finite element modelling and analysis in ansys workbench

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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