Buckling of Timoshenko beams in frictionless contact with an elastic half-plane

This paper deals with the buckling analysis of Timoshenko beams of finite length in frictionless contact with an elastic substrate in generalized plane stress or plane strain regime. The proposed finite element method makes use of a mixed variational formulation based on the boundary integral equation commonly referred to as Flamant solution. The corresponding finite element model for the soil-structure interaction system adopts two-node locking-free finite elements for Timoshenko beam and constant soil reaction underlying each foundation element. Significant cases are thoroughly discussed and a classical two-dimensional finite element model is developed in order to have reference solutions. Numerical examples show that the proposed model is very simple and effective, and the Timoshenko beam model appears to be very useful in determining buckling loads in good agreement with reference solutions. Conversely, the Euler-Bernoulli beam model provides satisfactory results for long beams on soft soil only.