2. Benchmark solution

2.1. Calculation method used for the reference solution

The reference solution is analytical.

Transition from the initial state to the deformed state:

where

\(a\) is the length of the deformation of the plate following \(Y\),

\({a}_{0}\) is the initial length of the plate,

\(b\) is the thickness of the deformed plate,

\({b}_{0}\) is the initial thickness of the plate.

Because

and shell hypotheses, we have

Green-Lagrange tensor:

By definition of the Green-Lagrange tensor, we have

With

, so we have

By substituting, we have

Deformation gradient:

By definition:

Either

Piola-Kirchhoff constraints of the second kind:

Let \(S\) be the constraint of \(\mathit{PK2}\), in our case,

Cauchy constraint

Let \(s\) be the Cauchy stress tensor, we have the relationship

, we deduce then that

2.2. Benchmark results

We calculate the \(\mathit{DX}\) and \(\mathit{DY}\) displacements at the node \(\mathit{NO3}\), the constraints of \(\mathit{PK2}\) and the Cauchy constraints on the mesh \(\mathit{M1}\).

2.3. Uncertainty about the solution

Analytical result.

2.4. Bibliographical references

Nil.