3. Modeling A#

3.1. Characteristics of modeling#

\(\mathrm{2D}\) axisymmetric modeling:

_images/100007CC000069BB000067DFBB97E607D5BD7D2E.svg

Figure 3.1-a: Geometry and modeling mesh

Boundary conditions:

\(\mathrm{Uy}=0\) on \(\mathrm{NO1}\) and \(\mathrm{NO2}\)

\(\mathit{Uy}={u}^{\mathit{meca}}=30\mathit{mm}\) on \(\mathrm{NO3}\) AND \(\mathrm{NO4}\)

3.2. Characteristics of the mesh#

Number of knots: 4

Number of meshes and types: 1 QUAD4, 1 SEG2.

3.3. Tested sizes and results#

Identification

Size

Reference

Tolerance

\(t=\mathrm{1.1s}\) \(\mathrm{NO3}\)

\(\mathrm{SIYY}\)

120.547945205

1.0E-4%

\(t=\mathrm{1.4s}\) \(\mathrm{NO3}\)

\(\mathrm{SIYY}\)

191.76201373

1.0E-4%

\(t=\mathrm{2.0s}\) \(\mathrm{NO3}\)

\(\mathrm{SIYY}\)

249.42791762

1.0E-4%

\(t=\mathrm{1.1s}\) \(\mathrm{NO3}\)

\(\mathrm{DY}\)

4.0

1.0E-4%

\(t=\mathrm{1.4s}\) \(\mathrm{NO3}\)

\(\mathrm{DY}\)

13.0

1.0E-4%

\(t=\mathrm{2.0s}\) \(\mathrm{NO3}\)

\(\mathrm{DY}\)

31.0

1.0E-4%

\(t=\mathrm{1.1s}\) \(\mathrm{NO3}\)

\(\mathrm{V1}\)

0.00239726027397

1.0E-4%

\(t=\mathrm{1.4s}\) \(\mathrm{NO3}\)

\(\mathrm{V1}\)

0.0110411899313

1.0E-4%

\(t=\mathrm{2.0s}\) \(\mathrm{NO3}\)

\(\mathrm{V1}\)

0.0287528604119

1.0E-4%

\(t=\mathrm{1.1s}\) \(\mathit{NO3}\)

\(\mathit{V7}\)

20.5479452055

1.0E-4%

\(t=\mathrm{1.4s}\) \(\mathit{NO3}\)

\(\mathit{V7}\)

91.76201373

1.0E-4%

\(t=\mathrm{2.0s}\) \(\mathit{NO3}\)

\(\mathit{V7}\)

149.42791762

1.0E-4%

\(t=\mathrm{1.1s}\) \(\mathrm{NO3}\)

\({\epsilon }^{\mathit{th}}\)

0.001

1.0E-4%

\(t=\mathrm{1.1s}\) \(\mathit{NO3}\)

\({\epsilon }_{\mathit{yy}}^{\mathit{meca}}\)

0.003

1.0E-4%

\(t=\mathrm{1.4s}\) \(\mathrm{NO3}\)

\({\epsilon }_{\mathit{yy}}^{\mathit{meca}}\)

0.012

1.0E-4%

\(t=\mathrm{2,0}s\) \(\mathrm{NO3}\)

\({\epsilon }_{\mathit{yy}}^{\mathit{meca}}\)

0.03

1.0E-4%

\(t=\mathrm{1.1s}\) \(\mathrm{NO3}\)

\({\epsilon }_{\mathit{yy}}^{\mathit{plas}}\)

0.00239726027397

1.0E-4%

\(t=\mathrm{1.4s}\) \(\mathrm{NO3}\)

\({\epsilon }_{\mathit{yy}}^{\mathit{plas}}\)

0.0110411899313

1.0E-4%

\(t=\mathrm{2,0}s\) \(\mathrm{NO3}\)

\({\epsilon }_{\mathit{yy}}^{\mathit{plas}}\)

0.0287528604119

1.0E-4%

\({\epsilon }^{\mathit{th}}\): thermal deformations - \({\epsilon }^{\mathit{meca}}\): mechanical deformations - \({\epsilon }^{\mathit{plas}}\): plastic deformations