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

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