Note
Go to the end to download the full example code
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:
\(l = 10.35 in\)
\(r = 4.953 in\)
\(t = 0.094 in\)
- 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}"
)
Selected element type is: SHELL181,
Printout the element list with its own properties:
LIST ELEMENT TYPES FROM 1 TO 1 BY 1
*****MAPDL VERIFICATION RUN ONLY*****
DO NOT USE RESULTS FOR PRODUCTION
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 \(\nu = 0.3125\).
LIST MATERIALS 1 TO 1 BY 1
PROPERTY= ALL
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)
*****MAPDL VERIFICATION RUN ONLY*****
DO NOT USE RESULTS FOR PRODUCTION
LIST SECTION ID SETS 1 TO 1 BY 1
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}")
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()
LIST ALL SELECTED ELEMENTS. (LIST NODES)
*****MAPDL VERIFICATION RUN ONLY*****
DO NOT USE RESULTS FOR PRODUCTION
ELEM MAT TYP REL ESY SEC 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
*****MAPDL VERIFICATION RUN ONLY*****
DO NOT USE RESULTS FOR PRODUCTION
ELEM MAT TYP REL ESY SEC NODES
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
LIST ALL SELECTED NODES. DSYS= 0
*****MAPDL VERIFICATION RUN ONLY*****
DO NOT USE RESULTS FOR PRODUCTION
NODE X Y Z THXY THYZ THZX
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 1.2937 0.00 0.00 0.00
45 1.8954 4.5760 1.2937 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
*****MAPDL VERIFICATION RUN ONLY*****
DO NOT USE RESULTS FOR PRODUCTION
NODE X Y Z THXY THYZ THZX
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 3.8812 0.00 0.00 0.00
71 3.5023 3.5023 3.8812 0.00 0.00 0.00
72 2.7517 4.1183 3.8812 0.00 0.00 0.00
73 1.8954 4.5760 3.8812 0.00 0.00 0.00
74 0.96628 4.8578 3.8812 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)
***** MAPDL 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.
*****MAPDL 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.
D I S T R I B U T E D D O M A I N D E C O M P O S E R
...Number of elements: 64
...Number of nodes: 81
...Decompose to 0 CPU domains
...Element load balance ratio = 0.000
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.
DISTRIBUTED SPARSE MATRIX DIRECT SOLVER.
Number of equations = 407, Maximum wavefront = 0
Memory available (MB) = 0.0 , Memory required (MB) = 0.0
Distributed sparse solver maximum pivot= 0 at node 0 .
Distributed sparse solver minimum pivot= 0 at node 0 .
Distributed 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()
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))}"
)
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.
LIST ALL SELECTED ELEMENTS. (LIST NODES)
*****MAPDL VERIFICATION RUN ONLY*****
DO NOT USE RESULTS FOR PRODUCTION
ELEM MAT TYP REL ESY SEC 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
*****MAPDL VERIFICATION RUN ONLY*****
DO NOT USE RESULTS FOR PRODUCTION
ELEM MAT TYP REL ESY SEC NODES
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
LIST ALL SELECTED NODES. DSYS= 0
*****MAPDL VERIFICATION RUN ONLY*****
DO NOT USE RESULTS FOR PRODUCTION
NODE X Y Z THXY THYZ THZX
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
*****MAPDL VERIFICATION RUN ONLY*****
DO NOT USE RESULTS FOR PRODUCTION
NODE X Y Z THXY THYZ THZX
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 0.64687 0.00 0.00 0.00
79 3.5023 3.5023 0.64688 0.00 0.00 0.00
80 3.1421 3.8287 0.64687 0.00 0.00 0.00
81 2.7517 4.1183 0.64687 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
*****MAPDL VERIFICATION RUN ONLY*****
DO NOT USE RESULTS FOR PRODUCTION
NODE X Y Z THXY THYZ THZX
101 3.5023 3.5023 1.2937 0.00 0.00 0.00
102 3.1421 3.8287 1.2937 0.00 0.00 0.00
103 2.7517 4.1183 1.2937 0.00 0.00 0.00
104 2.3348 4.3682 1.2937 0.00 0.00 0.00
105 1.8954 4.5760 1.2937 0.00 0.00 0.00
106 1.4378 4.7397 1.2937 0.00 0.00 0.00
107 0.96628 4.8578 1.2937 0.00 0.00 0.00
108 0.48548 4.9291 1.2937 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
*****MAPDL VERIFICATION RUN ONLY*****
DO NOT USE RESULTS FOR PRODUCTION
NODE X Y Z THXY THYZ THZX
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 3.8812 0.00 0.00 0.00
189 3.5023 3.5023 3.8812 0.00 0.00 0.00
190 3.1421 3.8287 3.8812 0.00 0.00 0.00
191 2.7517 4.1183 3.8812 0.00 0.00 0.00
192 2.3348 4.3682 3.8812 0.00 0.00 0.00
193 1.8954 4.5760 3.8812 0.00 0.00 0.00
194 1.4378 4.7397 3.8812 0.00 0.00 0.00
195 0.96628 4.8578 3.8812 0.00 0.00 0.00
196 0.48548 4.9291 3.8812 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
*****MAPDL VERIFICATION RUN ONLY*****
DO NOT USE RESULTS FOR PRODUCTION
NODE X Y Z THXY THYZ THZX
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()
***** MAPDL 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.
*****MAPDL 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.
D I S T R I B U T E D D O M A I N D E C O M P O S E R
...Number of elements: 64
...Number of nodes: 225
...Decompose to 0 CPU domains
...Element load balance ratio = 0.000
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.
DISTRIBUTED SPARSE MATRIX DIRECT SOLVER.
Number of equations = 1199, Maximum wavefront = 0
Memory available (MB) = 0.0 , Memory required (MB) = 0.0
Distributed sparse solver maximum pivot= 0 at node 0 .
Distributed sparse solver minimum pivot= 0 at node 0 .
Distributed 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
*** NODAL LOAD CALCULATION TIMES
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)
----------------------------------------------------------------------------
------------------------- 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 3.993 seconds)