PSI - Issue 78

Giuseppina Uva et al. / Procedia Structural Integrity 78 (2026) 1048–1055

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Mode I

Mode II

Mode III

Solid Model

Mode I

Mode II

Mode III

Shell Box Model

Figure 4. First three vibration modes of the two models: Solid Model (top); Shell-Box Model (bottom).

Finally, non-linear static analysis has been performed to validate the Shell Box Model in the non-linear field, assuming a load profile proportional to the 1 st mode according in the directions +/- Z, and as a control point the central point of the upper plane. Figure 5 shows the capacity curves obtained for the complete and the reduced model. It can be noticed that the two models have given substantially identical results, both with regard to the initial elastic stiffness and the post-elastic response. The main difference is about the computation time, since that the solid model takes about 70 hours to run, while the Shell-Box model takes about 8 minutes, thus allowing a reduction of about 99.81%. Regarding the damage development, the results (Figure 5) show that the Shell-Box Model is able to capture the distribution of damage sufficiently accurately, apart from a local spurious effect induced by the geometry of the shells, that determines a fictitious damage at the intersection of the shells. Thus, although the damage map is not as detailed and accurate as that of the solid model, it allows to correctly capture the collapse mechanism.