# Pinched Cylinder#

Problem Description:
• A thin-walled cylinder is pinched by a force $$F$$ at the middle of the cylinder length. Determine the radial displacement $$\delta$$ at the point where the force $$F$$ is applied. The ends of the cylinder are free edges.

Reference:
• R. D. Cook, Concepts and Applications of Finite Element Analysis, 2nd Edition, John Wiley and Sons, Inc., New York, NY, 1981, pp. 284-287. H. Takemoto, R. D. Cook, “Some Modifications of an Isoparametric Shell Element”, International Journal for Numerical Methods in Engineering, Vol.7 No. 3, 1973.

Analysis Type(s):
• Static Analysis ANTYPE=0

Element Type(s):
• 4-Node Finite Strain Shell Elements (SHELL181)

• 8-Node Finite Strain Shell Elements (SHELL281)

Material Properties
• $$E = 10.5 \cdot 10^6 psi$$

• $$\nu = 0.3125$$

Geometric Properties:
• $$l = 10.35 in$$

• $$r = 4.953 in$$

• $$t = 0.094 in$$

• $$F = 100 lb$$

Analysis Assumptions and Modeling Notes:
• A one-eighth symmetry model is used. One-fourth of the load is applied due to symmetry.

# sphinx_gallery_thumbnail_path = '_static/vm6_setup.png'


## Start MAPDL#

from ansys.mapdl.core import launch_mapdl

# Start mapdl.
mapdl = launch_mapdl()


## Initiate Pre-Processing#

Enter verification example mode and the pre-processing routine.

def start_prep7():
mapdl.clear()
mapdl.verify()
mapdl.prep7()

start_prep7()


## Define Element Type#

Set up the element type (a shell-type).

# Define the element type number.
def define_element(elem_type):
# Type of analysis: Static.
mapdl.antype("STATIC")

# Define the element type number.
elem_num = 1

if elem_type == "SHELL181":

# Element type: SHELL181.
mapdl.et(elem_num, elem_type)

# Special Features are defined by keyoptions of shell element:

# KEYOPT(3)
# Integration option:
# Full integration with incompatible modes.
mapdl.keyopt(elem_num, 3, 2)  # Cubic shape function

elif elem_type == "SHELL281":

# Element type: SHELL181.
mapdl.et(elem_num, "SHELL281")

return elem_type, mapdl.etlist()

# Return the number of the element type.
elem_type, elem_type_list = define_element(elem_type="SHELL181")
print(
f"Selected element type is: {elem_type},\n"
f"Printout the element list with its own properties:\n {elem_type_list}"
)


Out:

Selected element type is: SHELL181,
Printout the element list with its own properties:
ELEMENT TYPE        1 IS SHELL181     4-NODE SHELL
KEYOPT( 1- 6)=        0      0      2        0      0      0
KEYOPT( 7-12)=        0      0      0        0      0      0
KEYOPT(13-18)=        0      0      0        0      0      0

CURRENT NODAL DOF SET IS  UX    UY    UZ    ROTX  ROTY  ROTZ
THREE-DIMENSIONAL MODEL


## Define Material#

Set up the material properties, where: Young Modulus is $$E = 10.5 \cdot 10^6 psi$$, Poisson’s ratio is $$\nu = 0.3125$$.

# Define material number.
mat_num = 1

# Define material properties.
def define_material():
# Define material properties.
mapdl.mp("EX", mat_num, 10.5e6)
mapdl.mp("NUXY", mat_num, 0.3125)
return mapdl.mplist()

material_list = define_material()
print(material_list)


Out:

MATERIAL NUMBER        1

TEMP        EX
0.1050000E+08

TEMP        NUXY
0.3125000


## Define Section#

Set up the cross-section properties for a shell element.

# Define cross-section number and thickness of the shell element.
sec_num = 1
t = 0.094

# Define shell cross-section.
def define_section():
# Define shell cross-section.
mapdl.sectype(secid=sec_num, type_="SHELL", name="shell181")
mapdl.secdata(t, mat_num, 0, 5)
return mapdl.slist()

section_list = define_section()
print(section_list)


Out:

*****ANSYS VERIFICATION RUN ONLY*****
DO NOT USE RESULTS FOR PRODUCTION

SECTION ID NUMBER:           1
SHELL SECTION TYPE:
SHELL SECTION NAME IS:     shell181
SHELL SECTION DATA SUMMARY:
Number of Layers    =      1
Total Thickness     =     0.094000

Layer      Thickness   MatID   Ori. Angle  Num Intg. Pts

1        0.0940     1        0.0000     5

Shell Section is offset to MID surface of Shell

Section Solution Controls
User Transverse Shear Stiffness (11)=  0.0000
(22)=  0.0000
(12)=  0.0000
Added Mass Per Unit Area            =  0.0000
Hourglass Scale Factor; Membrane    =  1.0000
Bending     =  1.0000
Drill Stiffness Scale Factor        =  1.0000


## Define Geometry#

Set up the keypoints and create the area through the keypoints.

# Define geometry of the simplified mathematical model.
def define_geometry():
# Change active coordinate system
# to the global cylindrical coordinate system.
mapdl.csys(1)

# Define keypoints by coordinates.
mapdl.k(1, 4.953)
mapdl.k(2, 4.953, "", 5.175)

# Generate additional keypoints from a pattern of keypoints.
mapdl.kgen(2, 1, 2, 1, "", 90)

# Create an area through keypoints.
mapdl.a(1, 2, 4, 3)

if elem_type == "SHELL181":
# Plot the lines.
mapdl.lplot(color_lines=True, cpos="iso")

# Plot the area using PyVista parameters.
mapdl.aplot(
title="Display the selected area",
cpos="iso",
vtk=True,
color="#06C2AC",
show_line_numbering=True,
show_area_numbering=True,
show_lines=True,
)

define_geometry()

# Define the number of the keypoint where F is applied using inline function.
def keypoint_number(mapdl):
keypoint_num = mapdl.queries.kp(4.953, 90, 0)
return keypoint_num

# Call the function to get the number of keypoint.
top_keypoint = keypoint_number(mapdl)
print(f"The number of the keypoint where F is applied: {top_keypoint}")


Out:

The number of the keypoint where F is applied: 3


## Meshing#

Define line division of the lines, then mesh the area with shell elements.

# Define mesh properties and create the mesh with shell elements.
def meshing():
# Specify the default number of line divisions.
mapdl.esize(size="", ndiv=8)

# Mesh the area.
mapdl.amesh(1)

# Define global cartesian coordinate system.
mapdl.csys(0)

if elem_type == "SHELL181":
# Plot the mesh.
mapdl.eplot(
title="Plot of the currently selected elements",
vtk=True,
cpos="iso",
show_edges=True,
edge_color="white",
show_node_numbering=True,
color="purple",
)

# Print the list of elements.
print(mapdl.elist())

# Plot the nodes using VTK.
mapdl.nplot(
vtk=True, nnum=True, background="", cpos="iso", show_bounds=True, point_size=10
)

# Print the list of nodes.
print(mapdl.nlist())

meshing()


Out:

LIST ALL SELECTED ELEMENTS.  (LIST NODES)
1   1   1   1   0   1      1     3    33    32
2   1   1   1   0   1      3     4    40    33
3   1   1   1   0   1      4     5    47    40
4   1   1   1   0   1      5     6    54    47
5   1   1   1   0   1      6     7    61    54
6   1   1   1   0   1      7     8    68    61
7   1   1   1   0   1      8     9    75    68
8   1   1   1   0   1      9     2    11    75
9   1   1   1   0   1     32    33    34    31
10   1   1   1   0   1     33    40    41    34
11   1   1   1   0   1     40    47    48    41
12   1   1   1   0   1     47    54    55    48
13   1   1   1   0   1     54    61    62    55
14   1   1   1   0   1     61    68    69    62
15   1   1   1   0   1     68    75    76    69
16   1   1   1   0   1     75    11    12    76
17   1   1   1   0   1     31    34    35    30
18   1   1   1   0   1     34    41    42    35
19   1   1   1   0   1     41    48    49    42
20   1   1   1   0   1     48    55    56    49
21   1   1   1   0   1     55    62    63    56
22   1   1   1   0   1     62    69    70    63
23   1   1   1   0   1     69    76    77    70
24   1   1   1   0   1     76    12    13    77
25   1   1   1   0   1     30    35    36    29
26   1   1   1   0   1     35    42    43    36
27   1   1   1   0   1     42    49    50    43
28   1   1   1   0   1     49    56    57    50
29   1   1   1   0   1     56    63    64    57
30   1   1   1   0   1     63    70    71    64
31   1   1   1   0   1     70    77    78    71
32   1   1   1   0   1     77    13    14    78
33   1   1   1   0   1     29    36    37    28
34   1   1   1   0   1     36    43    44    37
35   1   1   1   0   1     43    50    51    44
36   1   1   1   0   1     50    57    58    51
37   1   1   1   0   1     57    64    65    58
38   1   1   1   0   1     64    71    72    65
39   1   1   1   0   1     71    78    79    72
40   1   1   1   0   1     78    14    15    79
41   1   1   1   0   1     28    37    38    27
42   1   1   1   0   1     37    44    45    38
43   1   1   1   0   1     44    51    52    45
44   1   1   1   0   1     51    58    59    52
45   1   1   1   0   1     58    65    66    59
46   1   1   1   0   1     65    72    73    66
47   1   1   1   0   1     72    79    80    73
48   1   1   1   0   1     79    15    16    80
49   1   1   1   0   1     27    38    39    26
50   1   1   1   0   1     38    45    46    39
51   1   1   1   0   1     45    52    53    46
52   1   1   1   0   1     52    59    60    53
53   1   1   1   0   1     59    66    67    60
54   1   1   1   0   1     66    73    74    67
55   1   1   1   0   1     73    80    81    74
56   1   1   1   0   1     80    16    17    81
57   1   1   1   0   1     26    39    25    18
58   1   1   1   0   1     39    46    24    25
59   1   1   1   0   1     46    53    23    24
60   1   1   1   0   1     53    60    22    23
61   1   1   1   0   1     60    67    21    22
62   1   1   1   0   1     67    74    20    21
63   1   1   1   0   1     74    81    19    20
64   1   1   1   0   1     81    17    10    19
1   4.9530        0.0000        0.0000          0.00     0.00     0.00
2   4.9530        0.0000        5.1750          0.00     0.00     0.00
3   4.9530        0.0000       0.64687          0.00     0.00     0.00
4   4.9530        0.0000        1.2937          0.00     0.00     0.00
5   4.9530        0.0000        1.9406          0.00     0.00     0.00
6   4.9530        0.0000        2.5875          0.00     0.00     0.00
7   4.9530        0.0000        3.2344          0.00     0.00     0.00
8   4.9530        0.0000        3.8812          0.00     0.00     0.00
9   4.9530        0.0000        4.5281          0.00     0.00     0.00
10   0.0000        4.9530        5.1750          0.00     0.00     0.00
11   4.8578       0.96628        5.1750          0.00     0.00     0.00
12   4.5760        1.8954        5.1750          0.00     0.00     0.00
13   4.1183        2.7517        5.1750          0.00     0.00     0.00
14   3.5023        3.5023        5.1750          0.00     0.00     0.00
15   2.7517        4.1183        5.1750          0.00     0.00     0.00
16   1.8954        4.5760        5.1750          0.00     0.00     0.00
17  0.96628        4.8578        5.1750          0.00     0.00     0.00
18   0.0000        4.9530        0.0000          0.00     0.00     0.00
19   0.0000        4.9530        4.5281          0.00     0.00     0.00
20   0.0000        4.9530        3.8812          0.00     0.00     0.00
21   0.0000        4.9530        3.2344          0.00     0.00     0.00
22   0.0000        4.9530        2.5875          0.00     0.00     0.00
23   0.0000        4.9530        1.9406          0.00     0.00     0.00
24   0.0000        4.9530        1.2937          0.00     0.00     0.00
25   0.0000        4.9530       0.64688          0.00     0.00     0.00
26  0.96628        4.8578        0.0000          0.00     0.00     0.00
27   1.8954        4.5760        0.0000          0.00     0.00     0.00
28   2.7517        4.1183        0.0000          0.00     0.00     0.00
29   3.5023        3.5023        0.0000          0.00     0.00     0.00
30   4.1183        2.7517        0.0000          0.00     0.00     0.00
31   4.5760        1.8954        0.0000          0.00     0.00     0.00
32   4.8578       0.96628        0.0000          0.00     0.00     0.00
33   4.8578       0.96628       0.64687          0.00     0.00     0.00
34   4.5760        1.8954       0.64688          0.00     0.00     0.00
35   4.1183        2.7517       0.64688          0.00     0.00     0.00
36   3.5023        3.5023       0.64688          0.00     0.00     0.00
37   2.7517        4.1183       0.64688          0.00     0.00     0.00
38   1.8954        4.5760       0.64688          0.00     0.00     0.00
39  0.96628        4.8578       0.64688          0.00     0.00     0.00
40   4.8578       0.96628        1.2937          0.00     0.00     0.00
41   4.5760        1.8954        1.2937          0.00     0.00     0.00
42   4.1183        2.7517        1.2937          0.00     0.00     0.00
43   3.5023        3.5023        1.2937          0.00     0.00     0.00
44   2.7517        4.1183        1.2938          0.00     0.00     0.00
45   1.8954        4.5760        1.2938          0.00     0.00     0.00
46  0.96628        4.8578        1.2937          0.00     0.00     0.00
47   4.8578       0.96628        1.9406          0.00     0.00     0.00
48   4.5760        1.8954        1.9406          0.00     0.00     0.00
49   4.1183        2.7517        1.9406          0.00     0.00     0.00
50   3.5023        3.5023        1.9406          0.00     0.00     0.00
51   2.7517        4.1183        1.9406          0.00     0.00     0.00
52   1.8954        4.5760        1.9406          0.00     0.00     0.00
53  0.96628        4.8578        1.9406          0.00     0.00     0.00
54   4.8578       0.96628        2.5875          0.00     0.00     0.00
55   4.5760        1.8954        2.5875          0.00     0.00     0.00
56   4.1183        2.7517        2.5875          0.00     0.00     0.00
57   3.5023        3.5023        2.5875          0.00     0.00     0.00
58   2.7517        4.1183        2.5875          0.00     0.00     0.00
59   1.8954        4.5760        2.5875          0.00     0.00     0.00
60  0.96628        4.8578        2.5875          0.00     0.00     0.00
61   4.8578       0.96628        3.2344          0.00     0.00     0.00
62   4.5760        1.8954        3.2344          0.00     0.00     0.00
63   4.1183        2.7517        3.2344          0.00     0.00     0.00
64   3.5023        3.5023        3.2344          0.00     0.00     0.00
65   2.7517        4.1183        3.2344          0.00     0.00     0.00
66   1.8954        4.5760        3.2344          0.00     0.00     0.00
67  0.96628        4.8578        3.2344          0.00     0.00     0.00
68   4.8578       0.96628        3.8812          0.00     0.00     0.00
69   4.5760        1.8954        3.8812          0.00     0.00     0.00
70   4.1183        2.7517        3.8813          0.00     0.00     0.00
71   3.5023        3.5023        3.8813          0.00     0.00     0.00
72   2.7517        4.1183        3.8813          0.00     0.00     0.00
73   1.8954        4.5760        3.8813          0.00     0.00     0.00
74  0.96628        4.8578        3.8813          0.00     0.00     0.00
75   4.8578       0.96628        4.5281          0.00     0.00     0.00
76   4.5760        1.8954        4.5281          0.00     0.00     0.00
77   4.1183        2.7517        4.5281          0.00     0.00     0.00
78   3.5023        3.5023        4.5281          0.00     0.00     0.00
79   2.7517        4.1183        4.5281          0.00     0.00     0.00
80   1.8954        4.5760        4.5281          0.00     0.00     0.00
81  0.96628        4.8578        4.5281          0.00     0.00     0.00


## Define Boundary Conditions#

Application of symmetric boundary conditions for simplified model.

# Select nodes by location and apply BC.
def define_bc():
# Select nodes by location and apply BC.
mapdl.nsel("S", "LOC", "X", 0)
mapdl.dsym("SYMM", "X", 0)
mapdl.nsel("S", "LOC", "Y", 0)
mapdl.dsym("SYMM", "Y", 0)
mapdl.nsel("S", "LOC", "Z", 0)
mapdl.dsym("SYMM", "Z", 0)
mapdl.nsel("ALL")

define_bc()


Apply the force of $$F = (100/4) lb$$ in the y-direction.

# Define loads.
# Parametrization of the :math:F load for the quarter of the model.
force = 100 / 4

# Application of the load to the model.
mapdl.fk(top_keypoint, "FY", -force)
mapdl.finish()



## Solve#

Enter solution mode and solve the system. Print the solver output.

def solve_procedure():
mapdl.run("/solu")
out = mapdl.solve()
mapdl.finish()
return out

simulation_info = solve_procedure()
print(simulation_info)


Out:

*****  ANSYS SOLVE    COMMAND  *****

TRANSFER SOLID MODEL BOUNDARY CONDITIONS TO FINITE ELEMENT MODEL
FORCES         TRANSFERRED FROM KEYPOINTS     =      1

*** NOTE ***                            CP =       0.000   TIME= 00:00:00
There is no title defined for this analysis.

*** SELECTION OF ELEMENT TECHNOLOGIES FOR APPLICABLE ELEMENTS ***
---GIVE SUGGESTIONS ONLY---

ELEMENT TYPE         1 IS SHELL181. IT IS ASSOCIATED WITH ELASTOPLASTIC
MATERIALS ONLY. KEYOPT(8)=2 IS SUGGESTED AND KEYOPT(3)=2 IS SUGGESTED FOR
HIGHER ACCURACY OF MEMBRANE STRESSES; OTHERWISE, KEYOPT(3)=0 IS SUGGESTED.

*****ANSYS VERIFICATION RUN ONLY*****
DO NOT USE RESULTS FOR PRODUCTION

S O L U T I O N   O P T I O N S

PROBLEM DIMENSIONALITY. . . . . . . . . . . . .3-D
DEGREES OF FREEDOM. . . . . . UX   UY   UZ   ROTX ROTY ROTZ
ANALYSIS TYPE . . . . . . . . . . . . . . . . .STATIC (STEADY-STATE)
GLOBALLY ASSEMBLED MATRIX . . . . . . . . . . .SYMMETRIC

*** NOTE ***                            CP =       0.000   TIME= 00:00:00
Present time 0 is less than or equal to the previous time.  Time will
default to 1.

*** NOTE ***                            CP =       0.000   TIME= 00:00:00
The conditions for direct assembly have been met.  No .emat or .erot
files will be produced.

L O A D   S T E P   O P T I O N S

LOAD STEP NUMBER. . . . . . . . . . . . . . . .     1
TIME AT END OF THE LOAD STEP. . . . . . . . . .  1.0000
NUMBER OF SUBSTEPS. . . . . . . . . . . . . . .     1
STEP CHANGE BOUNDARY CONDITIONS . . . . . . . .    NO
PRINT OUTPUT CONTROLS . . . . . . . . . . . . .NO PRINTOUT
DATABASE OUTPUT CONTROLS. . . . . . . . . . . .ALL DATA WRITTEN
FOR THE LAST SUBSTEP

*** NOTE ***                            CP =       0.000   TIME= 00:00:00
Predictor is ON by default for structural elements with rotational
degrees of freedom.  Use the PRED,OFF command to turn the predictor
OFF if it adversely affects the convergence.

Range of element maximum matrix coefficients in global coordinates
Maximum = 596623.888 at element 0.
Minimum = 596623.886 at element 0.

*** ELEMENT MATRIX FORMULATION TIMES
TYPE    NUMBER   ENAME      TOTAL CP  AVE CP

1        64  SHELL181      0.000   0.000000
Time at end of element matrix formulation CP = 0.

SPARSE MATRIX DIRECT SOLVER.
Number of equations =         407,    Maximum wavefront =      0
Memory available (MB) =    0.0    ,  Memory required (MB) =    0.0

Sparse solver maximum pivot= 0 at node 0 .
Sparse solver minimum pivot= 0 at node 0 .
Sparse solver minimum pivot in absolute value= 0 at node 0 .

*** ELEMENT RESULT CALCULATION TIMES
TYPE    NUMBER   ENAME      TOTAL CP  AVE CP

1        64  SHELL181      0.000   0.000000

TYPE    NUMBER   ENAME      TOTAL CP  AVE CP

1        64  SHELL181      0.000   0.000000
*** LOAD STEP     1   SUBSTEP     1  COMPLETED.    CUM ITER =      1
*** TIME =   1.00000         TIME INC =   1.00000      NEW TRIANG MATRIX


## Post-processing#

Enter post-processing for the model with elements shell181. Plotting nodal displacement. Get the the radial displacement at the node where force F is applied.

# Start post-processing mode.
def post_processing():
mapdl.post1()
mapdl.set(1)

post_processing()


## Plotting#

Plot nodal displacement using PyVista.

def plot_nodal_disp():
mapdl.post_processing.plot_nodal_displacement(
title="Nodal Displacements",
component="Y",
cpos="zx",
scalar_bar_args={"title": "Nodal Displacements", "vertical": True},
show_node_numbering=True,
show_axes=True,
show_edges=True,
)

plot_nodal_disp()


To determine the radial displacement $$\delta$$ at the point where F is applied, we can use Mapdl.get_value.

def get_displacements():
# Select keypoint by its number top_keypoint.
mapdl.ksel("S", vmin="top_keypoint")

# Select the node associated with the selected keypoint.
mapdl.nslk()

# Get the number of the selected node by :meth:Mapdl.get <ansys.mapdl.core.Mapdl.get>
top_node = int(mapdl.get("_", "node", 0, "num", "max"))

# Define radial displacement at the node where F is applied.
deflect_shell = mapdl.get_value(
entity="node", entnum=top_node, item1="u", it1num="y"
)

# Call the function and get the value of the deflection.
top_node_181, deflect_shell_181 = get_displacements()
print(
f"Number of the node attached to the top keypoint: {top_node_181},\n"
)


Out:

Number of the node attached to the top keypoint: 18,


## Rerun Model with SHELL281#

Perform the simulation again using the element type SHELL281.

# Restart pre-processing routine.
start_prep7()
elem_type = define_element(elem_type="SHELL281")
define_material()
define_section()
define_geometry()
meshing()
define_bc()


Out:

LIST ALL SELECTED ELEMENTS.  (LIST NODES)
1   1   1   1   0   1      1     4    73    63     3    72    65    64
2   1   1   1   0   1      4     6    95    73     5    94    87    72
3   1   1   1   0   1      6     8   117    95     7   116   109    94
4   1   1   1   0   1      8    10   139   117     9   138   131   116
5   1   1   1   0   1     10    12   161   139    11   160   153   138
6   1   1   1   0   1     12    14   183   161    13   182   175   160
7   1   1   1   0   1     14    16   205   183    15   204   197   182
8   1   1   1   0   1     16     2    20   205    17    19   219   204
9   1   1   1   0   1     63    73    75    61    65    74    66    62
10   1   1   1   0   1     73    95    97    75    87    96    88    74
11   1   1   1   0   1     95   117   119    97   109   118   110    96
12   1   1   1   0   1    117   139   141   119   131   140   132   118
13   1   1   1   0   1    139   161   163   141   153   162   154   140
14   1   1   1   0   1    161   183   185   163   175   184   176   162
15   1   1   1   0   1    183   205   207   185   197   206   198   184
16   1   1   1   0   1    205    20    22   207   219    21   220   206
17   1   1   1   0   1     61    75    77    59    66    76    67    60
18   1   1   1   0   1     75    97    99    77    88    98    89    76
19   1   1   1   0   1     97   119   121    99   110   120   111    98
20   1   1   1   0   1    119   141   143   121   132   142   133   120
21   1   1   1   0   1    141   163   165   143   154   164   155   142
22   1   1   1   0   1    163   185   187   165   176   186   177   164
23   1   1   1   0   1    185   207   209   187   198   208   199   186
24   1   1   1   0   1    207    22    24   209   220    23   221   208
25   1   1   1   0   1     59    77    79    57    67    78    68    58
26   1   1   1   0   1     77    99   101    79    89   100    90    78
27   1   1   1   0   1     99   121   123   101   111   122   112   100
28   1   1   1   0   1    121   143   145   123   133   144   134   122
29   1   1   1   0   1    143   165   167   145   155   166   156   144
30   1   1   1   0   1    165   187   189   167   177   188   178   166
31   1   1   1   0   1    187   209   211   189   199   210   200   188
32   1   1   1   0   1    209    24    26   211   221    25   222   210
33   1   1   1   0   1     57    79    81    55    68    80    69    56
34   1   1   1   0   1     79   101   103    81    90   102    91    80
35   1   1   1   0   1    101   123   125   103   112   124   113   102
36   1   1   1   0   1    123   145   147   125   134   146   135   124
37   1   1   1   0   1    145   167   169   147   156   168   157   146
38   1   1   1   0   1    167   189   191   169   178   190   179   168
39   1   1   1   0   1    189   211   213   191   200   212   201   190
40   1   1   1   0   1    211    26    28   213   222    27   223   212
41   1   1   1   0   1     55    81    83    53    69    82    70    54
42   1   1   1   0   1     81   103   105    83    91   104    92    82
43   1   1   1   0   1    103   125   127   105   113   126   114   104
44   1   1   1   0   1    125   147   149   127   135   148   136   126
45   1   1   1   0   1    147   169   171   149   157   170   158   148
46   1   1   1   0   1    169   191   193   171   179   192   180   170
47   1   1   1   0   1    191   213   215   193   201   214   202   192
48   1   1   1   0   1    213    28    30   215   223    29   224   214
49   1   1   1   0   1     53    83    85    51    70    84    71    52
50   1   1   1   0   1     83   105   107    85    92   106    93    84
51   1   1   1   0   1    105   127   129   107   114   128   115   106
52   1   1   1   0   1    127   149   151   129   136   150   137   128
53   1   1   1   0   1    149   171   173   151   158   172   159   150
54   1   1   1   0   1    171   193   195   173   180   194   181   172
55   1   1   1   0   1    193   215   217   195   202   216   203   194
56   1   1   1   0   1    215    30    32   217   224    31   225   216
57   1   1   1   0   1     51    85    48    34    71    86    49    50
58   1   1   1   0   1     85   107    46    48    93   108    47    86
59   1   1   1   0   1    107   129    44    46   115   130    45   108
60   1   1   1   0   1    129   151    42    44   137   152    43   130
61   1   1   1   0   1    151   173    40    42   159   174    41   152
62   1   1   1   0   1    173   195    38    40   181   196    39   174
63   1   1   1   0   1    195   217    36    38   203   218    37   196
64   1   1   1   0   1    217    32    18    36   225    33    35   218
1   4.9530        0.0000        0.0000          0.00     0.00     0.00
2   4.9530        0.0000        5.1750          0.00     0.00     0.00
3   4.9530        0.0000       0.32344          0.00     0.00     0.00
4   4.9530        0.0000       0.64687          0.00     0.00     0.00
5   4.9530        0.0000       0.97031          0.00     0.00     0.00
6   4.9530        0.0000        1.2937          0.00     0.00     0.00
7   4.9530        0.0000        1.6172          0.00     0.00     0.00
8   4.9530        0.0000        1.9406          0.00     0.00     0.00
9   4.9530        0.0000        2.2641          0.00     0.00     0.00
10   4.9530        0.0000        2.5875          0.00     0.00     0.00
11   4.9530        0.0000        2.9109          0.00     0.00     0.00
12   4.9530        0.0000        3.2344          0.00     0.00     0.00
13   4.9530        0.0000        3.5578          0.00     0.00     0.00
14   4.9530        0.0000        3.8812          0.00     0.00     0.00
15   4.9530        0.0000        4.2047          0.00     0.00     0.00
16   4.9530        0.0000        4.5281          0.00     0.00     0.00
17   4.9530        0.0000        4.8516          0.00     0.00     0.00
18   0.0000        4.9530        5.1750          0.00     0.00     0.00
19   4.9291       0.48548        5.1750          0.00     0.00     0.00
20   4.8578       0.96628        5.1750          0.00     0.00     0.00
21   4.7397        1.4378        5.1750          0.00     0.00     0.00
22   4.5760        1.8954        5.1750          0.00     0.00     0.00
23   4.3682        2.3348        5.1750          0.00     0.00     0.00
24   4.1183        2.7517        5.1750          0.00     0.00     0.00
25   3.8287        3.1421        5.1750          0.00     0.00     0.00
26   3.5023        3.5023        5.1750          0.00     0.00     0.00
27   3.1421        3.8287        5.1750          0.00     0.00     0.00
28   2.7517        4.1183        5.1750          0.00     0.00     0.00
29   2.3348        4.3682        5.1750          0.00     0.00     0.00
30   1.8954        4.5760        5.1750          0.00     0.00     0.00
31   1.4378        4.7397        5.1750          0.00     0.00     0.00
32  0.96628        4.8578        5.1750          0.00     0.00     0.00
33  0.48548        4.9291        5.1750          0.00     0.00     0.00
34   0.0000        4.9530        0.0000          0.00     0.00     0.00
35   0.0000        4.9530        4.8516          0.00     0.00     0.00
36   0.0000        4.9530        4.5281          0.00     0.00     0.00
37   0.0000        4.9530        4.2047          0.00     0.00     0.00
38   0.0000        4.9530        3.8812          0.00     0.00     0.00
39   0.0000        4.9530        3.5578          0.00     0.00     0.00
40   0.0000        4.9530        3.2344          0.00     0.00     0.00
41   0.0000        4.9530        2.9109          0.00     0.00     0.00
42   0.0000        4.9530        2.5875          0.00     0.00     0.00
43   0.0000        4.9530        2.2641          0.00     0.00     0.00
44   0.0000        4.9530        1.9406          0.00     0.00     0.00
45   0.0000        4.9530        1.6172          0.00     0.00     0.00
46   0.0000        4.9530        1.2937          0.00     0.00     0.00
47   0.0000        4.9530       0.97031          0.00     0.00     0.00
48   0.0000        4.9530       0.64688          0.00     0.00     0.00
49   0.0000        4.9530       0.32344          0.00     0.00     0.00
50  0.48548        4.9291        0.0000          0.00     0.00     0.00
51  0.96628        4.8578        0.0000          0.00     0.00     0.00
52   1.4378        4.7397        0.0000          0.00     0.00     0.00
53   1.8954        4.5760        0.0000          0.00     0.00     0.00
54   2.3348        4.3682        0.0000          0.00     0.00     0.00
55   2.7517        4.1183        0.0000          0.00     0.00     0.00
56   3.1421        3.8287        0.0000          0.00     0.00     0.00
57   3.5023        3.5023        0.0000          0.00     0.00     0.00
58   3.8287        3.1421        0.0000          0.00     0.00     0.00
59   4.1183        2.7517        0.0000          0.00     0.00     0.00
60   4.3682        2.3348        0.0000          0.00     0.00     0.00
61   4.5760        1.8954        0.0000          0.00     0.00     0.00
62   4.7397        1.4378        0.0000          0.00     0.00     0.00
63   4.8578       0.96628        0.0000          0.00     0.00     0.00
64   4.9291       0.48548        0.0000          0.00     0.00     0.00
65   4.8578       0.96628       0.32344          0.00     0.00     0.00
66   4.5760        1.8954       0.32344          0.00     0.00     0.00
67   4.1183        2.7517       0.32344          0.00     0.00     0.00
68   3.5023        3.5023       0.32344          0.00     0.00     0.00
69   2.7517        4.1183       0.32344          0.00     0.00     0.00
70   1.8954        4.5760       0.32344          0.00     0.00     0.00
71  0.96628        4.8578       0.32344          0.00     0.00     0.00
72   4.9291       0.48548       0.64687          0.00     0.00     0.00
73   4.8578       0.96628       0.64687          0.00     0.00     0.00
74   4.7397        1.4378       0.64687          0.00     0.00     0.00
75   4.5760        1.8954       0.64687          0.00     0.00     0.00
76   4.3682        2.3348       0.64687          0.00     0.00     0.00
77   4.1183        2.7517       0.64688          0.00     0.00     0.00
78   3.8287        3.1421       0.64688          0.00     0.00     0.00
79   3.5023        3.5023       0.64688          0.00     0.00     0.00
80   3.1421        3.8287       0.64688          0.00     0.00     0.00
81   2.7517        4.1183       0.64688          0.00     0.00     0.00
82   2.3348        4.3682       0.64688          0.00     0.00     0.00
83   1.8954        4.5760       0.64688          0.00     0.00     0.00
84   1.4378        4.7397       0.64688          0.00     0.00     0.00
85  0.96628        4.8578       0.64688          0.00     0.00     0.00
86  0.48548        4.9291       0.64688          0.00     0.00     0.00
87   4.8578       0.96628       0.97031          0.00     0.00     0.00
88   4.5760        1.8954       0.97031          0.00     0.00     0.00
89   4.1183        2.7517       0.97031          0.00     0.00     0.00
90   3.5023        3.5023       0.97031          0.00     0.00     0.00
91   2.7517        4.1183       0.97031          0.00     0.00     0.00
92   1.8954        4.5760       0.97031          0.00     0.00     0.00
93  0.96628        4.8578       0.97031          0.00     0.00     0.00
94   4.9291       0.48548        1.2937          0.00     0.00     0.00
95   4.8578       0.96628        1.2937          0.00     0.00     0.00
96   4.7397        1.4378        1.2937          0.00     0.00     0.00
97   4.5760        1.8954        1.2937          0.00     0.00     0.00
98   4.3682        2.3348        1.2937          0.00     0.00     0.00
99   4.1183        2.7517        1.2937          0.00     0.00     0.00
100   3.8287        3.1421        1.2937          0.00     0.00     0.00
101   3.5023        3.5023        1.2937          0.00     0.00     0.00
102   3.1421        3.8287        1.2938          0.00     0.00     0.00
103   2.7517        4.1183        1.2938          0.00     0.00     0.00
104   2.3348        4.3682        1.2938          0.00     0.00     0.00
105   1.8954        4.5760        1.2937          0.00     0.00     0.00
106   1.4378        4.7397        1.2938          0.00     0.00     0.00
107  0.96628        4.8578        1.2938          0.00     0.00     0.00
108  0.48548        4.9291        1.2938          0.00     0.00     0.00
109   4.8578       0.96628        1.6172          0.00     0.00     0.00
110   4.5760        1.8954        1.6172          0.00     0.00     0.00
111   4.1183        2.7517        1.6172          0.00     0.00     0.00
112   3.5023        3.5023        1.6172          0.00     0.00     0.00
113   2.7517        4.1183        1.6172          0.00     0.00     0.00
114   1.8954        4.5760        1.6172          0.00     0.00     0.00
115  0.96628        4.8578        1.6172          0.00     0.00     0.00
116   4.9291       0.48548        1.9406          0.00     0.00     0.00
117   4.8578       0.96628        1.9406          0.00     0.00     0.00
118   4.7397        1.4378        1.9406          0.00     0.00     0.00
119   4.5760        1.8954        1.9406          0.00     0.00     0.00
120   4.3682        2.3348        1.9406          0.00     0.00     0.00
121   4.1183        2.7517        1.9406          0.00     0.00     0.00
122   3.8287        3.1421        1.9406          0.00     0.00     0.00
123   3.5023        3.5023        1.9406          0.00     0.00     0.00
124   3.1421        3.8287        1.9406          0.00     0.00     0.00
125   2.7517        4.1183        1.9406          0.00     0.00     0.00
126   2.3348        4.3682        1.9406          0.00     0.00     0.00
127   1.8954        4.5760        1.9406          0.00     0.00     0.00
128   1.4378        4.7397        1.9406          0.00     0.00     0.00
129  0.96628        4.8578        1.9406          0.00     0.00     0.00
130  0.48548        4.9291        1.9406          0.00     0.00     0.00
131   4.8578       0.96628        2.2641          0.00     0.00     0.00
132   4.5760        1.8954        2.2641          0.00     0.00     0.00
133   4.1183        2.7517        2.2641          0.00     0.00     0.00
134   3.5023        3.5023        2.2641          0.00     0.00     0.00
135   2.7517        4.1183        2.2641          0.00     0.00     0.00
136   1.8954        4.5760        2.2641          0.00     0.00     0.00
137  0.96628        4.8578        2.2641          0.00     0.00     0.00
138   4.9291       0.48548        2.5875          0.00     0.00     0.00
139   4.8578       0.96628        2.5875          0.00     0.00     0.00
140   4.7397        1.4378        2.5875          0.00     0.00     0.00
141   4.5760        1.8954        2.5875          0.00     0.00     0.00
142   4.3682        2.3348        2.5875          0.00     0.00     0.00
143   4.1183        2.7517        2.5875          0.00     0.00     0.00
144   3.8287        3.1421        2.5875          0.00     0.00     0.00
145   3.5023        3.5023        2.5875          0.00     0.00     0.00
146   3.1421        3.8287        2.5875          0.00     0.00     0.00
147   2.7517        4.1183        2.5875          0.00     0.00     0.00
148   2.3348        4.3682        2.5875          0.00     0.00     0.00
149   1.8954        4.5760        2.5875          0.00     0.00     0.00
150   1.4378        4.7397        2.5875          0.00     0.00     0.00
151  0.96628        4.8578        2.5875          0.00     0.00     0.00
152  0.48548        4.9291        2.5875          0.00     0.00     0.00
153   4.8578       0.96628        2.9109          0.00     0.00     0.00
154   4.5760        1.8954        2.9109          0.00     0.00     0.00
155   4.1183        2.7517        2.9109          0.00     0.00     0.00
156   3.5023        3.5023        2.9109          0.00     0.00     0.00
157   2.7517        4.1183        2.9109          0.00     0.00     0.00
158   1.8954        4.5760        2.9109          0.00     0.00     0.00
159  0.96628        4.8578        2.9109          0.00     0.00     0.00
160   4.9291       0.48548        3.2344          0.00     0.00     0.00
161   4.8578       0.96628        3.2344          0.00     0.00     0.00
162   4.7397        1.4378        3.2344          0.00     0.00     0.00
163   4.5760        1.8954        3.2344          0.00     0.00     0.00
164   4.3682        2.3348        3.2344          0.00     0.00     0.00
165   4.1183        2.7517        3.2344          0.00     0.00     0.00
166   3.8287        3.1421        3.2344          0.00     0.00     0.00
167   3.5023        3.5023        3.2344          0.00     0.00     0.00
168   3.1421        3.8287        3.2344          0.00     0.00     0.00
169   2.7517        4.1183        3.2344          0.00     0.00     0.00
170   2.3348        4.3682        3.2344          0.00     0.00     0.00
171   1.8954        4.5760        3.2344          0.00     0.00     0.00
172   1.4378        4.7397        3.2344          0.00     0.00     0.00
173  0.96628        4.8578        3.2344          0.00     0.00     0.00
174  0.48548        4.9291        3.2344          0.00     0.00     0.00
175   4.8578       0.96628        3.5578          0.00     0.00     0.00
176   4.5760        1.8954        3.5578          0.00     0.00     0.00
177   4.1183        2.7517        3.5578          0.00     0.00     0.00
178   3.5023        3.5023        3.5578          0.00     0.00     0.00
179   2.7517        4.1183        3.5578          0.00     0.00     0.00
180   1.8954        4.5760        3.5578          0.00     0.00     0.00
181  0.96628        4.8578        3.5578          0.00     0.00     0.00
182   4.9291       0.48548        3.8812          0.00     0.00     0.00
183   4.8578       0.96628        3.8812          0.00     0.00     0.00
184   4.7397        1.4378        3.8812          0.00     0.00     0.00
185   4.5760        1.8954        3.8812          0.00     0.00     0.00
186   4.3682        2.3348        3.8812          0.00     0.00     0.00
187   4.1183        2.7517        3.8812          0.00     0.00     0.00
188   3.8287        3.1421        3.8813          0.00     0.00     0.00
189   3.5023        3.5023        3.8813          0.00     0.00     0.00
190   3.1421        3.8287        3.8813          0.00     0.00     0.00
191   2.7517        4.1183        3.8813          0.00     0.00     0.00
192   2.3348        4.3682        3.8813          0.00     0.00     0.00
193   1.8954        4.5760        3.8813          0.00     0.00     0.00
194   1.4378        4.7397        3.8813          0.00     0.00     0.00
195  0.96628        4.8578        3.8813          0.00     0.00     0.00
196  0.48548        4.9291        3.8813          0.00     0.00     0.00
197   4.8578       0.96628        4.2047          0.00     0.00     0.00
198   4.5760        1.8954        4.2047          0.00     0.00     0.00
199   4.1183        2.7517        4.2047          0.00     0.00     0.00
200   3.5023        3.5023        4.2047          0.00     0.00     0.00
201   2.7517        4.1183        4.2047          0.00     0.00     0.00
202   1.8954        4.5760        4.2047          0.00     0.00     0.00
203  0.96628        4.8578        4.2047          0.00     0.00     0.00
204   4.9291       0.48548        4.5281          0.00     0.00     0.00
205   4.8578       0.96628        4.5281          0.00     0.00     0.00
206   4.7397        1.4378        4.5281          0.00     0.00     0.00
207   4.5760        1.8954        4.5281          0.00     0.00     0.00
208   4.3682        2.3348        4.5281          0.00     0.00     0.00
209   4.1183        2.7517        4.5281          0.00     0.00     0.00
210   3.8287        3.1421        4.5281          0.00     0.00     0.00
211   3.5023        3.5023        4.5281          0.00     0.00     0.00
212   3.1421        3.8287        4.5281          0.00     0.00     0.00
213   2.7517        4.1183        4.5281          0.00     0.00     0.00
214   2.3348        4.3682        4.5281          0.00     0.00     0.00
215   1.8954        4.5760        4.5281          0.00     0.00     0.00
216   1.4378        4.7397        4.5281          0.00     0.00     0.00
217  0.96628        4.8578        4.5281          0.00     0.00     0.00
218  0.48548        4.9291        4.5281          0.00     0.00     0.00
219   4.8578       0.96628        4.8516          0.00     0.00     0.00
220   4.5760        1.8954        4.8516          0.00     0.00     0.00
221   4.1183        2.7517        4.8516          0.00     0.00     0.00
222   3.5023        3.5023        4.8516          0.00     0.00     0.00
223   2.7517        4.1183        4.8516          0.00     0.00     0.00
224   1.8954        4.5760        4.8516          0.00     0.00     0.00
225  0.96628        4.8578        4.8516          0.00     0.00     0.00


## Solve#

Enter solution mode and solve the system. Print the solver output.

solve_procedure()


Out:

*****  ANSYS SOLVE    COMMAND  *****

TRANSFER SOLID MODEL BOUNDARY CONDITIONS TO FINITE ELEMENT MODEL
FORCES         TRANSFERRED FROM KEYPOINTS     =      1

*** NOTE ***                            CP =       0.000   TIME= 00:00:00
There is no title defined for this analysis.

*** SELECTION OF ELEMENT TECHNOLOGIES FOR APPLICABLE ELEMENTS ***
---GIVE SUGGESTIONS ONLY---

ELEMENT TYPE         1 IS SHELL281. IT IS ASSOCIATED WITH ELASTOPLASTIC
MATERIALS ONLY. KEYOPT(8)=2 IS SUGGESTED.

*****ANSYS VERIFICATION RUN ONLY*****
DO NOT USE RESULTS FOR PRODUCTION

S O L U T I O N   O P T I O N S

PROBLEM DIMENSIONALITY. . . . . . . . . . . . .3-D
DEGREES OF FREEDOM. . . . . . UX   UY   UZ   ROTX ROTY ROTZ
ANALYSIS TYPE . . . . . . . . . . . . . . . . .STATIC (STEADY-STATE)
GLOBALLY ASSEMBLED MATRIX . . . . . . . . . . .SYMMETRIC

*** NOTE ***                            CP =       0.000   TIME= 00:00:00
Present time 0 is less than or equal to the previous time.  Time will
default to 1.

*** NOTE ***                            CP =       0.000   TIME= 00:00:00
The conditions for direct assembly have been met.  No .emat or .erot
files will be produced.

L O A D   S T E P   O P T I O N S

LOAD STEP NUMBER. . . . . . . . . . . . . . . .     1
TIME AT END OF THE LOAD STEP. . . . . . . . . .  1.0000
NUMBER OF SUBSTEPS. . . . . . . . . . . . . . .     1
STEP CHANGE BOUNDARY CONDITIONS . . . . . . . .    NO
PRINT OUTPUT CONTROLS . . . . . . . . . . . . .NO PRINTOUT
DATABASE OUTPUT CONTROLS. . . . . . . . . . . .ALL DATA WRITTEN
FOR THE LAST SUBSTEP

*** NOTE ***                            CP =       0.000   TIME= 00:00:00
Predictor is ON by default for structural elements with rotational
degrees of freedom.  Use the PRED,OFF command to turn the predictor
OFF if it adversely affects the convergence.

Range of element maximum matrix coefficients in global coordinates
Maximum = 3034922.21 at element 0.
Minimum = 3034922.21 at element 0.

*** ELEMENT MATRIX FORMULATION TIMES
TYPE    NUMBER   ENAME      TOTAL CP  AVE CP

1        64  SHELL281      0.000   0.000000
Time at end of element matrix formulation CP = 0.

SPARSE MATRIX DIRECT SOLVER.
Number of equations =        1199,    Maximum wavefront =      0
Memory available (MB) =    0.0    ,  Memory required (MB) =    0.0

Sparse solver maximum pivot= 0 at node 0 .
Sparse solver minimum pivot= 0 at node 0 .
Sparse solver minimum pivot in absolute value= 0 at node 0 .

*** ELEMENT RESULT CALCULATION TIMES
TYPE    NUMBER   ENAME      TOTAL CP  AVE CP

1        64  SHELL281      0.000   0.000000

TYPE    NUMBER   ENAME      TOTAL CP  AVE CP

1        64  SHELL281      0.000   0.000000
*** LOAD STEP     1   SUBSTEP     1  COMPLETED.    CUM ITER =      1
*** TIME =   1.00000         TIME INC =   1.00000      NEW TRIANG MATRIX


## Post-processing#

Enter post-processing for the model with elements shell281. Plotting nodal displacement. Get the the radial displacement at the node where force F is applied.

post_processing()
plot_nodal_disp()
top_node_281, deflect_shell_281 = get_displacements()


## Check Results#

Now we have the deflections, we can compare them to the expected values of radial deflection at the node where force $$F$$ was applied for both simulations. The expected value for $$\delta_{\mathrm{shell181}}$$ is 0.1139, and $$\delta_{\mathrm{shell281}}$$ is 0.1139.

# Results obtained by hand-calculations.
deflect_target_181 = 0.1139
deflect_target_281 = 0.1139

# Calculate the deviation.
deflect_ratio_shell_181 = abs(deflect_shell_181) / deflect_target_181
deflect_ratio_shell_281 = abs(deflect_shell_281) / deflect_target_281

# Print output results.
output = f"""
----------------------------------------------------------------------------
------------------------- VM3 RESULTS COMPARISON ---------------------------
----------------------------------------------------------------------------
|   TARGET   |   Mechanical APDL   |   RATIO   |
----------------------------------------------------------------------------
Deflection, in SHELL181{deflect_target_181:11.4f} {abs(deflect_shell_181):17.4f} {deflect_ratio_shell_181:15.3f}
Deflection, in SHELL281{deflect_target_281:11.4f} {abs(deflect_shell_281):17.4f} {deflect_ratio_shell_281:15.3f}
----------------------------------------------------------------------------
"""
print(output)


Out:

----------------------------------------------------------------------------
------------------------- VM3 RESULTS COMPARISON ---------------------------
----------------------------------------------------------------------------
|   TARGET   |   Mechanical APDL   |   RATIO   |
----------------------------------------------------------------------------
Deflection, in SHELL181     0.1139            0.1100           0.965
Deflection, in SHELL281     0.1139            0.1137           0.998
----------------------------------------------------------------------------


stop mapdl

mapdl.exit()


Total running time of the script: ( 0 minutes 3.144 seconds)

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