PSI - Issue 54

V.M.G. Gomes et al. / Procedia Structural Integrity 54 (2024) 561–567 Author name / Structural Integrity Procedia 00 (2023) 000–000

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iso-parametric elements formulated in the displacement field with quadratic shape functions and uniform reduced integration scheme (McMeeking and Rice (1975); Flanagan and Belytschko (1981); Zienkiewicz et. al. (2005)). All constituent components of the leaf spring are assumed to have a linear elastic behaviour so the constitutive matrix of the material, C , is defined by E = 202500 MPa and ν = 0.29. With regards contact formulation, in equations system (1), K c denoting the contact sti ff ness matrix and F c the contact force vector. The contact problem is symmetric, formulated to large deformation and large sliding, and it is solved the augmented Lagrangian method (Simo and Laursen (1992); Laursen and Simo (1993))with gap function defined via pinball algorithm (Belytschko and Neal (1991)). The contact stresses are computed in the Gauss points for quadrilateral (4 Gauss integration points) and triangular (3 Gauss points) contact elements.

3. Results

3.1. Characteristic Behaviour Curves

In terms of the characteristic curve, we can see in Figure 4 a comparison of the characteristic sti ff ness curve derived by the numerical model and the characteristic curve proposed by the UIC 517 standard (UIC 517 (2007)). The good match of the numerical model to the model proposed by UIC-517 in the di ff erent loading regimes should be highlighted from the comparison of these models. Regarding regime I, the numerical model is significantly more sti ff , with the transition point occurring near 70 mm rather than 62.9 mm as stated in the UIC 517 standard. A similar pattern may be seen in stage II, with the numerical model being more rigid than the standard one. It should be noted that the numerical model exhibits non-linear behaviour. In the case of the UIC model, the standard likewise exhibits non-linear behaviour, although in this comparison, its behaviour was linearized.

Fig. 4. Comparison between vertical spring sti ff ness in stages I and II.

3.2. Stress Analysis during Wagon Circulation

In this phase, the imposed displacement and stress spectra are observed as presented in Fig. 5. According to Fig. 5, the initial condition (wagon loaded) corresponds to a vertical displacement of 88 mm and a longitudinal stress of 920 MPa. Since the data collected by sensors have a certain value of intrinsic noise, the noise is removed by digital filtering techniques. The Butterworth low-pass digital filter with a cut-o ff frequency, f cut = 25 Hz and a 2nd-order Butterworth polynomial function is considered with a sampling frequency of f s = 2000Hz.