A mixed finite element formulation for Timoshenko beam on Winkler foundation

A mixed formulation for Timoshenko beam element on Winkler foundation has been derived by defining the total curvature in terms of the bending moment and its second order derivation. Displacement and moment have been chosen as primary variables, while slope and first derivation of moment have been chosen as secondary variables. The behaviour matrix for Timoshenko beam element has been obtained in mixed form by using weak formulation with equilibrium and compatibility equations. The presented formulation makes the analysis of beams free of shear locking.