PSI - Issue 58

Mikkel L. Larsen et al. / Procedia Structural Integrity 58 (2024) 73–79 M.L. Larsen et al. / Structural Integrity Procedia 00 (2024) 000–000

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The support conditions are modelled as close to reality as possible. The undersides of the supports are in the experimental setup welded to a thick steel table. The setup is quite rigid, thus a fully fixed support is applied on the underside of the supports in the FE model. The pins are free to rotate in the experimental setup, wherefore cylindrical joints are used in the FE model. The vertical force is applied as displacement d v in the direction indicated by the red arrow in Fig. 4. The applied deformation is similar to the experimentally applied deformation.

3.1. FE validation

The FE model is validated against the experimental results, by comparing the measured strains from experiments with the predicted strains at the same locations from the FE model. The comparisons are shown as graphs in Fig. 5. The strains have been normalized. Each point corresponds to a measured or predicted strain at a specific strain gauge and the dashed lines are used only for indicating the trend of the results. As seen from Fig. 5, the FE model predicts the strains much higher than the experimentally observed strains. This indicates that the FE model is too sti ff . As the experiment is displacement-controlled, the displacement in the experiments is applied directly to the FE model. As the strains are too high, it indicates that a too high force has to be applied to generate the desired displacement. This is also observed when examining the reaction force at the displacements. However, as seen from Fig. 5, the general trend of the FE model is corresponding to the experimental results.

Fig. 5. Comparison of experimentally obtained strains and FE predicted strains for the global gauges. The strains are normalised.

To quantify the accuracy of the model, the root-mean-square error (RMSE) between the FE model and the ex periment is calculated using the experimentally obtained strains ε exp and FE predicted strains ε FE . The root mean square error of the FE model is provided in Tab. 1. Furthermore, the prediction ratio P = ε FE /ε exp is determined. The prediction ratio will be greater than 1 if the FE predicted strains are higher than the experimentally obtained strains and vice-versa. The averaged prediction ratio P µ for all gauges are likewise given in Tab. 1. As seen from the table, the averaged prediction ratio is above two indicating that the FE predicts over double the strains as observed in the experiments. Furthermore, the RMSE is also relatively high. The results from the local gauges are disregarded as the global gauges are expected to perform the best. From the validation, it can be observed that the FE model is too sti ff as compared to the real experiments. This can be caused by several possible factors such as material model inconsistencies, geometry inconsistencies and incorrect modelling of boundary conditions (Arora (2011)). During the testing, it was observed that the top pin deformed slightly, see Fig. 6. Due to the simple cylindrical support in the FE model, this e ff ect is not captured correctly by the FE analysis. Thus, to better capture the real flexibility of the pinned connection in the experiments, the FE model is updated to include equivalent springs at the pin. Two springs are applied as shown in Fig. 6. The lower pinned connection is kept fixed in the FE model, as during the experiments no deformations were observed at this location. The spring sti ff ness of each spring is assumed to be identical and the sti ff ness is determined using a parameter-based model updating technique in ANSYS Workbench. An optimization scheme is applied where the strains from strain 3.2. FE model-updating