Shakedown analysis of train wheels by Fourier series and nonlinear programming

This paper presents a procedure for shakedown analysis of train wheels on the basis of given wheel–rail contact tractions. The main topics dealt with in the paper are: comparative formulations by both static and kinematic theorems; exploitation of the geometry and material axial symmetry by finite strip, Fourier series modelling in space and consequent reduction of the analysis to decoupled problems of much smaller sizes; numerical solutions by available nonlinear programming algorithms of the ad hoc formulated optimization problems; comparisons of the results with those obtained from step-by-step three-dimensional finite element analyses.