Fundamental solution and integral equations for Timoshenko beams

It is well known that Timoshenko’s theory is a refined beam theory which takes shear deformation and rotatory inertia into account. Here, for the first time, an integral equation description for all relevant states, the deflection, the rotation, the bending moment, and the shear forces is derived. Adding the well known integral equations for axial displacements and forces in bars under tension, arbitrary plane frame structures can be modelled by adequate combinations of these equations. Examples show the exactness of the results and demonstrate the applicability of this boundary integral formulation which can be considered as a first step to dynamic analyses of Timoshenko beam systems.