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Finite Element Modelling and Analysis in ANSYS Workbench
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Contents
Rectangular plate with circular hole Subjected to tensile load.
Modal analysis of Annular Plate.
Mixed model subjected to bending loads with solution combination.
Buckling of a stepped rod.
Harmonic response of a single degree of freedom system.
Harmonic response of two storied building under transverse loading.
Buckling of a circular arch.
Fatigue analysis of a rectangular plate subjected to edge moment.
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Rectangular plate with circular hole subjected to tensile load
Test case
A rectangular plate with a circular hole is fixed along one of the end faces and a tensile pressure load is applied on the opposite face.Find the maximum normal stress in the X direction on the cylindrical surface of the hole
Material Properties Geometric Properties Loading
E= 1000 pa
V=0.3
Length=15
Width=5
Thickness=1m
Hole radius=0.5m
Pressure=-100 pa
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Result Comparison
Results Verification manual results ANSYS results Error (%)
Maximum Normal X
Stress(pa)
312.5 318.07 1.8
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Modal analysis of annular Plate
Test case
The assembly of three annular plates has cylindrical support (fixed in redial ,tangential and axial direction )
applied on the cylindrical surface of the hole.
Find the first six mode of natural frequencies.Material Properties Geometric Properties Loading
E= 2.9008e7 psi
V=0.3
ρ = 0.28383 lbm/in3
Inner diameter of inner plate= 20 in
Inner diameter of middle plate= 28 in
Inner diameter of outer plate= 34 in
Outer diameter of outer plate= 40 in
Thickness =1 in
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Result Comparison
Results Verification manual results ANSYS results Error (%)
1st frequency mode (Hz) 310.911 310.33 -0.19
2nt frequency mode (Hz) 318.086 315.01 -0.97
3rd frequency mode (Hz) 318.086 315.84 -0.70
4th frequency mode (Hz) 351.569 347.1 -1.3
5th frequency mode (Hz) 351.569 347.21 -1.24
6th frequency mode (Hz) 442.451 435.71 -1.52
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Mixed model subjected to bending loads with solution combination
Test case
A mixed model (shell and beam) has one shell edge fixed as shown below. Bending loads are applied on the
free vertex of the beam as given below. Apply a global element size of 80 mm to get accurate results.
Scenario 1: Only a force load.
Scenario 2: Only a moment load.
Find the deformation in the y direction under Solution Combination with the coefficients for both the
environments set to 1.Material Properties Geometric Properties Loading
E= 2e5 pa
V=0.3
Shell = 160 mm x 500 mm x10 mm
Beam rectangular cross section = 10 x 10 mm
Beam length = 500 mm
Force F = -10 N (y direction)
Moment M = -4035 Nmm about z-axis
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Result Comparison
Results Verification manual results ANSYS results Error (%)
Maximum Y-Deformation(mm) -7.18742 -7.2853 0.93
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Buckling of stepped shaft
Test case
A stepped rod is fixed at one end face. It is axially loaded by two forces: a tensile load at the free end and a
compressive load on the flat step face at the junction of the two cross sections.
Find the Load Multiplier for the First Buckling Mode.
Material Properties Geometric Properties Loading
E= 2e11 pa
V=0.3
Larger diameter =0.011982 m
Smaller diameter = 0.010 m
Length of larger diameter = 0.2 m
Length of smaller diameter = 0.1 m
Force F = -10 N (y direction)
Moment M = -4035 Nmm about z-axis
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Result Comparison
Results Verification manual results ANSYS results Error (%)
Load Multiplier 22.5 22.985 2.1
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Harmonic response of a single degree of freedom system
Test case
An assembly where four cylinders represent massless springs in series and a point mass simulates a spring
mass system. The flat end face of the cylinder is fixed. Harmonic force is applied on the other end of
cylinder.
Find the z directional deformation frequency response of the system on the face to which force is applied for
the frequency range of 0 to 500 Hz for the following scenarios using Mode Superposition.
Solution intervals=20
Scenario 1: Damping ratio=0
Scenario 1: Damping ratio=0.05
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Material Properties
Material
Shaft 1
Shaft 2
Shaft 3
Shaft 4
E (pa)
1.1e11
1.1e11
4.5e10
4.5e10
V
0.34
0.34
0.35
0.35
ρ (kg/m3 )
1e-8
1e-8
1e-8
1e-8
Geometric properties Loading
Each cylinder:
Diameter = 20mm
Length = 50 mm
Force = 1 e 7 (z-direction)
Point mass =3.1044 kg
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Scenario 1: Damping ratio = 0 Scenario 1: Damping ratio=0.05
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Result Comparison
Results Verification manual results ANSYS results Error (%)
Maximum Amplitude without
damping (m)
0.1404 0.14185 1.03
Maximum Amplitude with
damping (m)
0.14 0.1414 1
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Harmonic response of two storied building under transverse loading
Test case
A two-story building has two columns (2K and K) constituting stiffness elements and two slabs (2M and M)
constituting mass elements. The material of the columns is assigned negligible density so as to make massless
springs. The slabs are allowed to move only in the y direction by applying frictionless supports on all the
faces of the slabs in the y direction. The end face of the column (2K) is fixed and a harmonic force is applied
on the face of the slab .
Find the y directional Deformation Frequency Response of the system at 70 Hz on each of the vertices for
the frequency range of 0 to 500 Hz using Mode Superposition.
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Material Properties
Material
Block 2
Shaft 2
Block 1
Shaft 1
E (pa)
2e18
4.5e10
2e18
9e10
V
0.3
0.35
0.3
0.35
ρ (kg/m3 )
7850
1e-8
15700
1e-8
Geometric properties Loading
Block1 and 2
40mm x 40mm x40mm
Shaft 1 and 2
20 mm x 20 mm x 200 mm
Force = -1 e 5 N (y-direction)
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Vertex A for harmonic response
Vertex B for harmonic response
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Amplitude on Vertex A at 70 Hz
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Amplitude on Vertex B at 70
Hz
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Result Comparison
Results Verification manual results ANSYS results Error (%)
Maximum Amplitude for Vertex
A (m)
0.20853 0.210287 1.4
Maximum Amplitude for Vertex
B (m)
0.074902 0.07583 1.2
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Buckling of Circular Arch
Test case
A circular arch of a rectangular cross section (details given below) is subjected to a pressure load as shown
below. Both the straight edges of the arch are fixed.
Find the Load Multiplier for the first buckling mode.Material
Properties
Geometric Properties Loading
E= 2e11 pa
V=0
Arch cross-section = 5
mm x 50 mm
Mean radius of arch =
50 mm
Included angle = 90°
Pressure = 1MPa
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Result Comparison
Results Verification manual results ANSYS
results
Error
(%)
Load Multiplier 544 574.6 5.6
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Fatigue Analysis of a rectangular plate subjected to edge moment
Test case
A plate of length L, width W, and thickness T is fixed along the width on one edge and a moment M is applied on the
opposite edge about the z-axis.
Find the maximum Bending Stress (Normal X Stress) and maximum Total Deformation of the plate. Also find the part life
and the factor of safety using Goodman, Soderberg, & Gerber criteria. Use the x-stress component. Consider load type as
fully reversed and a Design Life of 1e6 cycles, Fatigue Strength of 1, and Scale factor of 1.
Material Properties Geometric Properties
Loading
E = 2e11 Paν = 0.0Ultimate tensile strength = 1.29e9 PaEndurance strength = 1.38e8 PaYield Strength = 2.5e8 Pa
Length L = 12e-3 m Width W = 1e-3 m Thickness T = 1 e-3 m
Moment M = 0.15 Nm (counterclockwise z-axis)
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SN-Goodman
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SN-Soderberg
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SN-Gerber
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Result Comparison
Results Verification manual results ANSYS results Error (%)
Maximum normal x-stress (Pa) 9e8 9.71e8
Maximum total deformation (m) 6.48e-4 6.71e-4
SN-Goodman Safety factor 0.1533 0.1005
Life 1844.3 1800.5
SN-Soderberg Safety factor 0.1533 0.1244
Life 1844.3 1804.5
SN-Gerber Safety factor 0.1533 0.1005
Life 1844.3 1804.2