PSI - Issue 29

Gianni Bartoli et al. / Procedia Structural Integrity 29 (2020) 55–62 Bartoli et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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As reported in Table 1, the four different discretized models (Fig. 3) and the reduced one (Fig. 4), are used to perform the ana lyses, consisting in the self -weight of the structure (linear static ana lysis) and the ca lculation of the first frequency. It is highlighted how the required computation time increases greatly with the increase of the number of nodes and the subsequent amount of degrees of freedom. 3.3. Results comparison The results obta ined from the ana lyses are here compared in order to have a qua litative identification of the ma in quantities of interest. Specifica lly, the stress distribution in the model and the mode shapes and frequencies are obta ined for each model. The results show how some of the columns seem to be more interested by loca l intensification of stresses, particularly the one above thestatues. Based on the results, and the fields produced from the ana lyses, it is possible to extrapolate the quantities of interest from any part of the object. Specifica lly, a section cut is produced on a pre-determined height (around 1000 mm from the base), in order to check the stress distribution on the column sections. In this extraction some caution is necessary, as the quantity of interest (i) is obta ined from a projection of the stresses on the nodes and (ii) the interpola tion over the section cut is executed outside the Finite Element code, as it is performed within the Paraview context. This introduces a potentia l double source of error, as a first interpolation is performed with averaged va lues and not on the “rea l” solution of the computationa l problem, and a f urther interpolation is introduced because of the different meshes adopted inside the model. It is however not possible to completely avoid these sources of error, as the standard methods of extraction of the quantities of interest rely on these interpolat ion procedures, and different meshes are unavoidable in definingmodels with different decimation/approximation (Giacconeet a l. 2020).

(1)

(2)

(3)

(4)

Fig. 5. 1 st mode shape with different mesh refinements.

An assessment of the mesh influence on the finite element results is verified by comparing the genera l outputs reported in Fig. 5 where it is possible to qua litatively compare the deformed shape of the first vibration mode as obta ined with the different models: some minor differences are highlighted . In Table 2, to provide a globa l picture, the base reaction and the ma in frequency obta ined with the different models are reported. Sensitivity of the first frequency is reportedassumingas reference thefrequencyvalueprovidedby the finest model.

Table 2. Base reactions and modal frequencies obtained with the different models. Model Base reaction [MN]

1 st frequency ratio [-]

(1) Volumetric 3D (2) Volumetric 3D (3) Volumetric 3D (4) Volumetric 3D (5) Reduced 3D-1D

59,2501 59,0551 59,1509 57,4200 59,0700

1.000 1.022 1.039 1.030 1.033