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1.0 INTRODUCTION

The Engineering Design Process outlines the steps necessary in solving any type of

engineering problems. The engineering design process is a multi-step process including the

research, conceptualization, feasibility assessment, establishing design requirements,

preliminary design, detailed design, production planning and tool design, and finally

production. The sections to follow are not necessarily steps in the engineering design process,

for some tasks are completed at the same time as other tasks. This is just a general summary

of each part of the engineering design process. The Engineering Design Process is not a linear

process. Successful engineering requires going back and forth between the six main steps as

shown in Figure 1.

Figure 1 Engineering design process

During the engineering design process, designers frequently jump back and forth between

steps. Going back to earlier steps is common. This way of working is called iteration, and it is

likely that our process will do the same.

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In this project, we have to use the finite element method (FEM). Its practical application

often known as finite element analysis (FEA)) which is a numerical technique for finding

approximate solutions to partial differential equations (PDE) and their systems, as well as

(less often) integral equations. In simple terms, FEM is a method for dividing up a very

complicated problem into small elements that can be solved in relation to each other. FEM is

a special case of the more general Galerkin method with polynomial approximation

functions. The solution approach is based on eliminating the spatial derivatives from the

PDE. This approximates the PDE with

a system of algebraic equations for steady state problems,

a system of ordinary differential equations for transient problems.

These equation systems are linear if the underlying PDE is linear, and vice versa.

Algebraic equation systems are solved using numerical linear algebra methods. Ordinary

differential equations that arise in transient problems are then numerically integrated using

standard techniques such asEuler's method or the Runge-Kutta method.

In solving partial differential equations, the primary challenge is to create an equation

that approximates the equation to be studied, but is numerically stable, meaning that errors in

the input and intermediate calculations do not accumulate and cause the resulting output to be

meaningless. There are many ways of doing this, all with advantages and disadvantages. The

finite element method is a good choice for solving partial differential equations over

complicated domains (like cars and oil pipelines), when the domain changes (as during a

solid state reaction with a moving boundary), when the desired precision varies over the

entire domain, or when the solution lacks smoothness. For instance, in a frontal crash

simulation it is possible to increase prediction accuracy in "important" areas like the front of

the car and reduce it in its rear (thus reducing cost of the simulation). Another example would

be in Numerical weather prediction, where it is more important to have accurate predictions

over developing highly nonlinear phenomena (such as tropical cyclones in the atmosphere,

or eddies in the ocean) rather than relatively calm areas.

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2.0 MODEL DESCRIPTION

2.1 TASK 1

3D CAD model as the dimension A = 25mm, B= 20mm, w= 1500 N/m ,

Poisson’s Ratio (v) = 0.29, Em = 200GPa, Es= 400MPa

Figure 2 Original Beam

Figure 3 Design 1

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Figure 4 Design 2

Figure 5 Design 3

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2.2 ANALYSIS

ORIGINAL BEAM (3D)

Figure 6 Deformation of original beam

Figure 7 Von-mises stress

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Figure 8 Translational displacement

Figure 9 Principle stress

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Figure 10 Max & min nodal of Von-mises

Figure 11 Max & min nodal of translational displacement

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Figure 12 Max & min nodal of principle stress

Original Beam

MESH:

ELEMENT TYPE:

Entity Size

Nodes 256

Elements 771

Connectivity Statistics

TE4 771 ( 100.00% )

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ELEMENT QUALITY:

Materials.1

Static Case

Boundary Conditions

Figure 1

STRUCTURE Computation

Number of nodes : 256

Number of elements : 771

Number of D.O.F. : 768

Number of Contact relations : 0

Number of Kinematic relations : 0

Criterion Good Poor Bad Worst Average

Stretch 771 (

100.00% ) 0 ( 0.00% ) 0 ( 0.00% ) 0.410 0.587

Aspect Ratio 771 (

100.00% ) 0 ( 0.00% ) 0 ( 0.00% ) 3.865 2.234

Material Steel

Young's modulus 2e+011N_m2

Poisson's ratio 0.29

Density 7860kg_m3

Coefficient of thermal expansion 1.17e-005_Kdeg

Yield strength 4e+008N_m2

Linear tetrahedron : 771

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RESTRAINT Computation

Name: Restraints.1

Number of S.P.C : 90

LOAD Computation

Name: Loads.1

Applied load resultant :

STIFFNESS Computation

Number of lines : 768

Number of coefficients : 12642

Number of blocks : 1

Maximum number of coefficients per bloc : 12642

Total matrix size : 0 . 15 Mb

SINGULARITY Computation

Restraint: Restraints.1

Number of local singularities : 0

Number of singularities in translation : 0

Number of singularities in rotation : 0

Generated constraint type : MPC

CONSTRAINT Computation

Restraint: Restraints.1

Number of constraints : 90

Number of coefficients : 0

Number of factorized constraints : 90

Number of coefficients : 0

Number of deferred constraints : 0

FACTORIZED Computation

Method : SPARSE

Number of factorized degrees : 678

Number of supernodes : 135

Number of overhead indices : 3954

Number of coefficients : 26211

Maximum front width : 72

Maximum front size : 2628

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Size of the factorized matrix (Mb) : 0 . 199974

Number of blocks : 1

Number of Mflops for factorization : 1 . 356e+000

Number of Mflops for solve : 1 . 082e-001

Minimum relative pivot : 2 . 764e-002

Minimum and maximum pivot

Value Dof Node x (mm) y (mm) z (mm)

2.8078e+008 Tx 256 5.5259e+000 6.5176e+000 2.6446e+001

1.2646e+010 Ty 221 1.4819e+001 5.8076e+000 1.1835e+002

Minimum pivot

Value Dof Node x (mm) y (mm) z (mm)

3.1157e+008 Ty 256 5.5259e+000 6.5176e+000 2.6446e+001

8.5879e+008 Ty 240 8.8304e+000 1.2999e+001 1.0319e+002

8.8355e+008 Tz 225 1.0611e+001 1.9616e+001 5.6535e+001

8.8865e+008 Tx 244 6.1865e+000 5.9668e+000 8.2072e+001

8.9038e+008 Tz 243 1.0395e+001 1.3270e+001 9.3997e+001

8.9809e+008 Tz 226 1.0087e+001 1.9574e+001 6.5662e+001

9.0152e+008 Ty 251 1.0388e+001 1.3258e+001 5.6463e+001

9.0499e+008 Tx 227 9.4759e+000 1.9519e+001 7.4732e+001

9.1072e+008 Tx 226 1.0087e+001 1.9574e+001 6.5662e+001

Translational pivot distribution

Value Percentage

10.E8 --> 10.E9 3.0973e+000

10.E9 --> 10.E10 9.6313e+001

10.E10 --> 10.E11 5.8997e-001

DIRECT METHOD Computation

Name: Static Case Solution.1

Restraint: Restraints.1

Load: Loads.1

Strain Energy : 2.495e-005 J

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Equilibrium

Components Applied

Forces Reactions Residual

Relative

Magnitude Error

Fx (N) -2.2500e+002 2.2500e+002 9.9476e-013 2.3287e-014

Fy (N) -2.4980e-014 8.9084e-013 8.6586e-013 2.0270e-014

Fz (N) 4.5157e-014 7.1487e-013 7.6003e-013 1.7792e-014

Mx (Nxm) -1.0037e-014 -7.6279e-014 -8.6316e-014 1.3471e-014

My (Nxm) -1.6875e+001 1.6875e+001 1.5277e-013 2.3842e-014

Mz (Nxm) 2.8125e+000 -2.8125e+000 5.0626e-014 7.9011e-015

Static Case Solution.1 - Deformed mesh.2

Figure 2

On deformed mesh ---- On boundary ---- Over all the model

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Static Case Solution.1 - Von Mises stress (nodal values).2

Figure 3

3D elements: : Components: : All

On deformed mesh ---- On boundary ---- Over all the model

Global Sensors

Sensor Name Sensor Value

Energy 2.495e-005J

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2.3 TASK 2

DESIGN 1

Figure 13 Design 1

Figure 14 Deformation of Design 1

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Figure 15 Von-mises stress of Design 1

Figure 16 Translational displacement of Design 1

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Figure 17 Principle stress of Design 1

DESIGN 2

Figure 18 Design 2

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Figure 19 Deformation of Design 2

Figure 20 Von-mises stress of Design 2

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Figure 21 Translational displacement of Design 2

Figure 22 Principle stress of Design 2

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DESIGN 3

Figure 23 Design 3

Figure 24 Deformation of Design 3

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Figure 25 Von-mises stress of Design 3

Figure 26 Translational displacement of Design 3

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Figure 27 Principle stress of Design 3

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2.4 MORPHOLOGICAL CHART

DESIGN Original beam Design 1 Design 2 Design 3

A (mm) 25 25 25 25

B (mm) 20 20 20 20

w (N/m) 1500 1500 1500 1500

Poisson’s

ratio (v)

0.29 0.29 0.29 0.29

Em (GPa) 200 200 200 200

Es (MPa) 400 400 400 400

Von Misses

Stress (Nm2)

8.32x107 9.89x10

7 2.82x10

7 1.26x10

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Translational

Displacement

(mm)

0.000426 0.000507 0.000644 0.000277

Principal

Stress (Nm2)

1.09x107

1.31x107

1.91x107

1.07x107

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3.0 DISCUSSION

From the analysis above, I had done the finite element analysis (FEA) for original

just in 3D. The Von-Mises Stress obtained is 8.32 x107 Nm

2 , Translational displacement is

0.000426 mm, and Principle Stress is 1.09x107

Nm2 for 3D beam by using CATIA.

A beam is a structural element that is capable of withstanding load primarily by

resisting bending. The bending force induced into the material of the beam as a result of the

external loads, own weight, span and external reactions to these loads is called a bending

moment. In order to increase the stiffness of the bracket without compromising the

dimensions, we have to design 3 concepts to overcome the problem. However, only one out

from three of my design was successfully done. By increasing the stiffness of the beam, the

deflection of the rectangular support bracket must be reduced.

From the result obtained, the 1st design introduced us a poor result than the original

beam. The value of Von Misses Stress = 9.89x107

Nm2, Translational Displacement =

0.000507 mm and Principal Stress= 1.31x107Nm

2. All the value is much greater than the

original beam, thus this design cannot promote to increase the stiffness of the bracket.

For the 2nd

design, the value of the Von Misses Stress = 2.82x107

Nm2, Translational

Displacement = 0.000644 mm and Principal Stress = 1.91x107x10

7 Nm

2. This design also

gives the poor result than the original beam and design 1.

However, the third design was successfully obtained the exact value to increase the

stiffness due to its value for Von Misses Stress = 1.26 x107 Nm

2, Translational

Displacement = 0.000277 mm and Principal Stress = 1.07x107 Nm

2. This design is the best

among the other design because have less value than the original beam. So, this design can

be promote to increase the stiffness and reduced the deflection.

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4.0 CONCLUSIONS

As the conclusion, based on the translational displacement, the best design goes to the

3rd

design; where the translational displacement of the beam is smaller than the original beam

which is 0.000277 mm rather than 0.000426 mm. Thus this design can overcome the

problem.

5.0 APPENDIX

(a) ADDITIONAL STRESS CONTOUR PLOT

The program provides two types of stress contour plots: a von Mises-Hencky effective

stress plot and a Factor of Safety on Material Yield plot. In both of these plots the

maximum stress plotted is limited to the yield strength of the cable component. Thus,

where stress concentrations occur, the maximum stress reported by the program will

never exceed the yield strength.

The following stress contours are available:

1. Stress xx - contour;

2. Stress yy - contour;

3. Stress xy - contour;

4. Stress zz - contour;

5. Major Principal - contour;

6. Minor Principal - contour;

7. Stress 1/ Stress 3 - contour;

8. Max. Shear - contour;

9. P - mean stress. contour;

10. q - shear stress. is the second stress invariants;

11. q/p - ratio of q/p as defined above;

12. Pore pressure - pore water pressure;

13. Yield zone - PISA actually plots the the value of the yield zone function f for

plastic models.

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(b) REFERENCES

i. http://en.wikipedia.org/wiki/Beam_(structure)

ii. http://en.wikipedia.org/wiki/Finite_element_analysis

iii. http://answers.yahoo.com/question/index?qid=20081120131225AAbKEvM

iv. http://www.newport.com/Fundamentals-of

Vibration/140234/1033/content.aspx

v. http://cedb.asce.org/cgi/WWWdisplay.cgi?115570