Study of the influence of finite element shape functions on the numerical performance of pantograph–catenary interaction simulations

This thesis investigates the influence of the order of the shape functions adopted for an Euler–Bernoulli beam element and of refinement strategies on the numerical prediction of the contact force exchanged in the pantograph–catenary system. In particular, baseline configurations are compared with meshes featuring an increased number of elements (element refinement) and with formulations employing enriched elements (p-refinement), in order to quantify their impact on both accuracy and computational cost. The model is developed within a finite-element framework, using implicit Newmark time in- tegration and a penalty-based contact formulation, and it is validated against the reference solution by Collina and Bruni. Building on this basis, an adaptive strategy is proposed, based on the localized enrichment of elements within a moving window centred on the contact region, with the aim of reducing the computational time while maintaining an accuracy level comparable to that of a fixed mesh. The results indicate that a narrow window (nf = 2) with third-order local enrichment provides a particularly favourable trade-off for repeated simulations, whereas wider win- dows (e.g. nf = 10) may be preferable when a more global representation of the system response is required, capable of capturing wave propagation even in regions far from the contact zone.