Finite Element Analysis With Ansys BY NANGI PETROS

7/28/2019 Finite Element Analysis With Ansys BY NANGI PETROS

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TASK 1.1Create and present FE model of the frame (Discuss the procedure used as well)

Figure 1.1.1 Created FE model of the frame

Procedure used to create the FE model in ANSYS

Given data:

metresAB 3

metresBC 2


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PaE9

10200

29.0v

37860 mkg

12

101 4

I

The width of the frame was not given. An assumption of 0.27 metres was made for the

frames width. And then the following commands were performed from the ANSYS main

menu. PreprocessorModellingCreateAreasRectangleBy dimensions from

the dialogue box, the following dimensions was used to create BC; X1=0, X2=2, Y1=0

Y2=0.27 and AB; X1=0, X2=0.27, Y1=0, Y2=-3.

Figure 1.1.2 Creation of BC (X1=0, X2=2, Y1=0, Y2=0.27)

Figure 1.1.3 Creation of AB (X1=0, X2=0.27, Y1=0, Y2=-3)

After creating BC and AB, it was then necessary to add both areas. This process was done

with the following command, PreprocessorModellingOperateBooleansAdd

Areas from the dialogue box; Pick All.


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Figure 1.1.3 Added areas of BC and AB

TASK 1.2

Discuss real constants, material model and element chosen for FE analysis


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Element type

The element type chosen for this free vibration analysis is SHELL 93. SHELL 93 represents a

thin wall structure (like the FE model frame). SHELL 93 is particularly well suited to model

curved shells. The element has six (6) degree of freedom at each node: translation in the

nodal X, Y and Z direction and rotation about nodal X, Y and Z axes. The deformation shape

has plasticity, stress stiffening, large deflection and large strain capabilities (Adams &

Askenazi 2009).

The SHELL 93 element type, was selected with the following commands; Preprocessor

Element TypeAdd/Edit/Delete. From the popped-up box; Solid, 8 node 93 was selected

from the ANSYS library of elements (see Figure 1.2.1).

Figure 1.2.1 Shows the selected element type (SHELL 93)

Real Constant

The real constant for this free vibration analysis defines the FE model frame, with thickness

of metres0005.0 .This thickness value was assumed and used to show shell as solid by the

software tool (ANSYS). The following commands were used to input the thickness value

PreprocessorReal ConstantAdd/Edit/Delete. From the popped-up box; real constant

is defined with shell thickness at nodes I, J, K and L with thickness values of metres0005.0

(see figure 1.2.2).

Chosen Element Type;

SHELL 93


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Figure 1.2.2 Shows the assumed shell thickness input of metres0005.0 at nodes I, J, K and L

Material Model

The material model for the FE model frame is linear isotropic. This means that the extension

of the material is in direct proportion with the load applied to it (Hookes law). The material

for FE model frame is steel; since its Modulus of Elasticity is 2910200200 mNGPa . It

Poissons ratio is 0.29. Its weight density is 37860 mkg . These values were input with the

following commands PreprocessorMaterial PropsMaterial Models. From the

popped-up box, the followings were selected Structural

Linear

Elastic

Isotropic.The values for Modulus of elasticity and Poissons ratio were input. This preceded by input

the density value, which was done by clicking on Density and OK (see Figure 1.2.3 and

1.2.4).

Figure 1.2.3Elastic Modulus and Poissons ration input

Elastic Modulus

and Poissons ratio

input; 200GPa and

0.29 respectively


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Figure 1.2.4 Input for density ( 37860 mkg )

Density

Input of3

7860 mkg


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TASK 1.3

Present meshed FE model and discussed the procedure used for it

Figure 1.3.1 Mesh frame model

Mesh element type 8 node 93

Element edge length 0.05 metres

Mesh type: Manual meshing

process with H-method

H-method was selected because the variation on closeness

of natural frequency result only, was required for this

analysis (not the exact result).

Procedure used to create the mesh

Manual Meshing Process (with H-Method)


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The type of meshing used for this analysis is a manual meshing process. This means that the

area was divided by meshes of a particular edge length (0.05 metres) input manually to set up

jobs for the free vibration analysis problem. H-method was selected because the variation on

closeness of displacement only, was required for this analysis (not the exact result).

After selecting the element edge length (0.05 metres) as can be seen in Figure 1.3.2; the mesh

function was executed with the following commands PreprocessorMeshingMesh

AreasFree. From the popped-up menuPick all.

Figure 1.3.2 Selected element edge length (0.05 metres)

TASK 1.4

Elementedge length

0.05 meters


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Present your post processing results in textual and graphical form (three resonant

frequencies and mode are to be presented)

Boundary conditions used for the analysis

The analysis performed here-in is Modal analysis. The right angle frame is fixed at A.

Therefore all freedoms were constrained (DOF = 0) ad A. At C movement are arrested in

the Y direction. This constrain will help determine the natural frequencies under the action

of force inherent in the system (frame) itself.

Figure 1.4.1 Type of analysis chosen (modal)

Figure 1.4.2DOF = 0, assigned at point A of the frame

Analysis type chosen (modal)

Assigned DOF = 0


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Figure 1.4.3Movement arrested in the Y direction of point C

Figure 1.4.4 Complete constrained section of the frame

Execution calculation used includes the mode extraction method (PCG Lanczos)

For the mode extraction method; the PCG Lanczos was selected as the eigenvalue solver forthis typical un-damped modal analysis problem. This solver is useful when finding few

modes (up to about 100) of large models (ANSYS release 2008).

UY=0. Movement

arrested in the Y

direction of point C


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Figure 1.4.5 Mode of extraction method

PCG Lanczos

No. of modes

to extract 10


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Figure 1.4.6 First mode of vibration

VALUE TEXTUAL DATA

Displacement 0.742648 metres At node 271: UX = 0.742648 metres

Resonance Frequency 0.021412 Hz Load step = 1, Sub-step = 1,

Cumulative =1


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Figure 1.4.7 Second mode of vibration

VALUE TEXTUAL DATA

Displacement 1.153 metres At node 297: UX = 1.153 metres


Cumulative =2


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Figure 1.4.8 Third mode of vibration

VALUE TEXTUAL DATA

Displacement 0.1771596 metres At node 261: UX = 0.1771596 m


Cumulative =3

Conclusion

Table 1.4.1 Comparison of all three (3) modes of vibration collated

Displacement (metres) Resonance Frequency (Hz)

First mode of vibration 0.742648 0.021412


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Second mode of vibration 1.153 0.076245

Third mode of vibration 0.1771596 0.216144

Based on the vibration modes in Table 1.4.1; it is notable that large radial displacementappeared on the second mode of vibration. But failure or excessive deformation may be

caused if vibration occurs at a high resonant frequency (third mode of vibration). Resonance

is the tendency of a system, to oscillate at greateramplitude, at some frequencies than at

others.

TASK 2.1

Create a finite element (FE) model
http://en.wikipedia.org/wiki/Oscillatehttp://en.wikipedia.org/wiki/Amplitudehttp://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Amplitudehttp://en.wikipedia.org/wiki/Oscillate


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The material of the product is ASTM A-514 Steel. It is quenched and tempered steel with

high yield strength and allows thickness to be minimized. The yield strength of the ASTM A-

514 steel is 690 MPa. The load is shown as distributed load acting over the right part of the

wrench.

Table 2.1.1 Shows the available parameters to be used to create the finite element (FE)

model

X-last digit of I/C number

IC Number : P00097467

Radius of the circle mm105715

Distance between circles mm280740

Allowance from the centre of circle mm70710

Radius of the middle hexagon mm6379

Radius of the corner hexagon mm4977

Load mmN70710

Youngs Modulus (at room temperature) 2310210210 mmNGPa (efunda Inc

2011)

Poissons ratio (v) 0.27 (efunda Inc 2011)

Figure 2.1.1 Rough sketch of the FE model


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Figure 2.1.1 Created FE model

Procedure used to create the finite element (FE) model

Table 2.1.2 How the model was created in ANSYS

OPERATION PROCEDURE (all dimension in mm)

Rectangular

Dimension (in

mm)

From the ANSYS main menu, ModellingCreateAreas

RectangleBy dimension. X1=0, X2=873.049, Y1=0 and Y2=140


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Circular

Dimension (in

mm) on

different points

on the

rectangle

From the ANSYS main menu ModellingCreateAreasSolid

Circle. Left corner circular part; X=0, Y=70, Radius = 105Apply.

Middle circular part; X=436.524, Y=70 and Radius=105 Apply.

Right corner circular; X=873.049, Y=70 and Radius = 105

OK.

Adding created

areas

After creating the four different areas (three circles and one rectangle),

it is necessary to add them up as one area. This was done by performing

the following operation, Preprocessor ModellingOperate

Booleans AreasPick all

Hexagonal

dimensions (in

mm)

This step was preceded by the creation of hexagons from the centre of

the cicular part inluding middle and corners (left and right). The

following operations were used to create the hexagon, Preprocessor

ModellingCreateAreasPolygonHexagon. From the

popped-up box, dimensions were assigned. Dimension used to create

the middle hexagonal part of the wrench X=436.524, Y=70 and Radius

= 63Apply. The left corner hexagon was created with the following

dimension X=0, Y=50, Radius=49Apply. While the right corner

hexagon was with the following dimensions X=873.049, Y=70, Radius

=49OK.

Subtracting

hexagonal

areas

The hexagonal area was finally subtracted from the main area to

completely create the wrench FE model. The hexagonal areas were

subtracted by performing the following Preprocessor Modelling


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OperateBooleansSubtractAreas. The main area was

highlighted; the Apply button was clicked on, from the popped-up box.

This was followed by clicking on the hexagons and the OKbutton.

TASK 2.2

Discuss material model, element and real constant used for the analysis

Chosen type of study

The type of study chosen for the analysis is structural (stress) analysis. It is used to determine

the effects of static or dynamic loading on a component like the bicycle wrench.


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Figure 2.2.1 Study (structural) chosen from the ANSYS main menu

Chosen element for meshing (Quad 4 node 42) and why?

Quad 4 node 42 was chosen for this problem because of the need to use the PLANE42 (2D

plane stress or plane strain) element. This element is a rectangular node element which has 4

nodes each with 2 degrees of freedom (translation along the X and Y axes). It is known that,

for any element, DOF solution u is solved at nodes (usually accurate based on meshed

density). Therefore an element type with more nodes would yield a much more accurate

result. At this initial analysis, only a variation on the closeness of displacement result is

required and thus Quad 4 node 42 is chosen. A different element type will be chosen for

refine mesh later on, on subsequent task.

Structural

Analysis


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Figure 2.2.2 Element type (Plane 42) chosen from the ANSYS main menu

Assumption for Material properties

The material properties for the ASTM A-514 Steel are assumed to be linear isotopic with

Modulus of Elasticity 2310210210 mmNGPa and Poissons ratio (v) = 0.27. This

operation was performed in ANSYS with the following commands Pre-processor

Material PropertiesMaterial ModelsStructuralLinearElastic Isotropic

(see figure 1.3.3).

Figure 2.2.3 Defined material properties; Linear isotropic, Elastic modulus 210,0002

mmN .

Poisson Ratio 0.27

Plane 42 element (plane

strain/stress element)

Quad 4 node 42

(element chosen

for meshing)

Material model defined

as Linear Isotropic

Materials Elastic Modulus

210,0002

mmN . Poisson

Ratio 0.27


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Assumption for Real Constant

The geometry of the body (the wrench), has an element where one dimension is very small

compared to the other (i.e. the element is flat or thin). The stresses are negligible with respect

to the smaller dimension as they are not able to develop within the material and are small

compared to the in-plane stresses (Allan 2008). Therefore, the face of the element is not acted

by loads and so the structural element can be analysed as 2-dimensional planes stress

problem. Considering a plane stress condition for the bicycle wrench, thickness is measured

along the z-direction and it is small relative to its lateral dimensions. Since the original

thickness for the bicycle wrench is unknown; a uniform 1mm thickness is thereby assumed

for the plane stress problem

Figure 2.2.4 Selection as a plane stress problem with thickness

Figure 2.2.5 Assumed thickness selection of 1mm

This operation was performed in ANSYS with the following commands Pre-processor

Material PropertiesMaterial ModelsStructuralLinearElastic Isotropic

Selection of plane

stress with thickness

Assumed 1mm

thickness


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TASK 2.3

Present meshed model and discussed the procedure used for it

Figure 2.3.1 Shows the meshed FE model, created with two different element edge lengths

(10 and 20mm respectively)

Meshed Information

Table 2.3.1 Shows some mesh information used for the analysis

Mesh element type Quad 4 node 42

Critical region The fine meshing was increased at this region (by decreasing

element edge length to 10mm). This was done because the

region was more critical and likely to be the hub for stress

concentration

Criticalregion,Element

edgelength10mm

Non-criticalregion,

Elementedgelength

20mm


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Element edge length for

critical region

10 mm

Element edge length for

non-critical region

20 mm

Mesh type: H-refine H-refine was selected because the variation on closeness of

displacement only, was required for this analysis (not the

exact result).

Number of elements 441

Element 1has nodes: 174, 428, 525 and 525

Element 441 has nodes:273, 157, 156 and 274

Number of Nodes 526

At node 1: X = 623.61, Y = -25

At node 526: X = 665.53, Y = 22.99

The element edge length was created with the following operations MeshingSize Control

Manual SizeLinesPicked lines (e.g. the critical region was highlighted).

Figure 2.3.2 Element edge length used for the critical region (10 mm). The same procedure

was applied to the non-critical region (20mm)

TASK 2.4

Analyse the model and present the nodal displacements and Displacement plot obtained

from the analysis

Boundary condition: The side hexagonal holes in the wrench are necessary for fasteners

such as bolts, rivets, etc. It is necessary to know how stresses and deformations occur near

them. For this reason the left hexagonal hole is constrained with all DOF (degrees of

10 mm element edge

length, for the critical

region


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freedom) equal to zero (0). Pressure is expected to be applied at the right end of the wrench.

The pressure is expected to rotate the wrench in a clock-wise direction. The pressure is given

as;

mmN70

Since a thickness of mm1 is assumed;

mmmmNessure

1

170Pr

With the following commands, the all DOF constrain was applied to the left corner hexagonal

hole. SolutionDefine LoadsApplyStructuralDisplacementOn lines (left

corner hexagon was highlighted)Apply

Figure 2.4.1 All DOF = 0 constrain application, on the left corner hexagonal hole

270 mmN

All DOF

applied as 0


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Figure 2.4.2 Applied pressure value of 70 2mmN

Figure 2.4.3 Line plot based on the constrain assumption

Applied

pressure of2

70 mmN

All DOF = 0

Pressure on lines

(UDL) 70 2mmN


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Figure 2.4.3 shows the complete constrain of the 2D wrench model in a line plot. The left

corner of the wrench will be connected to a bolt, therefore all DOF (degrees of freedom) = 0.

A uniformly distributed load (pressure of 70

2

mmN ) will be required to rotate the wrench ina clock-wise direction. Please see the next page for graphical plot.


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Figure 2.4.4 Displacement plot

DISPLACEMENT VALUE POSITION/TEXTUAL DATA

Maximum displacement 62.099 mm At node 6:

UY = 31.442 mm; UX = 4.2578

Minimum displacement 0 mm At nodes 149 to 166:

UY = 0 mm; UX = 0


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Figure 2.4.5 Principal stress plot 1p

PRINCIPAL STRESS 1p VALUE POSITION/TEXTUAL DATA

Maximum 1p

23813 mmN At node 42:

23813 mmN

Minimum 1p

20 mmN At nodes 6:

20000.0 mmN


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Figure 2.4.6 Principal stress plot 2p

PRINCIPAL STRESS 2p VALUE POSITION/TEXTUAL DATA

Maximum 2p 2

182.546 mmN At node 41:2

182.546 mmN

Minimum 2p 2

612.499 mmN At nodes 81:

2612.499 mmN


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Figure 2.4.7 Shear Stress xy

SHEAR STRESSxy

VALUE POSITION/TEXTUAL DATA

Maximumxy

21163 mmN At node 88:

21163 mmN

Minimumxy

21055 mmN At nodes 130:

21055 mmN


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Figure 2.4.8 Von Mises Plot

VON MISES PLOT VALUE POSITION/TEXTUAL DATA

Maximum 23842 mmN At node 81:

23842 mmN

Minimum 2198876.0 mmN At nodes 10:

2198876.0 mmN

Procedure used to generate the graphical plot

The graphical plots were created after constrain conditions had been applied and solution

solved.


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Figure 2.4.9 Solution solved

After the solution had been solved, the following commands were used to generate the

graphical plot for displacement. General PostprocessorPlot ResultsNodal Solution

(from the popped-up box) DOF SolutionDisplacement Vector SumOK(see figure

2.4.10).

Figure 2.4.10 How the Displacement plot was generated

Similar steps were also used to generate the graphical plots for principal stresses. General

PostprocessorPlot ResultsNodal Solution (from the popped-up box) Stress 1st

Principal stress or2nd Principal Stress orShear Stress orVon Mises StressOK(e.g

see figure 2.4.11 [1st

principal stress]).


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Figure 2.4.11 How the 1st

Principal stress plot was generated

Conclusion

The given model does require changes in the dimension (especially thickness). The reason is

because, the Von Mises stress results (2

3842 mmN ) did not fulfil the maximum distortion

energy theory, which states that for a structure to be safe; the Von Mises stresses must not

exceed the yield strengh (690 2mmN ) of the material. Increasing the dimension will increase

the strength of the wrench (Allan 2008). Only then will the wrench fulfill the maximum

distortion enegy theory.

Reference:


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1. Allan Bower, F, 2008,Introduction to Finite Element Analysis in Solid Mechanics,Journal of Applied mechanics of solids, viewed 3 November 2011,

2. eFunda Inc. 2011, ASTM A514 Type A viewed 4 November 2011,

3. Engineers Edge 2011, Strength of material Mechanics of material viewed 5November 2011, < http://www.engineersedge.com/strength_of_materials.htm>

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Finite Element Analysis With Ansys BY NANGI PETROS