**3. Numerical solutions and interpretations of mathematical models**

The flat swaged circle fitting described in **Figure 6** and the other 4 swaged circle fittings from A to C are designed in 3D with commercial program (SolidWorks® 2013). The described 3D Models (A, B, and C) are transferred to the numerical commercial solver program (ANSYS Workbench® 14.5) using the Finite Element Method and analyzed by adding physical parameters.

In this study, FEM-Analysis was performed by considering 4 different geometric variations of swaged circle fitting. These have the following geometric design features shown in **Figure 6**:


The Finite Element Models of 4 different fitting designs is shown in **Figure 7** (in Mesh form).

**Figure 8** shows three separate stepwise loading cases applied in all of the Finite Element Models in Simulation.

The Finite Element Models are solved numerically elastically-plastically by nonlinear method. The pictures below show the deformation values of these solutions for the 3 loading cases described above. In particular, the high percentage of plastic deformation and homogeneity indicates the quality of the connection.

In the "Flat" Model in **Figure 9**, since plastic deformation is not lagging behind when the flat swaging circle fitting is released after being subjected to elastic–plastic

*Finite element model of swaged circle fitting design; a) flat; b) curve "a"; c) curved and fluted "B"; d) curved, ribbed and wavy "C" [13].*

**Figure 8.** *Applied load cases (LC: Load case) [13].*

*How Impact the Design of Aluminum Swaging Circle Fitting on the Sealing for Piping… DOI: http://dx.doi.org/10.5772/intechopen.99938*

deformation by applying pressure, it comes out under axial load very easily. Plastic deflection corresponds to approximately 12% of the total deflection. The pressure deformation in the inner pipe is very low.

In Model "A" in **Figure 10**; since plastic deformation is lagging behind when the small curved flat swaging circle fitting is released after being subjected to elastic– plastic deformation by applying pressure, it is now difficult to comes out under axial load. Plastic deflection corresponds to approximately 39% of the total deflection. Plastic deformation shows density in two places and is not homogeneous.

In Model "B" in **Figure 11**; since plastic deformation is lagging behind when the small curved flat swaging circle fitting with internal groove for sealing is released after being subjected to elastic–plastic deformation by applying pressure, it is now

#### **Figure 9.**

*Elastic–plastic deformations as flat fitting model FEM solution results [13].*

**Figure 10.** *Elastic–plastic deformations as model "a" FEM solution results [13].*

difficult to comes out under axial load. Plastic deflection corresponds to approximately 17% of the total deflection. Plastic deflection distribution is more homogeneous than Model "A" but has a lower percentage.

In Model "C" in **Figure 12**; since plastic deformation is lagging behind when the small curved, axially wavy flat swaging circle fitting with internal groove for sealing is released after being subjected to elastic–plastic deformation by applying pressure, it is now difficult to comes out under axial load. Plastic deflection corresponds to approximately 78% of the total deflection. In this model, plastic deflection is both high and in the most homogeneous state. The deflection in the connected pipes is

**Figure 11.** *Elastic–plastic deformations as model "B" FEM solution results [13].*

**Figure 12.** *Elastic–plastic deformations as model "C" FEM solution results [13].*

*How Impact the Design of Aluminum Swaging Circle Fitting on the Sealing for Piping… DOI: http://dx.doi.org/10.5772/intechopen.99938*

within the elastic limits. It is possible to say that this connection showed a very good solution in terms of both sealing and strength
