper. The beam is loaded by distributions of normal and tangential forces, and a uniaxial stress load is applied to the half-plane. The Timoshenko beam theory is extended in such a way that the tangential load is included when the shear contribution to the beam central line deflection is calculated. The layer is formulated as a generalized Winkler cushion including also shear stresses and strains. Governing singular integral equations are stated and numerically solved for the unknown interface stresses. A comparison with a corresponding FE-model is also performed.