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
   radius 500
   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.

Cylinder under torsion load: Mesh (Q4 shell elements).

Figure 53. Cylinder under torsion load: Mesh (Q4 shell elements).


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


Cylinder under torsion load: First buckling mode and applied generated torsional forces (Q4 shell elements).

Figure 54. Cylinder under torsion load: First buckling mode and applied generated torsional forces (Q4 shell elements).