Pinched Cylinder

The purpose of this test is to check shell elements. You will use 2D meshes.

Reference:

LINBERG G.M., OLSON M.D., New Developments in the Finite Element Analysis of Shells, COXP. Mech. Eng. and Nat. Aeronautical Establishment, National Research Council of Canada Vol. 4., 1969
 

Specifications

Geometry Specifications

Length:
L = 600 m

Radius:
R = 300 mm  

Thickness:
th = 3 mm

For symmetry reasons, only 1/8 of the body is modeled. The given results are the same for 1/8 or for the whole body.

Analysis Specifications

Young Modulus (material):
E = 3 MPa

Poisson's Ratio (material):
ν = 0.3

Mesh Specifications:

Imposed nodes on AB, BC, CD, DA
(see the table of results for values)

Restraints:

  • On edge AB: Tz = Rx = Ry = 0

  • On edge BC: Ty = Rx = Rz = 0

  • On edge CD: Tx = Ry = Rz = 0

  • On edge DA: Tx = Ty = Ry = 0

Loads (Distributed force):

F = 0.25 inward at C 
 

Results

  • The theoretical value of the radial displacement at the point load location is 18.25 mm.

  • The results correspond to the radial displacement at point C.
    The table below presents the analysis results.
    Normalized results (computed results divided by analytical solution) are listed.
     

 Nodes  

Values

Linear triangle
(TR3)

Parabolic triangle
(TR6)

Linear quadrangle
(QD4)

Parabolic quadrangle
(QD8)

Computed results
 [mm]

Normalized results

Computed results
 [mm]

Normalized results

Computed results
 [mm]

Normalized results

Computed results
 [mm]

Normalized results

3 x 3

0.98

0.054

8.1

0.4438

1.73

0.095

11.60

0.6356

5 x 5

8.13

0.4455

13.16

0.7211

10.09

0.5529

15.73

0.8619

7 x 7

13.28

0.7277

19.00

1.041

14.00

0.7671

16.98

0.9304

9 x 9

15.95

0.8740

19.87

1.089

16.34

0.8953

17.97

0.9847

11 x 11

15.7

0.8603

17.03

0.9332

17.00

0.9315

17.85

0.9781

13 x 13

17.05

0.9342

18.91

1.036

17.38

0.9523

17.81

0.9759

15 x 15

16.74

0.9173

17.55

0.9616

17.82

0.9764

18.06

0.9896

17 x 17

17.08

0.9359

17.77

0.9737

18.06

0.9896

18.21

0.9978

To Perform the Test:

The pinched_cylinder_17nodes_qd8.CATAnalysis document presents a complete analysis of this case, computed with a mesh formed of parabolic quadrangle elements (QD8).

To compute the case with other types of elements and number of nodes, proceed as follow:

  1. Open the CATAnalysis document.

  2. In the Advanced Meshing Tools workbench, change the mesh specifications as indicated above.

  3. Compute the case in the Generative Structural Analysis workbench.