*4.6. Structural Analysis*

The 3D model obtained in Rhinoceros was used in structure analysis software based on the FEM method. The finite element method is the most widely used method for solving problems of engineering and mathematical models, such as structural analysis, heat transfer, fluid flow, etc.

In this paper, an FEM model was used for structural analysis. In particular, Midas GTS NX software, developed by MIDAS Information Technology Co, was used for the several structural analyses. Midas GTS NX is a comprehensive finite element analysis software package that is equipped to handle the entire range of structural design applications.

The procedure that allowed structural information to be generated, starting from the 3D model, is quite simple. In fact, once the surface is imported into the Midas GTS NX structural software, it was possible to create structural meshes. Subsequently, the conditions of external, internal, deadweight (structural elements weight) and accidental loads constraint were assigned to the structure.

As for the materials, the customized information of each of them can be assigned within Rhinoceros through the "VisualARQ" plug-in. The styles of objects with such customize can be exported, in IFC (Industry Foundation Classes) format, in Revit software. These objects, recognized in Revit according to their style and custom information (material properties, costs per unit and custom metric information associated with any object in the model), are further enriched through the Revit libraries with the appropriate material characteristics useful for volumic, thermal, computational-maintenance elaborations. In order to use the advanced structural constitutive relation it is necessary to use FEM calculation software.

The object created in Rhinoceros was imported into Midas GTS NX through: "step" and "parasolid" format. The imported object is congruen<sup>t</sup> and all its structural parts are correctly connected. The object, however, represents a single solid of a single material. Through specific Boolean operations, such as "divide solid", it is possible to divide and auto-connect the di fferent surfaces. Therefore, each of the structural parts generated will be given the appropriate structural material. The materials are characterized by the appropriate constitutive relations (Mohr–Coulomb, Drucker–Prager, Von Mises). The elastic modulus, friction angle, Poisson coe fficient etc. were indicated in the software. Once the correct materials were assigned, through the congruence of the structural elements, linear and non-linear seismic analisys can be performed.

For example, Figure 15 shows a view of the results in terms of deformation of the San Nicola in Montedoro church.

**Figure 15.** Static analysis: results of deformations of the structure. The maximum value achieved was 1.8 mm (blue) while the minimum was 1.2 mm (red).

Of course, the same approach, but using a di fferent method related to the load of the structure and the constraints, was used for the masonry bridge. Specifically, the Mohr–Coulomb constitutive relation was used to assign the materials to the masonry bridge. This constitutive relation allows for linear and non-linear seismic analysis. This task was carried out within the structural software (see Figure 16).

**Figure 16.** Materials and constitutive relation assigned to the masonry arch of the bridge in Midas GTS NX software.

As a result, it was possible to analyse the deformation state of the masonry bridge. However, it is necessary to clarify that the analysis performed on the structures represents a test based on the evidence of the correctness of the structural model within the software. Therefore, in order to define a model of deformation closer to reality, it would be necessary to take into consideration further investigations of the dynamic effects, the geotechnical-geological characteristics of the soil, the hydraulic effects (in the case of the bridge), etc. However, the consideration of the latter aspects goes beyond the scope of this paper, whose goal was to identify a specific procedure that we considered more suitable to switch from a 3D point cloud representation (obtained through a geomatics survey) to a 3D model manageable in BIM and FEM environments.
