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The threat of rockfall impacting bridges in mountainous areas poses a great risk to the safety of passing trains. This study delves into the dynamics of rockfall impact and its implications on the interaction between train vehicles and bridges. Leveraging LS-DYNA, this study first captured the force–time history of rockfall impact on bridge structures. Subsequently, there was a comparison with the impact forces generated at various speeds with those predicted by established formulas, validating the accuracy of simulations. Employing BANSYS software, the dynamic responses of both bridge structures and the vehicle–bridge coupling system to falling rocks were analyzed. The investigation encompassed parameters such as impact speed, position, and train location. The findings reveal that escalating impact speeds correlate with increased average and maximum impact forces from falling rocks. Notably, the average impact force does not linearly correspond with rock speed and often exceeds values calculated by conventional formulas. Impact position minimally affects maximum impact force, yet alterations in position prolong impact duration, consequently reducing average impact force. Rockfall-induced impacts precipitate notable spikes in train lateral acceleration, lateral wheelset force, wheel unloading rate, and derailment coefficient, albeit with a comparatively lesser impact on vertical acceleration. Increasing impact speed and altering position intensifies the vehicle’s response, particularly when the train is in close proximity to the impact site.

Fundamental principles controlling the deflection behavior of a simply supported beam responding to the impact action of a solid object is revealed in this paper. The significant mitigating effects that the mass of the beam have upon its impact resistant behavior have been illustrated with examples. It is a myth that the static resistance of the beam is indicative of its impact resistance. The important effects of "cushioning" and the higher modes phenomenon have also been identified by the analytical study presented herein. Hand calculations and computer analysis methods are introduced and evaluated by comparison with results obtained from finite element analyses using LS-DYNA.

Numerical simulations were conducted to validate computational and constitutive models for steel materials through dynamic material tests involving both tension and compression. These simulations involved the numerical modeling of the split Hopkinson pressure bar (SHPB) apparatus, with the appropriate loading applied directly in compression and indirectly in tension. To induce a tensile wave within the specimen, a shoulder, such as a coupler or collar, was interposed between the bars. The simulations were carried out using the LS-DYNA finite element code. In these numerical simulations of the SHPB tests, the MAT-15 Johnson–Cook material model was applied to represent mild steel. The resulting stress–strain relationships obtained under both compression and tension conditions were subsequently compared to corresponding experimental data. The primary objectives of these simulations were to determine the optimal placement of strain gauges on both the input and output bars of the tensile SHPB setup. Additionally, the simulations aimed to assess the influence of the gauge length-to-diameter ratio on the behavior of the mild steel specimen subjected to dynamic tension and compression. The results showed that the pulse produced due to the mechanical mismatch of the element at boundaries can be avoided using the length of the input bar smaller than the output bar. Further, the location of the strain gauge in the case of the output bar should be toward the output bar-shoulder interface, while in the case of the input bar, it should be considered at the center of the span of the bar.

The penetration of a plate under a high-velocity impact loading exhibits a very complex dynamic response process with highly nonlinear characteristics. A failure criterion was presented for the cracking model of homogeneous isotropic material. Based on this failure criterion, numerical simulation was conducted on the process of homogeneous isotropic metal plate impacted by a rigid ball at high-velocity by using LS-DYNA program. The relationship between effective stress and time at the impact point was expressed and analyzed. The curves of energy versus time were also plot to illustrate the impact process obviously.