8. Pinched Cylinder (Clamped)

A cylinder is loaded with two opposite point loads in the axial direction cancelling each other. This problem can be modeled with an eight of a cylinder (half in the longitudinal direction and a fourth in the circumferential direction). The figure below display the meshes with Q4.S.MITC.E4, Q8.S.MITC, respective Q9.S.MITC elements. Boundary conditions are symmetry along both longitudinal edges and along one circumferential edge, the other circumferential edge being clamped. The intensity of the force varies between 0 and 600.

Pinched cylinder (clamped): Meshes for Q4.S.MITC.E4, Q8.S.MITC, Q9.S.MITC elements.

Figure 34. Pinched cylinder (clamped): Meshes for Q4.S.MITC.E4, Q8.S.MITC, Q9.S.MITC elements.


The test is run with Q4.S.MITC.E4, Q8.S.MITC, and Q9.S.MITC shell elements, comparing the radial tip displacement-load function against the reported solution[15][16] and against a solution obtained with a very fine (128 by 128) Q4.S.MITC.E4 element mesh:

Pinched cylinder (clamped): Convergence behaviour (Q4 mesh).

Figure 35. Pinched cylinder (clamped): Convergence behaviour (Q4 mesh).


Pinched cylinder (clamped): Convergence behaviour (Q8 mesh).

Figure 36. Pinched cylinder (clamped): Convergence behaviour (Q8 mesh).


Pinched cylinder (clamped): Convergence behaviour (Q9 mesh).

Figure 37. Pinched cylinder (clamped): Convergence behaviour (Q9 mesh).




[15] Eriksson A. & Pacoste C.: 'Element formulation and numerical techniques for stability problems in shells.', Computer Methods in applied mechanics and engineering, Vol 191, 2002, pp 3775 - 381.

[16] Areias et al.: , 'A finite strain quadrilateral shell element based on discrete Kirchoff-Love constraints', International Journal for Numerical Methods in Engineering, Vol 64, 2005, pp 1166 - 1206.