## 9. Pinched Cylinder with Free Ends

This test case is described by Sansour and Bernarczyk[17] and Rebel[18]. A thin cylinder whose ands are free is loaded by two concentrated forces at the centre. Due to symmetry, only one eight of the cylinder has to be modelled.

A nonlinear load-controlled analysis is performed. The case definition is as follows:

cases
case 1
analysis               nonlinear
ebc                    1
nbc                    1
max_newton_iterations  50
max_step               500
step_size_min          1.0e-10
step_size_max          0.02
step_size_init         0.01
end
end

The deformed configuration at P = 50, using a mesh of 16x8 Q4.S.MITC.E4 elements, is shown in the following figure:

The radial displacements at points A and B obtained with various types of MITC shell elements are plotted against the applied load, showing good agreement with the reference values and a the values for very fine mesh of Q4.S.MITC.E4 elements:

[1] Carlo Sansour, Herbert Bednarczyk. The Cosserat surface as a shell model, theory and finite-element formulation, Comput. Methods Appl. Mech. Engrg. 120 (1995), pp 26-27.

[2] Gert Rebel. Finite rotation shell theory including drill rotations and its finite element implementation, PhD thesis, Delft University Press, 1998.

[17] Carlo Sansour, Herbert Bednarczyk. The Cosserat surface as a shell model, theory and finite-element formulation, Comput. Methods Appl. Mech. Engrg. 120 (1995), pp 26-27.

[18] Gert Rebel. Finite rotation shell theory including drill rotations and its finite element implementation, PhD thesis, Delft University Press, 1998.