Stability of three-layered beam on elastic foundation

Abstract

Stability analysis of an axially compressed three-layered beam on an elastic foundation is the main objective of presented work. The analytical model of the beam on the elastic foundation has been proposed. New approach to the structures on the elastic foundation has been presented by the authors which referred to the generalization of common models of the foundation by adopting its variable properties. The assumption proposed by the authors allows for a continuous description of the interaction of the beam with the foundation and a modification of the parameters of this substrate, unlike the discrete Winkler model. The shape function for symmetrical properties of the foundation has been assumed. The critical loads as a function of geometric and mechanical properties of the three-layered beam and the parameters of the elastic foundation were calculated. The original shape function and the function of the deflection have been proposed. In addition, the numerical analysis has been prepared and performed. Sample analytical and numerical calculations have been carried out, sharing a good agreement between the results obtained with both models.