Shell

Mesh Convergence with Shell Elements

Tested with CGX 2.19 / CCX 2.19

• tri and quad elements
• linear or quadratic elements
• full or reduced integration, incompatible shape functions

This example may help with selection of shell elements.

File	Contents
shell.fbd	Parametric pre- and postprocessing script for CGX
shell.inp	CCX input
test.py	Python script to run the full example

Unstructured tri mesh	structured quad mesh

Reference solution

Mesh Convergence of the Normalized Results

The function shell_conv() in test.py creates a data file for each element type with the mesh density parameter setting, the number of nodes and the maximum displacement and stress values. An example (S3.txt):

# size NoN smax umax
200 8 0.513792 0.022522
100 12 0.616489 0.013121
50 20 1.2899 0.027729
20 84 0.792963 0.018026
10 178 1.03816 0.036069

The number of nodes refers to the expanded version of the shell elements.

The function shell_plot() in test.py generates the following plot of the results normalized by the analytical reference values.

Results

All plots sorted by element type and nodal distance (division).

• The S3 element is too stiff and shows strange stress pattersn
• The S4R element can't represent bending, the stiffness results just from shear stiffness.
• The S8R element exhibits hourglassing if there is just one element over the cross section. Yet the stress values and maximum displacements at the plane of symmetry are acceptable
• S4, S6 and S8 converge well, while S4 is most efficient, S8 is least efficient in terms of precision versus number of nodes. Efficience in terms of computing time may be different.

Type	200	100	50	20	10	5
S3
S4
S4R
S6
S8
S8R