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Magnetic: magnetic potentials, magnetic flux, magnetic current segments, source current density,
infinite surface.
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Electric: electric potentials (voltage), electric current, electric charges, charge densities, infinite
surface.
Fluid: velocities, pressures.
Solution:
What Is Solution?
In the solution phase of the analysis, the computer takes over and solves the simultaneous set of
equations that the finite element method generates. The results of the solution are:
Nodal degree-of-freedom values, which form the primary solution and Derived values, which form
the element solution.
An Overview of Post processing:
What Is Post processing?
After building the model and obtaining the solution, you will want answers to some critical
questions: Will the design really work when put to use? How high are the stresses in this region?
How does the temperature of this part vary with time? What is the heat loss across this face of my
model? How does the magnetic flux flow through this device? How does the placement of this
object affect fluid flow? The postprocessors in the ANSYS program can help you answer these
questions and others. Post processing means reviewing the results of an analysis. It is probably the
most important step in the analysis, because you are trying to understand how the applied loads
affect your design, how good your finite element mesh is, etc.
Two postprocessors are available to review your results: POST1, the general postprocessor, and
POST26, the time-history postprocessor. POST1 allows you to review the results over the entire
model at specific load steps and sub steps (or at specific time-points or frequencies). In a static
structural analysis, for example, you can display the stress distribution for load step 3. Or, in a
transient thermal analysis, you can display the temperature distribution at time = 100 seconds.
POST26 helps user to go over all the load steps at a time and observe the variation of quantities
with respect to time or frequency.
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ANSYS Menu Overview:
The above figure shows the typical ANSYS menu. ANSYS main is divided into preprocessor,
solution, post processor etc. Some of the frequently used options are available in ANSYS pull
down menu as well. Any action that is executed through these menus can also be performed by
typing an equivalent command in the command window. The Pan-Zoom-Rotate menu facilitates
easy visualization of the model in the graphics window.
Note: Save all your work until you get your final grade in your H: drive space. You may be asked
anytime to show your work before the final grading time.
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LAB # 8
Analysis of Truss - Tutorial
The goal of this tutorial is to guide you through the development of a finite element model for a
practical two-dimensional bridge truss structure. The geometry of the bridge is shown above. The
bridge is constructed from steel members with three unique cross sectional areas (denoted 1, 2, 3,
see Fig. 3). The areas are A1 = 13 cm2, A2 = 42 cm2, A3 = 20 cm2. The bridge is considered to be
loaded by a 3000 kg automobile as it traverses the span from one side to the other. The truss
members will be assumed to be weightless.
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Cross sectional area: 1 : 13 cm2
2 : 42 cm2
3 : 20 cm2
Boundary Conditions: Node N1 and N5 : Ux = Uy = 0.
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Problem statement:
Solve the above 2-dimensional truss problem using ANSYS to compute the following:
1. Displacements (Ux and Uy) at all joints (nodes) of the truss in the horizontal and vertical
directions.
2. Support reactions at the joints wherever the structure is supported.
3. Forces in each member (element).
4. Strain in each element.
5. Stress in each element.
6. Whether the structure is capable of withstanding the load?.
7. Where does the maximum displacement occur?.
8. Which element is stressed most?
Data:
1. Dimensions of the truss and cross sectional area are given above.
2. Boundary conditions are as shown in the Fig. 3.
3. Material properties:
Young’s modulus (E) = 211 GPa
Poisson’s ratio (υ) = 0.3
Yield strength = 390 MPa
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How to save image files for use in a lab report:
To save any picture which is visible at that instance on ANSYS graphics window follow these
guidelines:
In Ansys pull down menu click PlotCtrls. Then click on Hard Copy… It will open a little window
titled PS Hard Copy. Check following options:
Graphics window, Color, JPEG, Landscape and then in Save to option type the file name as
‘filename.JPG’. You can give any file name you want. This will save the picture currently being
displayed on graphics window in .jpg format in your current working directory.
How to save text files for use in a lab report:
To save any text file which is on current displays (text files show words and numbers). Click on
‘file’. Then click on ‘save as’. Then in file name type ‘filename.txt’. You can give any name
instead of filename to save the text file. Later you can even pull the file out on windows. To open
file on window open file with “ WordPad’ ( right click on file icon then ‘open with..’ and then
select word pad. That will show you formatted output).
General guidelines for solving the problem in ANSYS:
1. Open ANSYS window
2. Geometric Modeling
Create Key points
Create Lines
Create areas
Create volumes
3. Finite element modeling
Declare analysis type
Define element type
Define the key options (e.g., Plane stress, plane strain, axisymmetric)
Define element properties (real constants, e.g., thickness, area of cross section)
Define material properties (e.g., E, υ, ρ etc.)
Create nodes and elements (Meshing)
Merge items (if there is any overlapping among the entities)
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4. Solution
Specify analysis type
Apply boundary conditions (i.e., fixing the structure)
Apply loads
Specify the solution parameters
Solve the problem
5. Post processing
Get the displacements, reaction forces, strains and stresses.
Plot the output variables if needed.
Caution:
ANSYS does not make any distinction between units. It is the user’s responsibility to use correct
and consistent units while solving the problem. If inconsistent units are used, the solution will be
WRONG. For example, if the model is in meter, Young’s modulus must be in N/m2 and forces will
be in Newton, Pressure (if applied) will be in Pascal, mass density in kg/m3 etc. Similarly if model
is in inches, then E in psi, loads are in lb(f) etc.
Step by step procedure to solve the truss problem using ANSYS:
a) Open ANSYS window:
1. Log on to system, and open up Ansys.
2. Change the Simulation environment to Ansys.
3. Set the working directory as your username/fea/truss/tutorial.
4. Type “tutorial” in the menu Job Name as shown in Fig. 6.
5. Click on “run”.
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Figure 6
b) Geometric modeling:
Creating Key Points:
1. File – Change title
2. Type “ Two dimensional truss problem”
3. OK
4. Preprocessor
5. Modeling
6. Create
7. Keypoints
8. On working plane
9. Type the following numbers in ANSYS input window (Press enter key after typing each
coordinate. Note the values are in meter.)
0, 0
2.5, 0
5.0, 0
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7.5, 0.0
10.0, 0.0
1.25, 1.25
2.5, 1.25
5.0, 1.25
7.5, 1.25
8.75, 1.25
10. OK
11. File – Save as Jobname.db …
Creating Lines:
12. Modeling – Create – Lines – Lines
13. Straight Line
14. Go on clicking on start point and end point until you get the desired geometry. (You can
unselect any point by clicking right button of the mouse and reselect by clicking left
button.)
15. OK
c) Finite Element Modeling:
Declare analysis type:
1. Main menu
2. Preferences
3. Structural (as shown in Fig. 8)
4. OK
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Define element type:
5. Preprocessor
6. Element type
7. Add/Edit/Delete
8. Add
9. Link 3D finit stn 180 (as shown in Fig. 9).
10. OK
11. Close
Define Element properties (real constants for truss element):
12. Real constants
13. Add/Edit/Delete
14. Add
15. OK
16. Type 0.0013 in the Field AREA as shown in Fig. 10.
17. OK
18. Add
19. OK
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20. Type 0.0042
21. OK
22. Add
23. OK
24. Type 0.002
25. OK
26. Close
Figure 9
Figure 10
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Define Material properties:
27. Preprocessor
28. Material Props
29. Material Models
Structural
Linear
Elastic
Isotropic
EX 211e9 (this is Young’s modulus)
PRXY 0.3 (this is Poisson’s Ratio)
OK
Close the window
Create nodes and Elements (Meshing of Rod elements):
30. Preprocessor – Meshing – Mesh Tool
31. Size Controls: Lines - Set (See Fig. 11)
32. Pick all
33. Ndiv No of Element divisions (enter 1) (see Fig. 11)
34. OK
35. Mesh Attributes
36. Picked Lines
37. Pick all the lines with cross sectional area 13 cm2 (refer page 12).
38. OK
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Figure 11
39. Check the following attributes for the elements: (Fig. 12)
MAT, Material number =1,
REAL, Real constant set number = 1,
TYPE, Element type number = 1
40. OK
41. Mesh
42. Click on the lines with cross sectional area 13 cm2
43. OK
44. Plot
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45. Multi-Plots
46. PlotCtrls
47. Numbering
48. Check the Node numbers on (see Fig. 13)
49. Check the Element numbers on in Elements/Attrib numbering (see Fig. 13)
50. OK
51. Repeat the steps from 35 to 45.This time select the lines having cross sectional area of 42
cm2. Assign the REAL, Real constant set number = 2.
Figure 12
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Figure 13
52. Repeat steps from 35 to 45. This time select the lines having cross sectional area of 20 cm2.
Assign the REAL, Real constant set number = 3.
53. Type the command elist in the Command window and pay attention to Fig. 14 and note
that following are present in your model.
1 thru 17 3D truss elements (link elements)
All elements are of material type 1
Elements 1 thru 8 are having cross sectional area of 13 cm2
Elements 9 thru 14 are having cross sectional area of 42 cm2
Elements 15 thru 17 are having cross sectional area of 20 cm2
54. Type the commands rlist to verify the cross sectional areas you have specified are indeed
present.
55. Type the command mplist to verify the material properties you have specified are indeed
present.
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Figure 14
d) Solution:
Specify analysis type:
56. Solution
57. Analysis Type
58. New Analysis
59. Static
60. OK
Specify solution parameters:
61. Sol’n Controls
62. Check the following items in the Basic sub menu of solution controls dialog box as shown
in Fig.15.
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Analysis options - Small displacement static
Time at end of load step – 1
Write items to result file – All solution items
63. OK
Figure 15
Apply Boundary conditions:
64. Solution
65. Define Loads
66. Apply
67. Structural
68. Displacement
69. On Nodes
70. Click on node number 1 and 5 (Bottom left and bottom right nodes)
71. OK
72. Check on “All DOF” (As shown in Fig. 16).
73. OK (A horizontal and a vertical triangle appears indicating that the node is fixed both in x
and y directions.)
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Figure 16
Apply Loads:
74. Solution
75. Define Loads
76. Apply
77. Structural
78. Force/Moment
79. On Nodes
80. Click on Node no 2
81. OK
82. Check “FY” for Direction of Force/Moment and type a value of -30000 (as shown in Fig.
17 – This is the total weight of the vehicle W (N) = m (kg)*g (m/sec2) = 3000*10 = 30000
N, -ve sign indicates the load is acting downwards).
83. OK
84. Load Step Opts
85. Write LS File
86. Type the number 1 in the field LSNUM
87. OK
88. Define Loads
89. Delete
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90. Structural
91. Force/Moment
92. On Nodes
93. Click on Node Number 2 (Note: see node figure in problem statement and then click on
your model on that corresponding node , in your model the number might be different)
94. OK
95. Check “ALL” in the Lab field
96. OK
97. Repeat the steps 75 to 87 with the following changes:
Vertical load of -30000 N to be applied on Node no 3
Type the number 2 instead of 1 in step 86.
98. Now delete all the previous loads and ( follow steps 88-96)
99. Repeat the steps 75 to 87 with the following changes:
Vertical load of -30000 N to be applied on Node no 4
Type the number 3 instead of 1 in step 86.
100. File – Save as Jobname.db
Note: Here you have created 3 load steps for 3 different positions of car on the bridge,
i.e. on left side of bridge, in the middle and on right side of bridge and then you’ll solve
for all 3 positions one by one.
Figure 17
Solving the problem:
101. Solution
102. Solve
103. From LS Files ( Note:LS stands for Load Step )
104. Type 1, 3 and 1 for LSMIN, LSMAX and LSINC respectively as shown in Fig. 18.
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105. OK
106. You are OK if you get a dialog box “Solution is Done”. Otherwise contact instructor.
Figure 18
e) Post Processing the Results:
Read the result file and plot the deformed shape:
107. General Postproc
108. Data & File Opts
109. Check on “All items”, Click on “…” and select the file, “tutorial.rst” as shown in Fig.
19.
110. OK
111. Read Results
112. First Set
113. Plot Results
114. Deformed Shape
115. Check on “Def + undeformed”
116. OK
117. This gives the deformed shape overlapped on undeformed shape for load case 1 (Save it
as a picture: Plotctrls - Hard Copy - To File – Save to - <file.bmp> )
118. Read Results - Next Set and repeat steps 113-115.
119. Read Results - Last set and repeat steps 113-115.
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Figure 19
Check the reactions:
120. List Results
121. Reaction Solu
122. Check on All items
123. OK
124. Verify whether the reactions are summing up to give the applied load in vertical direction
and zero in horizontal direction (This is an important check).
Plot displacements:
125. Read Results – First Set
126. Plot Results – Contour Plot
127. Nodal Solu
128. Check on “DOF Solution” and “y – component of displacement”
129. OK (Compare your plot Fig. 21)
130. Save this picture.
131. Plotctrls - hard copy - to file – select the format you wish - save to - <file.bmp>
132. OK (The pictures will be stored in the current working directory).
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Figure 20: Deformed Vs Undeformed plot
Figure 21: Vertical displacement (Uy) of the Truss
List Nodal displacements, Element forces, stresses and strains:
133. List Results
134. Nodal Solution
135. Check on “DOF Solution” and and “Displacement vector sum”
136. OK (Compare your results with those in Fig. 22)
137. Save this file for future reference (File – Save as – <filename.txt>).
138. List Results
139. Nodal Loads
140. Check on “All struc forc F”
141. OK (Compare your results with those in Table 1).
142. List Results
143. Element Solution
144. Check on “Line Elem Results” and “Element Results”
145. OK. Stresses and Strains in Element coordinate system will be listed in this file (FORCE:
axial force in each truss; STRESS: axial stress in each truss. Positive sign of STRESS
means tension and negative compression). See Fig. 23 (Save this file for future reference:
File – Save as - <filename.txt>)
Animation:
146. PlotCtrls
147. Animate
148. Deformed Results
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149. Check on “DOF” Solution and “UY”
150. OK
Exit:
151. SAVE_DB
152. File – Exit (Quit No Save! OK)
Figure 22: Nodal displacements.
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PRINT F REACTION SOLUTIONS PER NODE ***** POST1 TOTAL REACTION SOLUTION LISTING ***** LOAD STEP= 0 SUBSTEP= 1 TIME= 1.0000 LOAD CASE= 0 THE FOLLOWING X,Y,Z SOLUTIONS ARE IN THE GLOBAL COORDINATE SYSTEM NODE FX FY FZ 1 22500. 22500. 0.0000 5 -22500. 7500.0 0.0000 TOTAL VALUES VALUE -0.72760E-11 30000. 0.0000
Understanding the line element results: EL= 1 element number is 1 NODES= 1 2 nodes 1 and 2 make up element 1 STRESS = 0.18301E-07 axial stress in element 1 made of nodes 1 and 2
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LAB # 9
ANALYSIS OF TRUSSES - Exercises 1.
The truss, shown in Fig. 1, is made of AL6061-T6. Use E=10e6 psi and Poisson’s ratio =
0.35. Assume a cross-sectional area of 1” for the outer elements (shown by thicker lines)
and ½” for the diagonal elements. (All dimensions in Fig. 1 are in inches). Find the values
of axial stresses in each member of the truss using ANSYS package. Repeat your stress
calculations for the truss by hand and provide an element-by element comparison with Part-
(a).
a) Show a picture showing the loads and boundary conditions on which the element numbers
are shown.
b) Show a picture showing the deformed and undeformed shapes
c) Show a picture of the undeformed shape on which the corresponding stress values of each
link are hand written beside the links.
d) Present the complete hand calculation that you did to find the stress values.
e) Present a table comparing the Ansys and hand calculated results. Use the same element
numbers in the first picture as reference.
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2. Find the values of axial stresses in each member of the truss shown in Figure 2. Also find
displacements at each node. List the values of the maximum displacement and axial stress in
the truss. Consider the following material and sectional properties to analyze the truss: Young’s
modulus of all elements: 13.6e6 psi. Poisson’s ratio is 0.35. Each member along
AB,CB,AC,BE,BF ,FE,HL( Shown by thick line) has hollow circular cross section With 4.5
inch outer diameter and 2.4 inch inner diameter. Each linking element (shown by thin lines)
has solid circular cross-section with diameter 2 inch.
Note: Use same type of element as tutorial problem for both these exercise problems
a) Show a picture showing the loads and boundary conditions on which the element numbers
are also shown.
b) Show a picture showing the deformed and undeformed shapes
c) Show a picture of the undeformed shape on which the maximum axial stress value and the
maximum y – displacement value are hand written beside the respective link and node.
Note: Do not submit any numerical printed results that are directly output from Ansys.
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LAB # 10 Analysis of Beam - Tutorial
Analysis of a Bicycle Handlebar
Analyze the bicycle handle bar shown in the Figure 1 (i) without and (ii) with the reinforcement
bar. For both cases find maximum stresses in each of the members and deflections at the end of
the handle. Find the value of maximum stress and its location. Consider the followings while
analyzing the model:
a) Each member of the handle has hollow circular section with 3/4” outer diameter and thickness
1/8”.
b) The reinforcing bar has a hollow circular cross section with outer diameter ½” and thickness
1/8”.
c) Consider the material as steel with Young’s modulus 30E6 psi and Poisson’s ratio 0.3.
d) Assume a distributed load of 100 lb(f) over the shaded regions of the handle.
Note: In this tutorial, the problem is solved with the reinforcement bar. You need to solve without
the reinforcement bar and compare the results in the lab.
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Step by step procedure to solve the beam problem using ANSYS:
1. Open Ansys in the working directory named “Tutorial” under “Beam”.
a) Geometric modeling:
Creating key points:
2. File – Change title
3. Type “Analysis of Bicycle handlebar using 2D beam element”
4. OK
5. Preprocessor
6. Modeling
7. Create
8. Key points
9. On Working Plane
10. Type the following numbers in ANSYS input window(Press enter key after typing each
number)
0,0
4,0
6,0
9,-5.196
12,-5.196
15,-5.196
18,0
20,0
24,0
12,-6.196
7.039,-1.8
16.961,-1.8
11. OK
12. Save the file
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Creating Lines:
13. Lines – Lines
14. Straight line
15. Go on clicking on start point and end point until you get the desired geometry (You can
unselect any point by clicking right button of the mouse)
16. OK (Make sure that you got the geometry shown in Fig. 2.
17. File – Save as Jobname.db
b) Finite element modeling:
Declare analysis type:
18. Main Menu
19. Preferences
20. Structural
21. OK
Define element type :
22. Preprocessor
23. Element Type
24. Add/Edit/Delete
25. Add
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26. Beam 2 node 188 (as Shown in Fig. 3.) (OR type command: et, 1, BEAM188 in –
command window) The selection must be displayed in selection display bar.
27. OK
28. Close
Define Element properties (real constants for beam element):
29. Preprocessor
30. Sections
31. Beam
32. Common Sections (a beam tool appears as shown in Fig. 4).
33. Type “Handle” in the Name section, Chose Hollow Circular cross sections
and type 0.25 in for inner radius and 0.375 in for outer radius. Leave ‘N’ blank.
34. Preview (Beam cross sectional properties appear as shown in Fig. 5).
35. OK
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36. Sections – Beam – Common Sections
37. Type ID = 2, Name = Reinforcing Bar
38. Choose Hollow Circular cross sections and type Ri=0.125 in, Ro = 0.25 in.
39. Preview
40. OK
41. Save the file
Define Material properties:
42. Material Props
43. Material Models
44. Structural (DOUBLE CLICK)
Linear
Elastic
Isotropic
Ex=30e6
Prxy = 0.3
45. OK
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46. Material – Exit
47. Save the file
48. Plot – Multi-Plot
Create nodes and Elements (Meshing):
49. Select
50. Entities
51. Check the following items
Lines
By Num/Pick
From Full
OK (Expand window if you don’t see OK button).
52. Mouse pick all the lines except reinforcement bar (long one)