Shell obstacle course: Pinched cylinder

Problem definition

The pinched cylinder test considers a cylindrical shell fixed by rigid diaphragms at it's axial ends. The loading consists of two opposing compressive point loads at the center of the shell. Isotropic material properties are as per the figure below. Due to symmetry only an eighth of the shell is modeled.

SETUP IMAGE HERE

The key result is the vertical displacement under the point load, denoted by "u" in the diagram above, for which the reference value is u_z = 1.8248E-5 [2].

Results

The results of the test for the thin and thick triangle Kratos shell elements are presented below. TRI RESULTS

The results of the test for the thin and thick quadrilateral Kratos shell elements are presented below. QUAD RESULTS

Both graphs above indicate all Kratos triangular and quadrilateral shell elements agree with the reference solution.

References

1. Ted Belytschko et al. “Stress projection for membrane and shear locking in shell finite elements”. In: Computer Methods in Applied Mechanics and Engineering 51.1-3 (1985), pp. 221–258.
2. Robin Bouclier, Thomas Elguedj, and Alain Combescure. “Efficient isogeometric NURBS-based solid-shell elements: Mixed formulation and method”. In: Computer Methods in Applied Mechanics and Engineering 267 (2013), pp. 86 –110.