The Raasch challenge test is a linear shell test case where drill
rotations, i.e shell in-plane rotations, play an essential role. The problem
has been presented by Knight^{[2]}. The geometry has the form of a clamped 'hook', i.e. a thick
curved strip with a small radius followed by an arc with a larger radius.
The model was used by G. Rebel in his PhD thesis^{[3]} to demonstrate the performance of his shell elements in
B2000++ However, in the example the MITC shell elements are used.

The FE model consist of two cylindrical patches, both with a length of
20. The first patch has a radius of 46 and spanning an angle of 150 degrees.
The second smaller patch has a radius of 14 and spanning an angle of 60
degrees in the other direction. The mesh can be parametrized (see the MDL
input file `raasch.mdl`

). Note that, in contrast to
previous versions of this model, both cylindrical mesh patches are placed in
the default branch 1, i.e the branch-endbranch is not specified
anymore.

The analysis is performed with 4, 8, and 9 node MITC shell
elements^{[4]}. The solution (deformed shape and von Mises stress) for the
`Q4.S.MITC.E4`

elements and a coarse grid, with the
undeformed shape plotted with outline only, is shown below

The reference solution by Knight for the tip displacement in z
direction is w_{ref}=4.9352. Reference solutions for
stresses are not given.

^{[2] }Knight N.F; Raasch Challenge for Shell Elements; AIAA Journal,
Vol. 35, No. 2, February 1997, pp. 375-381.

^{[3] }Rebel G.; Finite Rotation Shell Theory including Drill Rotations
and its Finite Element Implementation; Delft University Press
1998.

^{[4] }Note that the B2000++ MITC shell elements are 5/6 dof's per node
elements. To avoid singularities with in-plane rotations, B2000++
automatically defines the correct node types: Nodes with constraints
(EBC conditions) and nodes where elements at a given limit angle meet
will become 6 DOF nodes, while all other nodes are 5 DOF nodes or other
nodes,