This paper investigates the dynamics of a real-life aerospace structure possessing a strongly nonlinear component with multiple mechanical stops. A full-scale finite element model is built for gaining additional insight into the nonlinear dynamics that was observed experimentally, but also for uncovering additional nonlinear phenomena, such as quasiperiodic regimes of motion. Forced/unforced, damped/undamped numerical simulations are carried out using advanced techniques and theoretical concepts such as numerical continuation and nonlinear normal modes.