Static and buckling analysis of thin beams on an elastic layer

In this work, a simple and effective numerical model for sandwich composites and/or thin films on an elastic layer is proposed. The Euler–Bernoulli beam hypothesis and an approximate expression of the Green's function of an elastic layer on a rigid base are adopted. The procedure is based on existing contributions, but the resulting power series expansion is more accurate and validated by means of a finite element model of the layer. A simple finite element–boundary integral equation approach is then adopted for performing static and buckling analysis of the Euler–Bernoulli beam in frictionless contact with the elastic layer. The proposed approach is based on a mixed variational formulation that assumes both beam displacements and contact reactions between the beam and the layer as independent fields. The influence of the layer height and rigid base contact type is taken into account, together with a parameter that considers the ratio between the beam and layer stiffness. Numerical tests show that a beam on a thick layer unbonded to the rigid base behaves similarly to a beam on a half-plane. On the other hand, a beam on a thin layer bonded to the rigid base is characterized by less deformability, large contact reactions at beam ends, and by different critical loads, with a low convergence speed to the behavior of a beam on a half-plane.