## 2 Materials and Methods
### Computer-Aided Engineering (CAE)
#### 2.2.5 Meshing  
The discretization or meshing is the previous step to the static analysis. For this purpose, a variable geometry grid will be developed that characterizes the geometry of the mechanical dredger in the most approximate way, so that the size of the mesh grid determines the most reliable approximation to the model.  
In principle, the smaller the size of the mesh the better it fits, but this has its opposite in stress analysis, as an excessively small size of the mesh can distort it since, on small surfaces, the contact between elements can cause pressure to grow inappropriately. Because of this we must ensure that the mesh size is appropriate, avoiding the two extremes.  
Figure 16: Force exerted by the steam engine on the piston.  
Autodesk Inventor Professional provides an automatic mesh (Figure 17) whose purpose is to adapt itself in the most exact way to the geometry of the model. As is well known, meshing is a geometric simplification which enables us to process the set as a unitary element, dividing it into finite elements that it analyzes later. In the case of the present study, the type of finite element used has been the tetrahedron.  
The variables by which it is guided are: the average size of the mesh (10% of the length of the element face to be discretized); the minimum size of the mesh (at least 20% of the average size); the modification factor (between adjacent meshes there is no difference greater than 1.5), and the maximum angle of rotation (maximum of 60\({}^{\circ}\) between contiguous faces of the mesh). The values taken by default can be modified, but in the present research these values have been respected since they present a geometry very similar to the model and there is, at first sight, no element that presents problems in their discretization.  
In theory, as noted above, elements with a more complicated geometry can be meshed manually, determining the length of the mesh. The circular or spherical elements usually pose problems if they are of small size. In these elements it usually happens that, due to the convexity or concavity of the surface, the mesh converges in the interior zones, giving rise to an excessively small reticle that distorts the analysis. In these areas it is necessary to control the size of the mesh in order to avoid convergence.  
Figure 17: The automatic meshing obtained.  
On the other hand, some pieces, due to a complex geometry, suffer distortion because the mesh does not adapt well. In these cases, the mesh size should also be defined, giving a shorter length that fits better to the reality of the piece.  
In the present model after a study of automatic meshing, it has been decided to respect the values provided by Autodesk Inventor Professional, since the model apparently has a grid fairly approximate to its geometry. The pieces that present certain convergence in the interior parts, such as the bucket that collects the sand from the bottom, are not determinants at the structural level and therefore, not being subjected to a great solicitation, do not distort the results of the analysis (Figure 18).  
In terms of finite-element analysis, a convergence criterion is established in order to obtain the results as this analysis is carried out by iterative methods during some cycles. In the present study, the software compares the result with that of the previous cycle, and if the result varies by more than 5% the software re-iterates the analysis. However, if the difference is less than 5% the analysis stops, taking the result as definitive. Autodesk Inventor Professional establishes a maximum number of five iterations, since the time used in each iteration is high.  
In this study, taking into account available computer resources, we made the analyses using a grid size of 899,471 elements and 1,696,284 nodes.