## 2. Cylinder under Torsion Load

The torsion buckling load of a cylinder is computed. The cylinder is clamped on one end and subjected to a torsional load on the other free end. Dimensions of the cylinder as defined by the epatch command of the MDL input file:

   length 4000
phi1 0 phi2 360
thickness 1

The material is linear isotropic as defined by the emat command of the MDL input file.

emat
mid 1
type isotropic
e 70000
p 0.3
end
end

The cylinder is meshed with 36 elements (Q4) or 18 elements (Q8/Q9) in circumferential direction and 20 elements (Q4) or 10 elements (Q8/Q9) in axial direction.

Note: The cylinder mesh generator of epatch does not automatically close the cylinder if the angles are 0 and 360 respectively. This has to be done by the user with the join command:

join
set 0
automatic
end
end 

Analysis is performed with the meshes described above and compared to a reference solution obtained with a fine Q4 mesh 288 by 144 elements. Results are displayed in the table below: While the Q4 and Q8 meshes deliver results with a 15% error with respect to the reference solution, the Q9 mesh performs very well.

Table 3. Cylinder under torsion load: Eigenvalues λ.

 Element type λ1 λ2 λ3 λ4 Q4.MITC.E4 ref. 0.6004 0.6004 0.6277 0.6277 Q4.MITC.E4 0.709 0.709 0.727 0.727 Q8.S.MITC 0.709 0.709 0.727 0.727 Q9.S.MITC 0.6004 0.6004 0.6277 0.6277