1. Reference problem

1.1. Geometry

Pinched cap:

With

1.2. Material properties

Elastic behavior:

1.3. Boundary conditions and loads

We are looking for the successive states of equilibrium under the load

applied in \({P}_{1}{P}_{6}{P}_{2}{P}_{7}\)

Because of the geometric and physical symmetry of the problem, only quarter \({P}_{1}{P}_{2}{P}_{3}{P}_{4}\) is modeled, taking into account symmetry conditions. These conditions eliminate 5 rigid body movements. The last rigid body movement is eliminated by blocking the next movement.

. at point \({P}_{5}\),

Conditions aux limites :	\({P}_{5}\):		\(\mathrm{DZ}=0\)
Symmetry:	\(\mathrm{P2P3}\):		\(\mathrm{DY}=0.\)
		\(\mathrm{DRX}=0.\)	\(\mathrm{DRZ}=0.\)
	\(\mathrm{P4P1}\):	\(\mathrm{DX}=0.\)
		\(\mathrm{DRY}=\mathrm{0}\mathrm{.}\) \(\mathrm{DRZ}=0.\)

We are particularly interested in the movements of points \({P}_{1}\) and \({P}_{3}\) according to the loading directions.