laboratory manual
DESCRIPTION
Ansys Lab Manual for M.E.(Engineering Design)TRANSCRIPT
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LABORATORY RECORD
ED 7211
ANALYSIS AND SIMULATION LAB
M.E. ENGINEERING DESIGN
DEPARTMENT OF MECHANICAL ENGINEERING
RAJALAKSHMI ENGINEERING COLLEGE
THANDALAM-602105.
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BONAFIDE CERTIFICATE
Name :
Class :
Roll No :
REGISTER NO.
Certified that this is the bonafide record of work done by
the above student in the
Laboratory during the year 20 - 20
Signature of Lab-in-charge Signature of Head of the
Department
Submitted for the Practical Examination held on:
Examiner
ED 7211
RAJALAKSHMI ENGINEERING COLLEGE
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ANALYSIS AND SIMULATION LAB
List of Experiments
S.No. Date Name of the ExperimentPage No.
Signature
1.Stress analysis of beams(Candilever,Simply supported& fixed end)
2. Stress Analysis of a plate with circular hole
3. Stress Analysis of Rectangular L Bracket
4.Stress Analysis of an Axis- symmetric component
5.Mode frequency analysis of beams(Candilever,Simply supported,Fixed beam)
6. Mode frequency analysis of 2 βD element
7.Convective heart transfer analysis of a 2D component
8.Conductive heart transfer analysis of a 2D component
9. Thermal analysis of a 2D component
10. Harmonic analysis of a 2D component
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INTRODUCTION
Finite element analysis is the core of computer aided engineering dictates the
modern mechanical industry.
Finite element analysis is a technique to simulate material properties, loading
conditions and environment of any system and to approximately determine response of the
system to those conditions.
NEED FOR FEA:
1. To reduce the amount of prototype testing
2. To simulate design that is not suitable for prototype testing
3. Cost Saving and time saving
4. Create a more reliable, better quality and competitive designs
ABOUT ANSYS:
ANSYS is a complete FEA simulation software package developed by ANSYS Inc.
a corporate of USA.
It is used by engineers worldwide in virtually all fields of engineering:-
Structural
Thermal
Fluid (CFD, Acoustics)
Low & High Frequency Electromagnetic
APPLICATIONS OF ANSYS:
ANSYS software can be applied in
Engineering structures
Automobiles
Aerospace
Biomedical
Buildings and other civil structures
Electronics
Heavy equipments & machinery
OTHER PRODUCTS:
ANSYS LS DYNA - Non Linear structural problems
ANSYS Professional - Linear Structural Thermal Analysis
ANSYS Design Space Analysis - Linear structural & steady state thermal analysis
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ANSYS CFX - Fluid flow problems
CAPABILITIES OF ANALYSIS:
1. Structural Analysis: It is used to calculate the deformation, strain, stress and
reaction. The Eigen value problems where we find natural frequency of systems
also come under this category.
2. Thermal Analysis: It is used to determine the temperature distribution, amount of
heat lost or gained, thermal gradient and thermal flow.
3. Electromagnetic Analysis: It is used to calculate magnetic field effects in a
system. Often used with contact analysis.
4. Computational Field Analysis: It is used to determine the fluid flow
characteristics in a system like flow velocity, pressure, head loss, and even
temperature distribution.
5. Coupled Field Analysis: It is used to calculate the mutual interaction of two or
more of the above said disciplines. This is done by either sequential method or
simultaneous method.
STATIC STRESS ANALYSIS OF BEAMS (CANTILEVER, SIMPLY SUPPORTED, FIXED BEAM)
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STATIC STRESS ANALYSIS OF CANTILEVER BEAM
Ex No:
Date:
Aim:
To perform static stress analysis for the given beams (Cantilever beam) using ansys.
SOFTWARE USED:
ANSYS 13.0
PROCEDURE:
1. PREFERENCE:
Preference β structural β ok
2. PREPROCESSOR
Element type
Preprocessor β element type βadd β beam β 2node188βok
Material property
Preprocessor β material property β material model β structural β linear β elastic β isotropicβ Ex (2e3) βPRxy (0.3)β ok β close
Modeling
Preprocessor β section β beam β common section β section ID-1 β select sub type β rectangle β enter L*B (150* 300) β ok
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Preprocessorβ modeling β create β keypointsβ in active CS
Preprocessor β modeling β create β line β straight line β draw the lines b/w the keypoints
Meshing
Preprocessorβ meshing β mesh tool β set line option β pick line 1β apply β ok
Select mesh β pick all βok
3. SOLUTION:
Solution β define loads β apply βstructural β displacement β on keypoints β select first keypoint β ok β select all DOF β ok
Solution β define loads β apply β structural β force / moment β select third keypoint 3 β select Fy (30e3) β ok
Solution β define loads β apply β structural β pressure β select element1 β enter value 40
Solution β solve β current LS β ok
4. GENERAL POSTPROCESSOR:
General postproc β plot result β deformed shape &undeformed shape
KEYPOINTS X Y Z1 0 0 02 2000 0 03 1000 0 0
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General postprocessor β list result β nodal solution
Utility menu β plot ctrl β animation deformed shape
RESULT:
Thus the stress analysis of cantilever beam is performed using ANSYS and results are plotted.
Calculation:
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To find deflection,
Apply Maculayβs equation:
M x=β30 xβ20
2ΒΏ
EId2 yd x2 =β30 x
β202
ΒΏ
EIdydx
=β30x2
2+c1β
103
ΒΏ
EIy=β30x3
6+c1 x+c2β
1012
ΒΏ
At x=3 , y=0
EI (0 )=β3033
6+c1(3)+c2β
2024
ΒΏ
At x=3 ,dydx
=0
EI (0 )=β3033
2+c1β
206
ΒΏ
c1=161.66
ΒΏc1β(1 )ββββ c2=β336.4
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EIy=β30x3
6+161.66 xβ336.64β20
4ΒΏ
At x=1 , y= yb
EI yb=β3013
6+161.66(1)β336.64
yb=β2.53 mm
At x=0 , y= yc
EI yc=β3003
6+161.66(0)β336.64
yc=β4.74 mm
M c=30β1=30 kNm
M A=30β1+20β2β1=130 kNm
Ο c=30β106β300β12
150β2β30 03 =13.33N
mm2
Ο a=130β1 06β300β12
150β2β30 03 =57.77N
mm2
RA=(20β2 )+30=70 KN
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STATIC STRESS ANALYSIS OF SIMPLY SUPPORTED BEAM
Aim:
To perform static stress analysis for the given beams (Simply supported) using ansys.
SOFTWARE USED:
ANSYS 13.0
PROCEDURE:
PREFERENCE:
Preference β structural β ok
PREPROCESSOR
Element type
Preprocessor β element type βadd β beam β 2node188βok
Material property
Preprocessor β material property β material model β structural β linear β elastic β isotropicβ Ex (2e3) βPRxy (0.3)β ok β close
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Modeling
Preprocessor β section β beam β common section β section ID-1 β select sub type β rectangle β enter L*B (132* 264) β ok
Preprocessorβ modeling β create β keypointsβ in active CS
Key points X Y1. 0 02. 3000 03. 4000 04. 6000 0
Preprocessor β modeling β create β line β straight line β draw the lines b/w the keypoints
Meshing
Preprocessorβ meshing β mesh tool β set line option β pick line 1β apply β ok
Select mesh β pick all βok
5. SOLUTION:
Solution β define loads β apply βstructural β displacement β on keypoints β select first keypoint β ok β select all DOF β ok
Solution β define loads β apply β structural β force / moment β select third keypoint 3 β select Fy (20e3) β ok
Solution β define loads β apply β structural β pressure β select element1 β enter value 40
Solution β solve β current LS β ok
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6. GENERAL POSTPROCESSOR:
General postproc β plot result β deformed shape &undeformed shape
General postprocessor β list result β nodal solution
Utility menu β plot ctrl β animation deformed shape
RESULT:
Thus the stress analysis of simply supported beam is performed using ANSYS and results are plotted.
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Calculation:
1) Simply supported Beam
To find reaction
RA - Reaction at ARB - Reaction at B
Taking moment about A,
Rb x6=20 x3 x32+(20 x 4 )
Rb=28.33 kN
Ra+Rb=(20β3 )+20
ΒΏ51.67 KN
To find deflection:
Apply Maculeyβs method,
Bending moment at section βxβ from end B at distance βxβ
Mx = RB x -20(x-2)-20/2 (x-3)2
Mx =EI d2y/dy2
EId2y/dy2 = RB x -20(x-2)-20/2 (x-3)2
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EI dy/dx = RB x2/2 +C1-20/2(x-2)2-(10/3)(x-3)4
EI y = (RBx3)/6+C1x+C2(-20/6)(x-2)3(-10/2)(x-3)4
At x=0 , y=0
EI(0)=C2 --- C2=0
At x=6,y=0
EI(0) = RB/6(6)3 -20(4)3 +C1(6)-(10/12)3
C1=-143.73
EI(y)=(RBx3)/6-20/6(x-2)3-143.73x-(10/12)(x-3)4
At x=2,y=yo
EIyD = 28.33/6 * 23-143.73(2)
YD = -5.96mm
At x=3,y=yc
Yc=-5.11mm
Mc=28.11*3-20*1=65kNm
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Md=RB*2=56.66kNm
Ο D=M Dβ y
I=
56.6β106β(264 /2)132β2643
12
Ο D=36.95 N /mm2
Ο C=M Dβy
I=
65β106β(264 /2)132β2643
12
Ο C=42.38 N /mm2
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STATIC STRESS ANALYSIS OF FIXED BEAM
Aim:
To perform static stress analysis for the given beams (Fixed supported) using ansys.
SOFTWARE USED:
ANSYS 13.0
PROCEDURE:
PREFERENCE:
Preference β structural β ok
PREPROCESSOR
Element type
Preprocessor β element type βadd β beam β 2node188βok
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Material property
Preprocessor β material property β material model β structural β linear β elastic β isotropicβ Ex (2e3) βPRxy (0.3)β ok β close
Modeling
Preprocessor β section β beam β common section β section ID-1 β select sub type β rectangle β enter L*B (572* 1144) β ok
Preprocessorβ modeling β create β keypointsβ in active CS
Key points X Y1. 0 02. 4000 03. 6000 04. 8000 0
Preprocessor β modeling β create β line β straight line β draw the lines b/w the keypoints
Meshing
Preprocessorβ meshing β mesh tool β set line option β pick line 1β apply β ok
Select mesh β pick all βok
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7. SOLUTION:
Solution β define loads β apply βstructural β displacement β on keypoints β select first keypoint β ok β select all DOF β ok
Solution β define loads β apply β structural β force / moment β select third keypoint 3 β select Fy (80e3) β ok
Solution β define loads β apply β structural β pressure β select element1 β enter value 160
Solution β solve β current LS β ok
8. GENERAL POSTPROCESSOR:
General postproc β plot result β deformed shape &undeformed shape
General postprocessor β list result β nodal solution
Utility menu β plot ctrl β animation deformed shape
RESULT:
Thus the stress analysis of Fixed supported beam is performed using ANSYS and results are plotted.
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Calculation:
To find deflection,
M x=RB xβM Bβ80 ( xβ2 )β402
ΒΏ
EIdydx
=RB x2
2βM B x+c1β
802
ΒΏ
EIy=RB x3
6β
M B x2
2+c1 x+c2β
806
ΒΏ
At x=0 , y=0
EI (0 )=RB (0 )βM B (0 )+C1 (0 )+C2
At x=0 ,dydx
=0ββββ C2=0
EI (0 )=RB
2(0 )βM B (0 )+C1 (0 )=ΒΏ=ΒΏC1=0
EIy=RB x3
6β
M B x2
2β80
6ΒΏ
At x=8 , y=0
EI (0)=RB(8)3
6β
M B(8)2
2β80
6ΒΏ
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EI (0 )=85.33 RBβ32 M Bβ2880β426.65
At x=8 ,dydx
=0
EI (0 )=RB 82
2βM B(8)β80
2(8β2)β40
2ΒΏΒΏ
32 M Bβ8M B=1866.66
Solving the above eq:
RB=97.49 kN ; M B=156.63 kNm
RA +RB=80+40β4=ΒΏ=ΒΏ=ΒΏ RA=142.51kN
M A=80β6+40β4β2+156.63β97.49β8βββββ M A=176.71 kNm
At x=2 , y= yd
EI yd=97.49β23
6β156.63β23
2ββββ yd=1.22β1 0β2 mm
At x=4 , y= yc
EI yc=97.49β43
6β156.63β43
2β80ΒΏΒΏ
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Ο d=M d y
I=38.35β106ΒΏΒΏ
y=d2
, I=bd3
12
Ο c=M c y
I=73.33β1 06 ΒΏΒΏ
M d=β156.63+97.49β2βββ M d=38.35 kNm
M c=β80β2β156.63+97.49β4βββ M c=73.33 kNm
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STRESS ANALYSIS OF A RECTANGULAR PLATE WITH CILRCULAR HOLE
Ex No:
Date:
Aim:
To perform static stress analysis for the given rectangular plate with circular hole using ANSYS
Description:
A steel plate of dimension ( 100 Γ 15 Γ 25mm ) having 3 holes of diameter 3mm, 5mm & 10mm. It is fixed at one end and force of 20 KN acts on the other end of the plate. The stress induced at the holes due to the force is to be determined.
DIAGRAM:
Φ3mmΦ5mm Φ10mm
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Formula used:
1. Normal stress ΒΏP
(wβd ) t
P β Load (N).
w β Width of the plate (mm).
d β Diameter of hole (mm).
t β Thickness of the plate (mm).
2. Maximum stress ΒΏΟ N Γ k f
Kf β Stress concentration factor.
PROCEDURE:
Pre-processing: Defining the Problem
1. Open ANSYS APDL from start menu.
2. Define the type of problem,
Pre-processor β preference β structural β ok
3. Define the Type of Element
Pre-processor β Element Type β Add/Edit/Delete [Add the element: Solid - PLANE82]
4. Define Geometric Properties
Pre-processor β Real Constants β Add/Edit/Delete [Enter a thickness as 15mm]
5. Element Material Properties
Pre-processor β Material Properties β Material models β Structural β linear β Elastic β Isotropic [We are going to give the properties of Steel. Enter the following when prompted: EX β 2.1E5, PRXY β 0.3]
6. Create the main rectangular shape
Pre-processor β Modelling β Create β Areas β Rectangle β By 2 Corners [Enter the following values: WPX β 0, WPY β 0, Width β 100, Height β 25]
7. Create the circle
Pre-processor β Modelling β Create β Areas β Circle β Solid Circle [Enter the following values: Circle 1: WPX β 25, WPY β 12.5, Radius β 1.5; Circle 2: WPX β 50, WPY β 12.5, Radius β 2.5; Circle 3: WPX β 75, WPY β 12.5, Radius β 5]
20KN25mm
25mm 25mm 25mm 25mm
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8. Subtraction of circles
Pre-processor β Modelling β Operate β Booleans β Subtract β Areas [First select the base area from which the area has to be deleted (rectangle) and then select the area that has to be deleted (circle).
9. Meshing
Pre-processor β mesh β mesh tool β Areas [set] β select the area β apply β enter element size as 10 β ok
Click mesh β select the area β ok
Solution Phase: Assigning Loads and Solving
10. Define constraints
Solution β define load β apply β structural β displacement β on lines [Select the line, select all DOF & click ok]
11. Define load
Solution β define load β apply β structural β pressure β on line [Select the line, enter the pressure value as 53.33 N/mm2]
12. Solving the System
Solution β Solve β Current LS
Post processing: Viewing the Results
13. Deflection
General Postproc β Plot Results β Nodal Solution β DOF solution β X-component
14. Stress
General Postproc β Plot Results β Nodal Solution β von mises stress
15. Stress values
General postproc β list result β nodal solution β von mises stress [Note down the stress values on respective nodes.
Result:
Thus static stress analysis for the given rectangular plate with circular hole has been successfully done using ANSYS.
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Calculation:
1. For 3mm hole
Ο N= P(wβd )t
P = 20KN ; d = 3mm
w = 25mm ; t = 15mm
Ο N= 20 Γ103
(25β3 ) Γ15
= 60.61 N/mm2
From PSG Data book page 7.10, kf = 2.65 (d/w = 0.12)
Ο max=ΟN Γ k f = 60.61 x 2.65
Ο max=ΒΏ161.62 N/mm2
2. For 5mm hole
Ο N= P(wβd )t
P = 20KN ; d = 5mm
w = 25mm ; t = 15mm
Ο N= 20 Γ103
(25β5 ) Γ15
= 66.67 N/mm2
From PSG Data book, kf = 2.5 (d/w = 0.2)
Ο max=ΟN Γ k f = 66.67 x 2.5
Ο max=ΒΏ166.68 N/mm2
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3) For 10mm hole
Ο N= P(wβd )t
P = 20KN ; d = 10mm
w = 25mm ; t = 15mm
Ο N= 20 Γ103
(25β10 ) Γ15
= 88.89 N/mm2
From PSG Data book, kf = 2.25 (d/w = 0.4)
Ο max=ΟN Γ k f = 88.89 x 2.25
Ο max=ΒΏ200 N/mm2
Observation:
SL.No Hole size Analytical Simulation
1 3 161.62 136.87
2 5 166.68 144.60
3 10 200 191.48
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STRESS ANALYSIS OF A RECTANGULAR L-BRACKET
Ex No:
Date:
AIM:
To determine a deform shape and stress analysis for a given L- bracket using ANSYS software.
FORMULA USED:
M / I = Ο b / Y
Where,
M - Bending moment
I - Moment of inertia of cross sectional area
Ο b - Bending stress
Y - Distance from neutral axis to the outer most fiber
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PROCEDURE:
The modules available in ANSYS are ,
i. Preferences ii. Pre- Processor iii. Solution iv. General Post Processor module
1. Preferences > Structural > OK
2. In Pre Processor module, element type for analysis in chosen by Pre- Processor > Element type > Add > Solid >Quad 4 node 182
2. The Material properties are given by Pre β Processor > Material modal > Linear > Elastic > Isotropic >Define youngβs modulus and Poisson ratio
3. Modeling of the L section
Modeling > Create >Area > Rectangle > By 2 Corners > X=0,Y=0,Width= 335,Height= 70
Modeling > Create >Area > Rectangle > By 2 Corners > X=165,Y=70,Width= 70, Height = 150
Modeling > Create >Area > Circle > Solid circle > X=300, Y=220,Radius=45
Modeling >Operate > Boolean > Add > Areas> Pick all > OK
Modeling > Create >Area > Circle > Solid circle > X=300, Y=220,Radius=35
Modeling >Delete > Areas Only > Pick the areas to be deleted > OK
4. The area is divided into finite no. of elements by Meshing > mesh tool > Area >Pick all>Edge Length = 20 >mesh tool > mesh.
5. The boundary condition is defined at the both end after beam by arresting displacements in Y- direction by Solution > loads > structural > displacement > on areas >arrest All DOF.
6. Load is applied on the nodes at the top edge by solution> loads >Structural > Force > on nodes
7. Now the system is ready to solve and is done by solution > solve > current L.S.
8. By general post processor > Plot result > counter plot > nodal solution.> DOF solution > displacement
9. The stress is also obtained by General post processor > plot result > counter plot > Nodal solution> Von-Mises Stress
RESULT:
Thus the deformed shape and stress analysis for the L bracket is done
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CALCULATION:
Resolving the forces 5KN
Horizontal component P H = P Sin 60Β°= 4.33 KN
Vertical component PV = P Cos 60Β° = 5 cos 60 Β° = 2.5 KN
Bending moment due to PH :
MH = 4.33x150x100
MH = 649.5x103 N mm
Bending stress Ο bh = My /Z
649.5x103x6/3.5x102 = 22.72 N/mm2
Bending moment due to Pv :
MV = 2.5x106x300 = 750 x 103 N mm
Bending moment due to Pv :
Ο bv = MY /Z
Ο bv = 750x103x6/35x102
= 26.33 N\ mm2
Direct stress due to Vertical force PV
Ο dv = PV / A = 2.5x 103/ 70x35 = 1.02 N\ mm2
Total Stress = Ο bh+Οbv +Οdv
= 50.16 N\ mm
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STRESS ANALYSIS OF AN AXIS -SYMMETRIC COMPONENT
Ex No:
Date :
AIM:
To analyze a cylindrical pressure vessel (axis symmetric) for hoop stress and longitudinal stress
DIAGRAM:
PROCEDURE:
Preprocessing: Defining the Problem:
1. Give example a Title Utility Menu > File > Change Title...2. Open preprocessor menu ANSYS Main Menu > Preprocessor 3. Create Areas Preprocessor > Modeling > Create > Areas > Rectangle > By Dimensions4. Add Areas Together Preprocessor > Modeling > Operate > Booleans > Add > Areas 5. Define the Type of Element Preprocessor > Element Type > Add/Edit/Delete... For this problem we will use the PLANE2 [Axisymmetric]
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6. Define Element Material Properties Preprocessor > Material Props > Material Models > Structural > Linear > Elastic > Isotropic
7. Define Mesh Size Preprocessor > Meshing > Size Cntrls>ManualSize> Areas > All Areas [An element edge length of 2mm]8. Mesh the frame Preprocessor > Meshing > Mesh > Areas > Free > click 'Pick All'
Solution Phase: Assigning Loads and Solving:
1. Define Analysis Type Solution > Analysis Type > New Analysis > Static2. Apply Constraints Solution > Define Loads > Apply > Structural > Displacement > Symmetry B.C. > On Lines Pick the two edges on the left, at x=0. Utility Menu > Select > Entities [Select Nodes and By Location from the scroll down menus. Click Y coordinates and type in 50] Solution > Define Loads > Apply > Structural > Displacement > On Nodes > Pick All Constrain the nodes in the y-direction (UY).3. Utility Menu > Select > Entities
[In the select entities window, click Select All to reselect all nodes.]4. Apply Loads
Solution > Define Loads > Apply > Structural > Force/Moment > On Key points [Pick the top left corner of the area and click OK. Apply a load of 100 in the FY direction. Pick the bottom left corner of the area and click OK. Apply a load of -100 in the FY direction. ]5. Solve the System
Solution > Solve > Current LS
Post processing: Viewing the Results
1. Determine the Stress Through the Thickness of the Tube
Utility Menu > Select > Entities... Select Nodes > By Location > Y coordinates and type 45, 55 in the Min, Max box.
General Postproc> List Results > Nodal Solution > Stress > Components SCOMP 2. Plotting the Elements as Axisymmetric
Utility Menu >PlotCtrls> Style > Symmetry Expansion > 2-D Axi-symmetric...
RESULT:
Thus the analyze a cylindrical pressure vessel (axis symmetric) for hoop stress and longitudinal stress
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CALCULATION:
P=1.5MN/m2
P=1.5 N/mm2
d =1000 mm t=15 mm
Ο c= pd2 t
Ο C= 1.5β1000
2β15
Ο C = 50 N/mm2
![Page 34: Laboratory Manual](https://reader035.vdocuments.net/reader035/viewer/2022062303/55725c1d497959da6be88ee7/html5/thumbnails/34.jpg)
MODAL ANALYSIS OF BEAMS (CANTILEVER, FIXED, SIMPLY SUPPORTED)
MODAL ANALYSIS OF BEAMS CANTILEVER BEAM
Ex. No.
Date:
AIM
To perform modal analysis of a (cantilever beam) using ANSYS
PROCEDURE :
1. The modules available in ANSYS are
i. Preferences
ii. Pre-Processor
iii. Solution
iv. General post processor module
2. In the pre-processor module the element type for the analysis of the cantilever beam is
Chosen
Pre-processor > element type > add > beam3 > 2D ELASTIC 3
3. The Density & Young Modulus are given.
Main menu > Pre-processor > Material properties > Enter the Density & Young Modulus
4. Create two key points and a line to connect the points.
Modeling > create > key points > inactive c.s
Modeling > create > lines > between key points.
5. Mesh the line using mesh tool.
Main menu > Pre-processor > Meshing > mesh tool > line > mesh.
6. The boundary condition is defined for the beam.
Solutions > load > structural > displacement > On Left Key point > all DOF.
7. Solution: Assigning loads and solving, Define analysis type
Solution > analysis type > new analysis > modal
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8. Set options for analysis type:
Solution > Analysis type > Analysis optionsβ¦.
Enter 10 for no. of modes to extract and no. of modes to expand in subspace and
Expand mode shapes.
9. Reduced method is chosen.
10. Apply constrains
Solution > Define loads > Apply > Structural > Displacement < On
Key points.
11. Solve the system
Solution > Solve > Current LS
12. Post processing: Viewing the results
General Postproc > Result Summary.
13. To view mode shapes
General Postproc > Read results > First set
General Postproc > Plot results > Deformed shape
Repeat the process for the next set to view the next mode shapes.
14. To Animate mode shapes
Utility menu > Plot ctrls > Animate > Mode shapes
RESULT :
Thus the cantilever beam is modeled and analyzed in ANSYS for Modal
Analysis. Various mode shapes and respective frequencies are obtained.
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MODAL ANALYSIS OF BEAMS SIMPLY SUPPORTED BEAM
Ex. No.
Date:
AIM :
To perform modal analysis of a (simply supported) beam using ANSYS
PROCEDURE:
1. The modules available in ANSYS are
i. Preferences
ii. Pre-Processor
iii. Solution
iv. General post processor module
2. In the pre-processor module the element type for the analysis of the Simply Supported beam is
chosen
Pre-processor > element type > add > beam3 > 2DELASTIC 3
3. The Young Modulus and Material Density are given.
Main menu > Pre-processor > Material Properties > Enter the Young Modulus & Density
4. Create two key points and a line to connect the points.
Modeling > create > key points > inactive c.s
Modeling > create > lines > between key points.
5. Mesh the line using mesh tool.
Main menu > Pre-processor > Meshing > mesh tool > line > mesh.
6. The boundary condition is defined for the beam.
Solutions > load > structural > displacement > on key points > UY
7. Solution: Assigning loads and solving
Define analysis type
Solution > analysis type > new analysis > modal
8. Set options for analysis type:
Solution > Analysis type > Analysis options
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Enter 10 for no. of modes to extract and no. of modes to expand in subspace and
Expand mode shapes.
9. Reduced method is chosen.
10. Apply constrains
Solution > Define loads > Apply > Structural > Displacement > on key points.
11. Solve the system
Solution > Solve > Current LS
12. Post processing: Viewing the results
General post processing > Result Summary.
13. To view mode shapes
General post processing > Read results > First set
General post processing > Plot results > Deformed shape
Repeat the process for the next set to view the next mode shapes.
14. To Animate mode shapes
Utility menu > Plot ctrls > Animate > Mode shapes
RESULT :
Thus the simple supported beam is modeled and analyzed in ANSYS for
Modal analysis. Various mode shapes and respective frequencies are obtained.
![Page 38: Laboratory Manual](https://reader035.vdocuments.net/reader035/viewer/2022062303/55725c1d497959da6be88ee7/html5/thumbnails/38.jpg)
MODAL ANALYSIS OF BEAMS FIXED BEAM
Ex. No.
Date:
AIM
To perform modal analysis of a (Fixed beam) using ANSYS
PROCEDURE
1. The modules available in ANSYS are
i. Preferences
ii. Pre-Processor
iii. Solution
iv. General post processor module
2. In the pre-processor module the element type for the analysis of the Fixed beam is
Chosen
Pre-processor > element type > add > beam3 > 2D ELASTIC 3
3. The Young Modulus and Material Density are given.
Main menu > Pre-processor > Material Properties > Enter the Young Modulus & Density
4. Create two key points and a line to connect the points.
Modeling > create > key points > inactive c.s
Modeling > create > lines > between key points.
5. Mesh the line using mesh tool.
Main menu > Pre-processor > Meshing > mesh tool > line > mesh.
6. The boundary condition is defined for the beam.
Solutions > load > structural > displacement > on key points > All DOF
7. Solution: Assigning loads and solving
Define analysis type
Solution > analysis type > new analysis > modal
8. Set options for analysis type:
Solution > Analysis type > Analysis optionsβ¦.
Enter 10 for no. of modes to extract and no. of modes to expand in subspace and
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Expand mode shapes.
9. Reduced method is chosen.
10. Apply constrains
Solution > Define loads > Apply > Structural > Displacement > On key points.
11. Solve the system
Solution > Solve > Current LS
12. Post processing: Viewing the results
General post processing > Result Summary.
13. To view mode shapes
General post processing > Read results > First set
General post processing > Plot results > Deformed shape
Repeat the process for the next set to view the next mode shapes.
14. To Animate mode shapes
Utility menu > Plot ctrls > Animate > Mode shapes
RESULT :
Thus the Fixed beam is modeled and analyzed in ANSYS for
Modal analysis. Various mode shapes and respective frequencies are obtained.
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Description:
Cross section= 0.125*0.125
Formula:
Frequency, fn= Ξ»2
2 Ο l2 β EIm
where, E = youngβs modulus (N/m2)
I = moment of inertia
m = mass (kg)
Ξ» = wavelength (m)
Ξ» values for the raw mechanical vibration:
Mode Cantilever SSB Fixed
1 1.875 Ο 4.730
2 4.697 2Ο 7.853
3 7.853 3Ο 10.995
![Page 41: Laboratory Manual](https://reader035.vdocuments.net/reader035/viewer/2022062303/55725c1d497959da6be88ee7/html5/thumbnails/41.jpg)
Calculation:
E = 2.1*105N/mm2 for alloy steel
I = bd3/12 = 0.125*0.1253/12 = 2.03*10-3 m4
Density, Ο = 7700 kg/m3
Mass = Ο*v = 7700*0.125*0.153
m = 120.8kg/m3
Cantilever beam:
Mode 1:
fn = Ξ»2
2 Ο l2 β EIm
= 1.8752
2 Οβ52 β 2.1β104β2.03β105
120.8
= 4.217 Hz
Mode 2:
fn = 4.6972
2 Οβ52 β 2.1β104β2.03β105
120.8
= 26.429 Hz
Mode 3:
fn = 7.8532
2 Οβ52 β 2.1β104β2.03β105
120.8
= 73.97 Hz
Simply Supported beam:
Mode 1:
fn = Ο 2
2 Οβ52 β 2.1β104β2.03β105
120.8
= 11.85 Hz
Mode 2:
fn= (2 Ο )2
2 Οβ52 β 2.1β104β2.03β105
120.8
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= 44.35 Hz
Mode 3:
fn = (3 Ο )2
2 Οβ52 β 2.1β104β2.03β105
120.8
= 106.5 Hz
Fixed beam:
Mode 1:
fn = 4.7302
2 Οβ52 β 2.1β104β2.03β105
120.8
= 26.82 Hz
Mode 2:
fn = 7.8532
2 Οβ52 β 2.1β104β2.03β105
120.8
= 73.94 Hz
Mode 3:
fn = 10.9952
2 Οβ52 β 2.1β104β2.03β105
120.8
= 144.81 Hz
Result:
Beam Analytical value Simulation valueCantilever Mode 1 4.217 4.2169Cantilever Mode 2 26.429 26.488Cantilever Mode 3 73.97 74.592
SSB Mode 1 11.85 11.862SSB Mode 2 44.35 47.710SSB Mode 3 106.5 108.33
Fixed beam Mode 1 26.82 26.905Fixed beam Mode 2 73.94 74.636Fixed beam Mode 3 144.81 147.75
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Mode Frequency analysis of 2d component .
EX NO:
DATE:
Aim:
To perform a mode frequency analysis of the given component using ANSYS
Description:
A simply supported steel plate of dimension ( 1000 Γ 500 Γ 25mm ). A fixed circular plate with thickness 25mm and diameter 200mm
Diagram:
Formula used:
Ο=β DΟ [(mΟ
a )2
+( nΟb )
2]D= βh3
12 (1βΞ³2 )
β = 2.1 x 1011 N/m2
Ξ³ = 0.28 (Poisson Ratio)
Ο = 7700 kg/m3
h = thickness of plate for rectangular lamina
m = number of parts of modal value
n = number of parts value in horizontal direct
Circular lamina:
Ξ»2 = Ο a2 β ΟD
500
1000
![Page 45: Laboratory Manual](https://reader035.vdocuments.net/reader035/viewer/2022062303/55725c1d497959da6be88ee7/html5/thumbnails/45.jpg)
Ξ» = Wavelength
a = radius
Ο = 2Οs
S = Number of parts modal value in radial direction
n = number of parts modal value in circular direction.
Procedure:
Rectangular plate :
Pre-processing: Defining the Problem
1. Open ANSYS APDL from start menu.
2. Define the type of problem,
Pre-processor β preference β structural β ok
3. Define the Type of Element
Pre-processor β Element Type β Add/Edit/Delete [Add the element: Solid - PLANE82]
4. Define Geometric Properties
Pre-processor β Real Constants β Add/Edit/Delete [Enter a thickness as 25mm]
5. Element Material Properties
Pre-processor β Material Properties β Material models β Structural β linear β Elastic β Isotropic [We are going to give the properties of Steel. Enter the following when prompted: EX β 2.1E11, PRXY β 0.3]
Pre-processor β Material Properties β Material models β Structural β Density [ Enter the density value as 7700]
6. Create the main rectangular shape
Pre-processor β Modelling β Create β Areas β Rectangle β By 2 Corners [Enter the following values: WPX β 0, WPY β 0, Width β 1, Height β .5]
7. Meshing
Pre-processor β mesh β mesh tool β Areas [set] β select the area β apply β enter element size as 10 β ok
Click mesh β select the area β ok
Solution Phase: Assigning Loads and Solving
8. Analysis type
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Solution β Analysis type β New analysis β Modal β ok
Analysis type β Analysis Option [ no of modes to extract β 10 ; Nmode number of modes to expand 10] β ok
9. Define constraints
Solution β define load β apply β structural β displacement β on lines [Select the left and right lines, select UY & click ok]
Solution β define load β apply β structural β displacement β on lines [Select the Bottom and top lines, select UX & click ok]
10. Solving the System
Solution β Solve β Current LS
Post processing: Viewing the Results
11. Mode Shape
General Postproc β Read Results β by pick [Select the frequency and click read] β close
Plot controls β animate β Mode shape [select DOF solution ; Deformed shape] β ok
12. Repeat step 11 for different frequency values.
Circular plate :
Pre-processing: Defining the Problem
1. Define the type of problem,
Pre-processor β preference β structural β ok
2. Define the Type of Element
Pre-processor β Element Type β Add/Edit/Delete [Add the element: Solid - PLANE82]
3. Define Geometric Properties
Pre-processor β Real Constants β Add/Edit/Delete [Enter a thickness as 25mm]
4. Element Material Properties
Pre-processor β Material Properties β Material models β Structural β linear β Elastic β Isotropic [We are going to give the properties of Steel. Enter the following when prompted: EX β 2.1E11, PRXY β 0.3]
Pre-processor β Material Properties β Material models β Structural β Density [ Enter the density value as 7700]
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5. Create the circular shape
Pre-processor β Modelling β Create β Areas β circle β solid circle [Enter the following values: WPX β 0, WPY β 0, Radius = .1]
7. Meshing
Pre-processor β mesh β mesh tool β Areas [set] β select the area β apply β enter element size as 10 β ok
Click mesh β select the area β ok
Solution Phase: Assigning Loads and Solving
8. Analysis type
Solution β Analysis type β New analysis β Modal β ok
Analysis type β Analysis Option [ no of modes to extract β 10 ; Nmode number of modes to expand 10] β ok
9. Define constraints
Solution β define load β apply β structural β displacement β on lines [Select Circumference, select all Dof & click ok]
10. Solving the System
Solution β Solve β Current LS
Post processing: Viewing the Results
11. Mode Shape
General Postproc β Read Results β by pick [Select the frequency and click read] β close
Plot controls β animate β Mode shape [select DOF solution ; Deformed shape] β ok
12. Repeat step 11 for different frequency values. Result:
RESULT:
The mode frequency analysis of given 2D component has been successfully done using ANSYS.
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Calculation:
For Rectangular plate :
D= βh3
12 (1βΞ³2 ) = 2.1Γ 1011 Γ0.0253
12 (1β0.28 )2 = 296698.67
Ο1=β DΟ [(mΟ
a )2
+( nΟb )
2] = β 296698.67192.5 [( Ο
1 )2
+( Ο.5 )
2]f1 =
Ο2 Ο
=308.34 Hz
f 2=β 296698.67
192.5 [( 2 Ο1 )
2
+( Ο.5 )
2]2 Ο
= 493.3Hz
f 3=β 296698.67
192.5 [( 3 Ο1 )
2
+( Ο.5 )
2]2 Ο
= 801.75Hz
f 4=β 296698.67
192.5 [( Ο1 )
2
+( 2 Ο.5 )
2]2 Ο
= 1048.36Hz
f 5=β 296698.67
192.5 [( 2 Ο1 )
2
+( 2 Ο.5 )
2]2 Ο
= 1233.36Hz
f 6=β 296698.67
192.5 [( 4Ο1 )
2
+( Ο.5 )
2]2Ο
= 1233.36Hz
f 7=β 296698.67
192.5 [( 3 Ο1 )
2
+( 2 Ο.5 )
2]2 Ο
= 1547.71Hz
f 8=β 296698.67
192.5 [( 5 Ο1 )
2
+( Ο.5 )
2]2 Ο
= 1788.38Hz
f 9=β 296698.67
192.5 [( 4Ο1 )
2
+( 2Ο.5 )
2]2 Ο
= 1973.38Hz
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f 10=β 296698.67
192.5 [( Ο1 )
2
+( 3 Ο.5 )
2]2 Ο
= 2281.72Hz
For circular plate :
D= 296698.67 a = 1m
Ο= 192.5 Ο= 2ΟF
Ξ»2 = Ο a2 β ΟD
10.2158=2 Ο F1 Γ12 β 192.5296698.67
F1 = 63.83Hz
21.26=2 Ο F2Γ12 β 192.5296698.67
F2 = 132.84Hz
34.83=2 Ο F4Γ 12β 192.5296698.67
F4 = 217.63Hz
34.771=2 Ο F6 Γ12 β 192.5296698.67
F6 = 248.5Hz
51.04=2 Ο F7Γ 12β 192.5296698.67
F7 = 318.92Hz
60.82=2 Ο F9 Γ12 β 192.5296698.67
F9 = 380.03Hz
RESULT :
Mode M n Mode shape Frequency Analytical Simulated
1 1 1 308.34 307.932 2 1 493.3 492.293 3 2 801.73 798.974 1 3 1048.36 1043.25 4 1 1233.36 1226.86 2 2 1233.36 1226.8
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7 3 2 1541.71 1531.58 5 1 1788.4 1774.89 4 2 1968.38 1956.610 1 3 2281.72 2260.0
Mode M n Mode shape
WavelengthΞ»
FrequencyAnalytical simulated
1 0 0 10.158 63.81 63.8122 0 1 21.26 132.71 132.773 0 1 21.26 132.71 132.774 0 2 34.83 217.63 217.635 0 2 34.83 217.63 217.636 1 0 34.73 248.5 248.247 0 3 51.04 318.92 318.378 0 3 51.04 318.07 318.459 1 1 60.82 380.07 379.4510 1 1 60.82 380.07 379.45
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CONVECTIVE HEAT TRANSFER ANALYSIS OF A 2 D COMPONENT
EX NO:
DATE:
AIM:
To find the convective heat transfer analysis of a 2 D component
DIAGRAM:
PROCEDURE:
1) Preference > Thermal > ok
2) Preprocessor > Element type > Add/edit/delete > add > solid > Quad4node55 > ok
3) Material properties > material models > thermal > conductivity(Enter the value 50
w/mk)
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4) Modeling > create > areas > rectangle > by 2 corners (Enter the value
w=0.012m;h=0.1m)
5) Meshing > mesh tool > area set > pick the area > ok > size element > edge
length(0.02m) > ok
6) Mesh tool > mesh > pick the area > ok
7) Loads > define loads > apply > thermal > convection > on lines > pick the inside
lines > ok(Enter the value of inside h and inside T) > on lines > pick the outside lines
> ok(Enter the value of outside h and outside T)
8) Solution > solve > current LS
9) See the result in General post processor > list results > nodal solution > DOF solution
> nodal temperature > ok
RESULT:
The temperature and heat flux are shown and results are completed.
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CALCULATION:
T β Temperature of water (β)
T a β Atmospheric temperature (β)
T i - Inner wall temperature (β)
T 0 - Outer wall temperature (β)
u β Overall heat transfer coefficient
K β Thermal conductivity
ho - Heat transfer coefficient at outer
surface(w/m2 k)
hi - Heat transfer coefficient at inner
surface(w/m2 k)
1u= 1
hi
+ 1k+ 1
h0
= 1
2850+ 0.012
50 +
110
u = 9.94 w/m2 k
q =u (T 0βT a)
= 9.94(393-293)
q = 795.2 w/m2
q = hi(T 0βT i)
795.2= 2850 (373-T iΒΏ
T i = 372.72 K
T i = 99.72 β
q = ho(T0βT a)
![Page 54: Laboratory Manual](https://reader035.vdocuments.net/reader035/viewer/2022062303/55725c1d497959da6be88ee7/html5/thumbnails/54.jpg)
795.2= 10 (T 0β293)
T 0 = 372.52 K
T 0 = 99.52 β
CONDUCTIVE HEAT TRANSFER ANALYSIS OF A 2-D ELEMENT
Ex No :
Date :
AIM:
To Conduct heat transfer analysis of a 2-D element for the given example and determine the temperature at the specified points
DIAGRAM:
FORMULAE USED:
Q = βToverall/R
h1 = l 1
k 1a1 +
l 2k 2a 2
+ l 3
k 3a 3
T1, T2, T3, T4 = Temperatures of wall section
R = Resistance
k1, k2, k3 = Thermal Conductivity (W/mK)
A1, A2, A3 = Area of wall
![Page 55: Laboratory Manual](https://reader035.vdocuments.net/reader035/viewer/2022062303/55725c1d497959da6be88ee7/html5/thumbnails/55.jpg)
q = heat flux
PROCEDURE:
Preprocessing: Defining the Problem
1. Give example a Title
2. Open pre-processor menu ANSYS Main Menu > Preprocessor
3. Define the Type of Element Preprocessor > Element Type > Add/Edit/Delete> click 'Add' > Select Link 3D conduction 33
4. Define Real ConstantsPreprocessor >Real Constants>Add>Select the element>Define Cross-sectional area as 1
5. Element Material Properties Preprocessor > Material Props > Material Models > Thermal > Conductivity > Isotropic > KXX1 = 1.05 (Thermal conductivity) > Select New Model > KXX2 = 0.15> Select new model> KXX3 = 0.85
6. Create geometry Preprocessor > Modeling > Create >Key points>On active CS >By dimensions> X=0, Y=0, Z=0 , X=0.25, X=0.37, X=0.57Preprocessor > Modeling > Create >lines>Straight lines
7. Mesh Preprocessor > Meshing > Mesh Attributes>Picked Lines > Pick the line>OK> Define the Material Number
Preprocessor > Meshing > Mesh Tool> Pick Lines> OK> Edge Length > .05> OK> Mesh
8. Define Loads
Preprocessor >Loads > Define Loads > Apply > Thermal > Temperature > On Keypoints> Define The Temp at T1=850 and T2= 65
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Solution Phase: Assigning Loads and Solving
1. Solve the System Solution > Solve > Current LS
Post processing: Viewing the Results
1. Results Using ANSYS Plot Temperature General Postproc> Plot Results > Contour Plot > Nodal Solution > DOF solution, Temperature
General Postproc> List Results > Nodal Solution > Report for Node 7 and 9
RESULT :
Thus the temperatures at the specified points were found throughconductive heat transfer analysis successfully.
![Page 57: Laboratory Manual](https://reader035.vdocuments.net/reader035/viewer/2022062303/55725c1d497959da6be88ee7/html5/thumbnails/57.jpg)
CALCULATIONS :
Q = βToverall/R
h1 = l 1
k 1a1 +
l 2k 2a 2
+ l 3
k 3a 3
q = QA
= 850
0.251.005
+0.120.15
+0.2
0.85
q = 616.46 W/m2
Temperature at the surface, clay fire and insulation brick
To find T2
q = T 1βT 4
k =
T 1βT 2k
= T 2βT 3
k =
T 2βT 4k
q = T 1βT 2
kA =
T 1βT 2h 1k 1
616.46 = 850βT 20.25/1.05
T2 = 703.22 K
Temperature at the surface of insulation brick and red brick
q = QA
= T 2βT 3h 2/k 2
616.46 = 703.22βT 30.12/0.15
T3 = 210.056 K
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THERMAL STRESS ANALYSIS OF 2D COMPONENT
Ex No :
Date :
AIM:
To perform thermal stress analysis of a given 2D component using solid works simulation software.
DIAGRAM
PROBLEM DESCRIPTION:
A rectangular plate of dimensions 50mmΓ25mmΓ2.5mm in subjected to a uniform temperature from 0oC to 38oC. Determine the maximum displacement and normal stress in X direction. The properties of the plate are, Youngβs modulus (E) =2.1Γ10Λ5 N/mm2, Poissonβs ratio (Ξ½) =.28 and thermal coefficient of expansion (Ξ±) =1.3Γ10Λ-5 K-1
FORMULA USED:
Normal stress in X direction = EΞ±ΞΞ€1. Displacement in Y direction = Ξ±ΞTb(1+ Ξ½)
Where, E β Youngβs modulus
Ξ± β Thermal co-efficient
ΞΞ€ β Temperature difference
b β Breadth
Ξ½ β Poissonβs ratio
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PROCEDURE:
1. Open ANSYS APDL from start menu.
2. Give Title name.
File β Change title β Enter new title β ok.
PREFERENCE:
3. Define the type of problem,
Preferences β structural & thermalβ ok
PREPROCESSOR:
4. Define the Type of Element
Pre-processor β Element Type β Add/Edit/Delete β Add β Solid β Quad
4 node 182 β ok β options β plane strs w/thk β ok β close.
5. Define Geometric Properties
Preprocessor β Real Constants β Add/Edit/Delete β Add β ok β THK =
0.0025m β ok β close
6. Element Material Properties
Pre-processor β Material Properties β Material models β Structural β
linear β Elastic β Isotropic β EX = 2.1Γ10Λ11 & PRXY = 0.24 β ok β Thermal
expansion β Secant coefficient βIsotropic β ALPX = 1.3Γ10Λ-5 β ok β close.
7. Create the main rectangular shape
Pre-processor β Modeling β Create β Areas β Rectangle β By 2 Corners
β WP X β 0, WP Y = 0, Width = .05, Height .025 β ok.
8. Meshing
Pre-processor β mesh β mesh tool β Areas [set] β select the area β apply
β enter element size = .001 β ok β mesh β select the area β ok
9. Define temperature
Solution β define loads β apply β structural βtemperature β on lines β
Pick line β ok β VAL1 temperature = 273 β apply β Pick line β ok β VAL1
temperature = 311 β ok.
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SOLUTION:
10.Solving the System
Solution β Solve β Current LS.
GENERAL POSTPROCESSOR:
11.Stress
General Postproc β Plot Results β Contour Plot β Nodal Solution β Nodal
Solution β X component of stress β ok.
12.Stress values
General postproc β list result β Nodal Solution β Nodal Solution β X
component of stress β ok β Note values from the table.
13.Displacement values
Note the value of DMX
RESULT:
Thus the thermal stress analysis of 2D component has been done and results are obtained.
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CALCULATION:
Normal stress in X- direction,
Οx = EΞ±ΞΞ€
Οx = 2.1Γ10Λ5Γ1.3Γ10Λ-5Γ38
= 103.74 N/mm 2
Displacement in Y-direction
y = Ξ±ΞTb(1+ Ξ½)
= 1.3Γ10Λ-5Γ38Γ25Γ(1+0.25)
= 1.524Γ10Λ -2 mm
Note: Restrain geometry along X direction and rotation on all directions.
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HARMONIC ANALYSIS OF 2D COMPONENT
Ex No:
Date :
AIM:
To calculate the peak vs displacement and bending stress at the centre of square plate of side 10m and thickness 0.05m subjected to a steady state harmonic pressure
All dimensions are in mm
PROBLEM DESCRIPTION:
To calculate and perform harmonic analysis of a given 2D component with the given dimensions of side 10m and thickness 0.05m
PROCEDURE:
1. Utility Menu > Change Job Name > Enter Job Name.
Utility Menu > File > Change Title > Enter New Title.
2. Preference > Structural > OK.
3. Preprocessor > Element type > Add/Edit/ delete > Solid 8node 82 > options > plane stress with thickness > close.
4. Preprocessor > Real Constant > Add/Edit/Delete > thickness = 0.05 > Ok
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5. Preprocessor > Material Properties > Material Model > Structural > Linear > Elastic > Isotropic > EX = 200 E9, PRXY = 0.3 & Density = 8000.
6. Preprocessor>Modeling>create>Areas>Rectangle> By dimensions>Enter the Value
7. Preprocessor > meshing > mesh tool > size control > Areas >Enter the Element edge length > Ok > mesh > Areas > free> pick all.
8. Solution > Analysis Type > New Analysis > harmonic > OK > analysis options > real + imaginary (full solution method).
9. Solution > define loads > apply > structural > force/moment > on nodes > click right corner > FY real value> Enter the Value & Imaginary value = 0 > Ok.
10. Solve > current L.S > ok.
11. Load step option > time frequency > frequency & sub steps > Enter the Value > stepped > Ok.
12. Time history postprocessor > variable viewer > add > nodal solution > DOF solution > Y-component of displacement > click right corner > ok > graph data > Ok.
13. Utility Menu > plot controls > style > graphs > modify axis ( change the Y-axis scale to logarithmic)
14. Utility menu > plot > replot.
Model Damping Rayleigh DampingPeak U = displacement at Center (mm)
7.831mm at 2.088Hz 7.0833mm at 2.087Hz
Peak Bending Stress at Center 5.4N/mm2 at 2.088Hz 5.4N/mm2 at 2.087Hz
RESULT:
Thus the thermal stress analysis of 2D component has been done and results are obtained.
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CALCULATION:
Density = 8000 kg / mΒ³
E=200 x109 N / M Β²
Harmonic option = 0.10 Hz
Model damping: Damping ratio = 0.2
Poisson Ratio = 0.3
Rayleigh damping: Ξ±= 0.299
Ξ² = 0.00139
.