2. Benchmark solution#
2.1. Calculation method used for the reference solution#
Analytical solution, obtained with the hypothesis of uniaxiality of the constraints:
or in frame \((A,L,T)\):
By the law of orthotropic elastic behavior, using the conventions of Code_Aster with respect to \({\mathrm{NU}}_{LT}\), (cf. document for using the DEFI_MATERIAU [§3.5.2] command), we obtain directly (see for example [bib1]):
,
with:
As the deformations are uniform in the plate, by integration, we obtain, by integration, the displacements in the reference frame \((A,x,y)\):
2.2. Benchmark results#
Travel in frame \((A,x,y)\) (in \(m\)):
Point |
\(B\) |
\(C\) |
\(D\) |
5.917 10—7 |
5.917 10—7 |
||
—2.292 10—7 |
—5.028 10—7 |
—7.319 10—7 |
|
Constraints in the coordinate system linked to orthotropy:
\({\sigma }_{LL}(x,y)=7500\mathrm{Pa}\), \({\sigma }_{\mathrm{TT}}(x,y)=2500\mathrm{Pa}\), \({\sigma }_{LT}(x,y)=4330.127\mathrm{Pa}\)
2.3. Uncertainty about the solution#
Analytical solution.
2.4. Bibliographical references#
GAY D: « Composite materials »; 3rd edition, Hermès