3. Modeling A#

3.1. Characteristics of modeling#

_images/1000000000000201000001660F44B3FB7F0E466F.png

Modeling DKT (TRIA3)

  • The plate is located in the plane \(Y=0.5\)

  • Point \(A\) \((0.4;0.5;0.25)\)

  • Boundary conditions:

    • Side \(\mathrm{BC}\): - Side \(v=0\)

\(\mathrm{CD}\): \(v=0\)

  • Symmetry conditions: (local coordinate system)

    • Side \(\mathrm{AB}\): \(u={\theta }_{y}=0\)

  • Side \(\mathrm{AD}\): \(v={\theta }_{x}=0\)

3.2. Characteristics of the mesh#

Number of knots: 49

Number of meshes and types: 72 TRIA3

3.3. Tested sizes and results#

Identification

Reference type

Reference values

Tolerance \((\text{\%})\)

\(w(\mathrm{0,}\mathrm{0,}0)\)

ANALYTIQUE

0.01507

1.1

\(\mathit{SIXX}(\mathrm{0,}\mathrm{0,}h\mathrm{/}2)\)

SOURCE_EXTERNE

2.4216 107

2.1

\(\mathit{SIYY}(\mathrm{0,}\mathrm{0,}h\mathrm{/}6)\) layer to \(90°\)

SOURCE_EXTERNE

5.7810 106

2.7

\(\mathit{SIXY}(a\mathrm{/}\mathrm{2,}a\mathrm{/}\mathrm{2,}h\mathrm{/}2)\)

SOURCE_EXTERNE

1.2825 106

4.6

\(\mathit{SIXZ}(a\mathrm{/}\mathrm{2,}\mathrm{0,}0)\)

SOURCE_EXTERNE

—2.3526 105

37

\(\mathit{SIYZ}(\mathrm{0,}a\mathrm{/}\mathrm{2,}0)\)

SOURCE_EXTERNE

8.8950 104

3.1

3.4. notes#

The constraints are expressed in the orthotropy coordinate system defined by ANGL_REP (AFFE_CARA_ELEM), and by the normal of the element.

The components \(\mathrm{SIXX}\), \(\mathrm{SIYY}\), and \(\mathrm{SIYZ}\) are the average values of the two cells competing at points \(A\) and \(C\).

The difference obtained on \(\mathrm{SIXZ}\) is due to the difference in transverse shear modeling: in the reference, a transverse shear correction coefficient of 5/6 is used. In Code_Aster, we calculate the distribution of shear in the thickness, which is assumed to be parabolic in each layer.

The sign of \(\mathrm{SIXZ}\) is the opposite of that of the reference solution.