Three-Dimensional Shakedown Solutions for Railway Structure Under Train Loads

Shakedown analysis is a robust approach to solve the strength problem of a structure under cyclic or repeated loading, e.g. railway structures subject to rolling and sliding loads. A three-dimensional analytical shakedown solution is developed in this paper for the strength analysis of railway structure under multiple wheel loads, in which wheel/rail contact load is idealized as a Hertz distribution with circle contact area. In order to apply the Melan static shakedown theorem to the stability analysis of railway structures, an analytical solution of the elastic stress distribution in a single layer half-space under moving train loads is derived. Meanwhile, the residual stress distribution in the railway structure is simplified. Finally, the shakedown limit can be obtained in a direct way. Parametric study show that the shakedown limit significantly decreases with the increase of frictional coefficient from 0.0 to 1.0 and the Poisson's ratio has little effect on the shakedown limit. The obtained results give a useful reference for the engineering design of the railway structure.