Stacked multibody systems, exemplified by overhead cranes in nuclear power plants (OCNPP), play a crucial role in engineering applications. Under strong earthquakes, non-smooth behaviors, including detachment and stick-slip between wheels and rails, may induce uncertain motions, potentially triggering catastrophic accidents. In this study, a co-simulation method using ANSYS and MATLAB is proposed for modeling the stacked components. The wheel-rail relationship is modeled with multiple frictional unilateral constraints, which are delineated by a set-valued force law. The resultant contact-impact problem is formulated as a nonlinear complementarity problem, and then reconstructed and rescaled using a model smoothing method combined with a normalization technique to facilitate convergence. Lastly, numerical simulations are conducted, taking into account various wheel locking conditions, to explore the nonlinear behavior and stress distribution. The results illustrate the non-smooth characteristics of frictional contact within the stacked components. The presented work is expected to guide the structural optimization of stacked multibody systems.