## 3. Raasch Challenge Test

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. 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 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. Figure 6. Raasch challenge: Geometry

The analysis is performed with 4, 8, and 9 node MITC shell elements. 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 Figure 7. Raasch challenge: Deformed structure (amplified x 4).

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

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

 Rebel G.; Finite Rotation Shell Theory including Drill Rotations and its Finite Element Implementation; Delft University Press 1998.

 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,