1. Reference problem

1.1. Geometry

Coordinates of the points:

	\(O\)	\(A\)	\(B\)		\(C\)		\(D\)	\(E\)	\(F\)
\(x\)			\(1/\sqrt{2}\)		0.5		0.4
\(y\)			\(1/\sqrt{2}\)			0.5	0.4
\(z\)	0

1.2. Material properties

\(E=1\mathrm{Pa}\) Young’s module

\(\nu =0.3\) Poisson’s ratio

\(\rho =1\mathrm{kg}/{m}^{3}\) Density

1.3. Boundary conditions and loads

Mounting on the edge of the plate:

at all \(P\) points such as \(\mathrm{OP}=R\):: \(u=v=w=0\), \({\theta }_{x}={\theta }_{y}={\theta }_{z}=0\).

For all the models, except the N model, we have the following loads:

FORCE_COQUE	Uniform pressure	\(P=1N/{m}^{2}\)
FORCE_COQUE	Normal distributed load	\(\mathrm{F3}=–1N/{m}^{2}\)
PESANTEUR	\(g=10m/{s}^{2}\) next \(Z\) from where	\(\mathrm{FZ}=\rho gt=–1N/{m}^{2}\)

These three charges lead to the same solution.

For the N modeling, a loading of pressure \(p=0.01172\mathit{MPa}\) is imposed on the upper face which corresponds to a maximum displacement along \(Z\) at the center of the plate of \(2\mathit{mm}\) (application of the formula in the following paragraph in \(r=0\)).