Buckling of beams and coatings of finite width in bilateral frictionless contact with an elastic half-space

In this work, a simple and efficient finite element–boundary integral equation coupling method is adopted for studying the buckling of beams and coatings resting on a three-dimensional elastic halfspace. For this purpose, a mixed variational formulation based on the Green function of the substrate is adopted by assuming as independent fields beam displacements and contact pressures. Euler-Bernoulli beams with finite width and different combinations of end restraints are considered. Some numerical tests illustrate the accuracy of the proposed formulation, with particular attention to the convergence to existing analytical and numerical solutions and to the proposal of new estimates of beams and coatings buckling wavelength and critical loads for varying length-to-width ratio and beam substrate relative stiffness.