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)

VM6 Pinched Cylinder Problem Sketch
Material Properties
  • \(E = 10.5 \cdot 10^6 psi\)

  • \(\nu = 0.3125\)

Geometric Properties:
  • \(l = 10.35 in\)

  • \(r = 4.953 in\)

  • \(t = 0.094 in\)

Loading:
  • \(F = 100 lb\)

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}")
  • vm 006 pinched cylinder
  • vm 006 pinched cylinder

Out:

/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/pyvista/core/dataset.py:1401: PyvistaDeprecationWarning: Use of `point_arrays` is deprecated. Use `point_data` instead.
  warnings.warn(
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/pyvista/core/dataset.py:1541: PyvistaDeprecationWarning: Use of `cell_arrays` is deprecated. Use `cell_data` instead.
  warnings.warn(
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()
  • vm 006 pinched cylinder
  • vm 006 pinched cylinder

Out:

/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/pyvista/core/dataset.py:1401: PyvistaDeprecationWarning: Use of `point_arrays` is deprecated. Use `point_data` instead.
  warnings.warn(
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/pyvista/core/dataset.py:1541: PyvistaDeprecationWarning: Use of `cell_arrays` is deprecated. Use `cell_data` instead.
  warnings.warn(
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()

Define Distributed Loads

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

# Define loads.
def 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()

define_loads()

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

   *** NODAL LOAD CALCULATION TIMES
     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()
vm 006 pinched cylinder

Out:

/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/pyvista/core/dataset.py:1401: PyvistaDeprecationWarning: Use of `point_arrays` is deprecated. Use `point_data` instead.
  warnings.warn(
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/pyvista/core/dataset.py:1541: PyvistaDeprecationWarning: Use of `cell_arrays` is deprecated. Use `cell_data` instead.
  warnings.warn(

Getting the radial displacements

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')

    return top_node, deflect_shell

# 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"
      f"Radial displacement: {(round(deflect_shell_181, 4))}")

Out:

Number of the node attached to the top keypoint: 18,
Radial displacement: -0.11

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()
define_loads()
vm 006 pinched cylinder

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  *****\n\n TRANSFER SOLID MODEL BOUNDARY CONDITIONS TO FINITE ELEMENT MODEL\n      FORCES         TRANSFERRED FROM KEYPOINTS     =      1\n\n *** NOTE ***                            CP =       0.000   TIME= 00:00:00\n There is no title defined for this analysis.                            \n\n *** SELECTION OF ELEMENT TECHNOLOGIES FOR APPLICABLE ELEMENTS ***\n                ---GIVE SUGGESTIONS ONLY---\n\n ELEMENT TYPE         1 IS SHELL281. IT IS ASSOCIATED WITH ELASTOPLASTIC \n MATERIALS ONLY. KEYOPT(8)=2 IS SUGGESTED.\n\n\n   *****ANSYS VERIFICATION RUN ONLY*****\n     DO NOT USE RESULTS FOR PRODUCTION\n\n                       S O L U T I O N   O P T I O N S\n\n   PROBLEM DIMENSIONALITY. . . . . . . . . . . . .3-D                  \n   DEGREES OF FREEDOM. . . . . . UX   UY   UZ   ROTX ROTY ROTZ\n   ANALYSIS TYPE . . . . . . . . . . . . . . . . .STATIC (STEADY-STATE)\n   GLOBALLY ASSEMBLED MATRIX . . . . . . . . . . .SYMMETRIC  \n\n *** NOTE ***                            CP =       0.000   TIME= 00:00:00\n Present time 0 is less than or equal to the previous time.  Time will   \n default to 1.                                                           \n\n *** NOTE ***                            CP =       0.000   TIME= 00:00:00\n The conditions for direct assembly have been met.  No .emat or .erot    \n files will be produced.                                                 \n\n                      L O A D   S T E P   O P T I O N S\n\n   LOAD STEP NUMBER. . . . . . . . . . . . . . . .     1\n   TIME AT END OF THE LOAD STEP. . . . . . . . . .  1.0000    \n   NUMBER OF SUBSTEPS. . . . . . . . . . . . . . .     1\n   STEP CHANGE BOUNDARY CONDITIONS . . . . . . . .    NO\n   PRINT OUTPUT CONTROLS . . . . . . . . . . . . .NO PRINTOUT\n   DATABASE OUTPUT CONTROLS. . . . . . . . . . . .ALL DATA WRITTEN\n                                                  FOR THE LAST SUBSTEP\n\n\n *** NOTE ***                            CP =       0.000   TIME= 00:00:00\n Predictor is ON by default for structural elements with rotational      \n degrees of freedom.  Use the PRED,OFF command to turn the predictor     \n OFF if it adversely affects the convergence.                            \n\n\n Range of element maximum matrix coefficients in global coordinates\n Maximum = 3034922.21 at element 0.                                      \n Minimum = 3034922.21 at element 0.                                      \n\n   *** ELEMENT MATRIX FORMULATION TIMES\n     TYPE    NUMBER   ENAME      TOTAL CP  AVE CP\n\n        1        64  SHELL281      0.000   0.000000\n Time at end of element matrix formulation CP = 0.                       \n\n SPARSE MATRIX DIRECT SOLVER.\n  Number of equations =        1199,    Maximum wavefront =      0\n  Memory available (MB) =    0.0    ,  Memory required (MB) =    0.0    \n\n Sparse solver maximum pivot= 0 at node 0 .                              \n Sparse solver minimum pivot= 0 at node 0 .                              \n Sparse solver minimum pivot in absolute value= 0 at node 0 .            \n\n   *** ELEMENT RESULT CALCULATION TIMES\n     TYPE    NUMBER   ENAME      TOTAL CP  AVE CP\n\n        1        64  SHELL281      0.000   0.000000\n\n   *** NODAL LOAD CALCULATION TIMES\n     TYPE    NUMBER   ENAME      TOTAL CP  AVE CP\n\n        1        64  SHELL281      0.000   0.000000\n *** LOAD STEP     1   SUBSTEP     1  COMPLETED.    CUM ITER =      1\n *** 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()
vm 006 pinched cylinder

Out:

/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/pyvista/core/dataset.py:1401: PyvistaDeprecationWarning: Use of `point_arrays` is deprecated. Use `point_data` instead.
  warnings.warn(
/opt/hostedtoolcache/Python/3.8.12/x64/lib/python3.8/site-packages/pyvista/core/dataset.py:1541: PyvistaDeprecationWarning: Use of `cell_arrays` is deprecated. Use `cell_data` instead.
  warnings.warn(

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
----------------------------------------------------------------------------

Total running time of the script: ( 0 minutes 3.228 seconds)

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