
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 
8.19 
0.449 
1.73 
0.095 
12.07 
0.662 
5 x 5 
8.13 
0.445 
13.38 
0.733 
10.09 
0.551 
16.43 
0.901 
7 x 7 
13.28 
0.728 
19.12 
1.047 
14.00 
0.767 
17.29 
0.948 
9 x 9 
15.95 
0.874 
19.98 
1.095 
16.34 
0.895 
18.17 
0.996 
11 x 11 
15.87 
0.870 
17.10 
0.937 
17.04 
0.934 
17.97 
0.985 
13 x 13 
17.09 
0.936 
18.91 
1.036 
17.42 
0.955 
17.81 
0.976 
15 x 15 
16.87 
0.924 
17.56 
0.962 
17.86 
0.978 
18.08 
0.991 
17 x 17 
17.19 
0.942 
17.82 
0.976 
18.09 
0.991 
18.33 
1.004 


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:

Open the CATAnalysis document.

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

Compute the case in the Generative Structural
Analysis workbench.
