3. Modeling A#

3.1. Characteristics of modeling#

_images/100000000000011C000000D7038EF5011D44D4C8.png

The arch is meshed using POU_D_E straight beam elements.

Boundary conditions:

  • At point \(A\) such as \(X\mathrm{=}R\), \(Y\mathrm{=}0\): \(\mathit{DX}\mathrm{=}\mathit{DY}\mathrm{=}\mathit{DZ}\mathrm{=}0\), and \(\mathit{RY}\mathrm{=}0\)

  • At point \(B\) such as \(X\mathrm{=}0\), \(Y\mathrm{=}R\): \(\mathit{DY}\mathrm{=}\mathit{DZ}\mathrm{=}0\), and \(\mathit{RX}\mathrm{=}0\)

For static analysis, unit moments around \(Z\) are defined at nodes 1 and 19.

3.2. Characteristics of the mesh#

Number of knots: 19

Number of stitches: 18 POU_D_E

3.3. Tested sizes and results#

Critical load

3.3.1. CALC_MODES with SOLVEUR_MODAL =_F (METHODE = “SORENSEN”)#

Identification Critical load number

Reference

Code_Aster

\(\text{\%}\) difference

1

2.86074

2.75137

3.823

2

8.63207

8.30613

3.776

3

-8.78382

-8.39554

4.420

4

14.4147

13.93216

3.348

5

-14.5551

-14.01104

3.738

3.3.2. CALC_MODES with OPTION = “PROCHE”#

Identification Critical load number

Reference

Code_Aster

\(\text{\%}\) difference

1

2.86074

2.75137

3.823

2

8.63207

8.30613

3.776

3

-8.78382

-8.39554

4.420

4

14.4147

13.93216

3.348

5

-14.5551

-14.01104

3.738

3.3.3. CALC_MODES with OPTION = “SEPARE”#

Identification Critical load number

Reference

Code_Aster

\(\text{\%}\) difference

1

2.86074

2.75137

3.823

2

8.63207

8.30613

3.776

3

-8.78382

-8.39554

4.420

4

14.4147

13.93216

3.348

5

-14.5551

-14.01104

3.738

3.3.4. CALC_MODES with OPTION = “AJUSTE”#

Identification Critical load number

Reference

Code_Aster

\(\text{\%}\) difference

1

2.86074

2.75137

3.823

2

8.63207

8.30613

3.776

3

-8.78382

-8.39554

4.420

4

14.4147

13.93216

3.348

5

-14.5551

-14.01104

3.738