2. Benchmark solution#

2.1. Calculation method used for the reference solution#

Analytical solution, obtained with the hypothesis of uniaxiality of the constraints:

_images/Object_1.svg

or in frame \((A,L,T)\):

_images/Object_2.svg

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]):

_images/Object_3.svg

,

_images/Object_4.svg _images/Object_5.svg

with:

_images/Object_6.svg _images/Object_7.svg _images/Object_8.svg

As the deformations are uniform in the plate, by integration, we obtain, by integration, the displacements in the reference frame \((A,x,y)\):

_images/Object_9.svg _images/Object_10.svg

2.2. Benchmark results#

Travel in frame \((A,x,y)\) (in \(m\)):

Point

\(B\)

\(C\)

\(D\)

_images/Object_11.svg

5.917 10—7

5.917 10—7

_images/Object_12.svg

—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#

  1. GAY D: « Composite materials »; 3rd edition, Hermès