4. B modeling#

4.1. Characteristics of modeling#

_images/Shape4.gif
_images/10000000000001E0000001E04FCDAA3B7314596F.png

Modeling DKTG (QUAD4)

  • Boundary conditions:

. Rating \(\mathit{A2A4}\): \(\mathit{DZ}\mathrm{=}0\)

  • Symmetry conditions

. Side \(\mathit{A1A2}\): \(\mathit{DY}\mathrm{=}\mathit{DRX}\mathrm{=}0\). Side \(\mathit{A1A3}\): \(\mathit{DX}\mathrm{=}\mathit{DRY}\mathrm{=}0\)

The slab is symmetric with respect to planes \((X\mathrm{=}0)\) and \((Y\mathrm{=}0)\), the calculations are carried out on a quarter of the slab.

4.2. Characteristics of the mesh#

Number of knots: 169

Number of meshes and type: 144 QUAD4

4.3. Tested features#

The macro command POST_COQUE makes it possible to extract the forces and the deformations at any point in the shell.

4.4. Tested values#

Identification

Reference Type

Reference

Tolerance (%)

\(\mathrm{DZ}(\mathrm{A1})\)

“ANALYTIQUE”

2.433 10-4

6%

\(\mathrm{MXX}(\mathrm{A1})\)

“ANALYTIQUE”

2%

\(\mathrm{KXX}(\mathrm{A1})\)

“ANALYTIQUE”

7.21 10-4

5%

Identification

Reference type

Reference

Tolerance (%)

\(\mathit{MXX}\)

\(\mathit{M133}\)

\(\mathit{Point}4\)

“NON_REGRESSION”

4044.05

1.e-6

\(\mathit{KXX}\)

\(\mathit{M133}\)

\(\mathit{Point}4\)

“NON_REGRESSION”

7.1995 10-4

1.e-6

  • The quantities are expressed in the coordinate system defined by the nautical angles \(\alpha \mathrm{=}33°\) and \(\beta \mathrm{=}12°\).

Identification

Reference Type

Reference

Tolerance (%)

\(\mathrm{DZ}(\mathrm{A1})\)

“ANALYTIQUE”

2.433 10-4

6%

\(\mathit{MXX}(\mathit{A1})\)

“NON_REGRESSION”

2848.64

1.e-6

\(\mathit{MYY}(\mathit{A1})\)

“NON_REGRESSION”

1201.35

1.e-6

\(\mathit{MXY}(\mathit{A1})\)

“NON_REGRESSION”

-1849.92

1.e-6

\(\mathit{KXX}(\mathit{A1})\)

“NON_REGRESSION”

5.0713 10-4

1.e-6

\(\mathit{KYY}(\mathit{A1})\)

“NON_REGRESSION”

2.1387 10-4

1.e-6

\(\mathit{KXY}(\mathit{A1})\)

“NON_REGRESSION”

-3.2933 10-4

1.e-6

Identification

Reference type

Reference

Tolerance (%)

\(\mathit{MXX}\)

\(\mathit{M133}\)

\(\mathit{Point}4\)

“NON_REGRESSION”

2844.46

1.e-6

\(\mathit{MYY}\)

\(\mathit{M133}\)

\(\mathit{Point}4\)

“NON_REGRESSION”

1199.59

1.e-6

\(\mathit{MXY}\)

\(\mathit{M133}\)

\(\mathit{Point}4\)

“NON_REGRESSION”

-1847.21

1.e-6

\(\mathit{KXX}\)

\(\mathit{M133}\)

\(\mathit{Point}4\)

“NON_REGRESSION”

5.0639 10-4

1.e-6

\(\mathit{KYY}\)

\(\mathit{M133}\)

\(\mathit{Point}4\)

“NON_REGRESSION”

2.1356 10-4

1.e-6

\(\mathit{KXY}\)

\(\mathit{M133}\)

\(\mathit{Point}4\)

“NON_REGRESSION”

-3.2885 10-4

1.e-6

4.5. notes#

The coefficients of the following elasticity matrices, used during the calculations, were calculated with \({\nu }_{b}\mathrm{=}0\):

  1. Membrane elasticity matrix: \(\left\{\begin{array}{ccc}4614.& 0& 0\\ 0& 4614.& 0\\ 0& 0& 2142.\end{array}\right\}{10}^{6}N\mathrm{/}m\)

  2. Flexural elasticity matrix: \(\left\{\begin{array}{ccc}5.617& 0& 0\\ 0& 5.617& 0\\ 0& 0& 2.57\end{array}\right\}{10}^{6}N\mathrm{/}m\)

To be certain of staying within the elastic domain, the elastic limits, expressed in the orthotropy coordinate system, are set arbitrarily to a very high value:

Elastic limits in positive flexure:

Direction \(x\): \({1.10}^{10}\mathit{MNm}\mathrm{/}\mathit{ml}\)

Direction \(y\): \({1.10}^{10}\mathit{MNm}\mathrm{/}\mathit{ml}\)

Elastic limits in negative flexure:

Direction \(x\): \(–{1.10}^{10}\mathit{MNm}\mathrm{/}\mathit{ml}\)

Direction \(y\): \(–{1.10}^{10}\mathit{MNm}\mathrm{/}\mathit{ml}\)

As the structure remains in the elastic domain, the kinematic recall coefficient (Prager constant) can take any value.