PSI - Issue 64

Elide Nastri et al. / Procedia Structural Integrity 64 (2024) 153–160 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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3.1. FE model setup The modelling process comprised several stages. Initially, a geometric model has been developed based on the photogrammetric survey of the bell tower. Subsequently, the model has been partitioned into analyzable components to facilitate targeted investigation. Structured and sweep hexahedral meshes have been utilized to enhance analysis accuracy and avoid distortion and shear locking. The mesh consisted of three-dimensional, deformable solid elements (C3D8R eight-node brick elements with reduced integration type), with an average size of 250 mm for structured elements and 150 mm for sweep elements, balancing accuracy with computational efficiency (Fig. 3a). Regarding boundary conditions and interactions, tie-type constraints were applied to assemble various floor blocks, while a fixed base was assumed to neglect soil effects. Interaction with the adjacent church was considered by constraining contact surfaces with axial springs in the x and y directions (Fig. 3b), calibrated based on AVT results. Additional masses representing bell rings were incorporated into the analysis. a b

Fig. 3. (a) Mesh pattern; (b) BCs and interactions setup.

3.2. FE materials calibration and model updating

The bell tower predominantly consists of locally sourced grey tuff, a volcanic material prevalent in the area, while limestone is utilized for the basement, foundations, and arch framings. Recently, the roof has been reconstructed using reinforced concrete covered by tiles. The dynamic model underwent calibration via modal analysis, referencing results from Ambient Vibration Testing (AVT) conducted by Chisari et al. The first three mode frequencies, approximately 1 = 1.93 , 2 = 2.03 , and 3 = 4.00 , corresponding to translational mode shapes in the y and x directions and rotational mode shape with respect to the z direction, respectively. The model has updated by adjusting five parameters in a multi-objective approach (Brincker et al. (2001), Allemang (2003)), particularly the elastic moduli of the constituent materials (tuff E t , limestone E l , concrete E c ), modelled through a homogeneous equivalent approach, and the stiffness of the contact springs ( k x , k y ), to minimize discrepancies between the model and experimental data in terms of frequencies ( ω f ) and mode shapes ( ω MAC ). The adopted values and the comparison in terms of discrepancy functions ω f and ω MAC with the values obtained by Chisari et al. (2023), are reported in Table 1.