# Finite Element Analysis And Mechanincal Elements Engineering

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- Chapter-2
- Introduction to each mechanical component considered for analysis
- Frame-truss
- Seat belt lingua
- Shaft
- Bracket
- Chapter-3
- Problem definition of each mechanical constituent
- Frame-truss
- Seat belt lingua
- Shaft
- Bracket
- Chapter-4
- Design and analysis of each mechanical constituent
- Frame-truss
- Design & A ; Analysis Solution
- Nodal co-ordinates
- Element connectivity tabular array
- Directional cosines- ,
- Stiffness matrix-k
- For element-1
- For element-2
- For Element -3
- For element-4
- Assembling K matrix
- Stresss
- Strains
- Component considered for analysis in ansys
- Beam2D- elastic 3
- BEAM3 Stress Output
- Figure-BEAM3 Stress Output
- For 1×1 cross subdivision
- For 2×2 Cs job
- For 3×3 Cs job
- Comparative tabular array among the values for different transverse subdivisions of frame-truss
- A
- Consequences
- Seat belt lingua
- Design & A ; Analysis Solution
- Fem related equations to cipher the emphasis and strain
- Component considered for analysis in ansys
- Solid-quad 4node 42 ( plane 42 )
- Figure-PLANE42 Geometry
- For 2.5mm thickness
- For 5mm thickness
- Comparison
- Consequences
- Shaft
- Design & A ; Analysis Solution
- Fem related equations to cipher the emphasis and strain
- Component considered for analysis in ansys
- Beam -3D-2node 188
- Figure-BEAM188 Geometry
- for shaft radius=25mm
- for shaft radius=35mm
- Comparison
- Consequences
- Bracket
- Design & A ; Analysis Solution
- Fem related equations to cipher the emphasis and strain
- Component considered for analysis in ansys
- Beam2D- elastic 3
- BEAM3 Stress Output
- Figure-BEAM3 Stress Output
- For cs=35×70
- For cs=35×35
- Comparison
- Consequences
- Chapter-5
- Decisions
- Recommendation
- Chapter-6
- General process carried to work out the jobs in ansys.

In the present competitory universe, merchandises should be designed to be dependable in every facet, taking into consideration the dependability of the constituent to map under the different applied tonss without any failure. After the design of the constituent is completed we need to cognize whether the designed constituent is able to carry through the needed conditions without any failure. So design is the really of import portion where maker can analyze the behavior of the constituent. Therefore usage of Finite Element Analysis ( FEA ) is now widespread in technology design. While it is progressively the norm to utilize FEA, many initial design computations are still carried out utilizing approximative stress-strain ( e.g. strength of stuffs ) techniques.

This undertaking addresses FEA attacks in the Engineering Design field. Mechanical elements such as shaft, structure/frames, brackets and place belt lingua is analysed utilizing FEA and approximative emphasis analysis attacks. The analysis includes fluctuation in sizes in each machine component and besides,

Collection of equations and computation of approximative stress-strain analysis for mechanical elements.

FEA consequences for mechanical elements.

Comparative analysis of consequences from approximative stress-strain analysis and FEA.

Recommendations /guidelines choosing analysis attack for mechanical elements design.

## Chapter-2

## Introduction to each mechanical component considered for analysis

## Frame-truss

A frame or infinite construction is a truss-like, lightweight stiff construction constructed from meshing prances in a geometric form. Frames normally utilize a multidirectional span, and are frequently used to carry through long spans with few supports. They derive their strength from the built-in rigidness of the triangular frame ; flexing tonss ( flexing minutes ) are transmitted as tenseness and compaction tonss along the length of each prance.

Most frequently their geometry is based on Platonic solids. The simplest signifier is a horizontal slab of meshing square pyramids built from aluminum or cannular steel prances. In many ways this looks like the horizontal jib of a tower Crane repeated many times to do it wider. A stronger purer signifier is composed of meshing tetrahedral pyramids in which all the prances have unit length. More technically this is referred to as an isotropic vector matrix or in a individual unit width an eight truss. More complex fluctuations change the lengths of the prances to swerve the overall construction or may integrate other geometrical forms.

Figure-frame-truss

## Seat belt lingua

Seat belt plays a critical function in cars particularly in autos. Seat belts prevent the auto driver from clashing with the maneuvering other co-travellers hitting from front board, at the clip accident. Seat belt possesses a ego locking system, which works rule of whip lash action. When a force or burden is applied all of a sudden the place belt gets locked.

Figure -seat belts with locking system

Therefore the locks are really of import in forestalling the accidents. Failure of these locks causes life loss. This is of imperativeness tantrum type. As shown in the above figures.

## Shaft

Shaft is a mechanical constituent for conveying torsion and rotary motion, normally used to link other constituents of a thrust train that can non be connected straight because of distance or the demand to let for comparative motion between them. Drive shafts are bearers of torsion: they are capable to tortuosity and shear emphasis, tantamount to the difference between the input torsion and the burden. They must hence be strong plenty to bear the emphasis, whilst avoiding excessively much extra weight as that would in bend increase their inactiveness.

Figure-shafts

Shafts based upon nature of work called with different names as axle, thrust shaft, airing shafts, etc

## Bracket

A bracket is a mechanical constituent made of metal or metal metals that overhangs a wall to back up or transport weight. It may besides back up a statue, the spring of an arch, a beam, or a shelf. Brackets are frequently in the signifier of coils, and can be carved, dramatis personae, or moulded.

Figure-bracket

Brackets besides act as an component in the systems used to mount modern facade cladding systems onto the exterior of modern edifices every bit good as inside

## Chapter-3

## Problem definition of each mechanical constituent

## Frame-truss

Frame figure with dimensions ( inches )

Loads= perpendicular =25000lb.

=horizontal =20000lb

Thickness of the cross section= ( 1×1 ) in2, ( 2×2 ) in2, ( 3×3 ) in2

Material considered= steel= E=29.5 e 6 pounds per square inch

=0.3

Frame is fixed and provided tonss as shown in the figure, perpendicular and horizontal. Design and analysis is done by sing these tonss and changing the thickness.

## Seat belt lingua

Seat belt tongue figure with dimensions ( millimeter )

Load= 1000N.

Thickness=2.5mm and 5mm

Material considered= Aluminium metal, E=71.1e3 N/mm2,

=0.34

Due to flog lash minute, sudden burden is applied on the place belt lingua. Design and analysis is done sing this burden and changing the thickness.

## Shaft

Shaft figure with dimensions ( millimeter )

Loads= axial=2000N.

Radius of the shaft=25mm, 35mm

Material considered= steel, E=2e5N/mm2

=0.3

Shaft is fixed at one terminal and is made to back up burden, axial. Design and analysis is done by sing this burden and changing the shaft radius.

## Bracket

Bracket figure with dimensions ( millimeter )

Loads= perpendicular =2500N.

=horizontal =4330N

Thickness of the cross section= ( 35×35 ) mm2, ( 35×70 ) mm2

Material considered= steel, E=2.1e5MPa

=0.3

Bracket is fixed at one terminal and is made to back up burden, perpendicular and inclined ( constituents are resolved and considered as horizontal and perpendicular tonss ) . Design and analysis is done by sing these tonss and changing the thickness.

## Chapter-4

## Design and analysis of each mechanical constituent

## Frame-truss

Mechanical properties-E=29.5 vitamin E 6 pounds per square inch, v=0.3

Area of cross subdivision considered 1X1 sq.in, 2X2 sq.in and 3×3 sq.in

Element Number — —

Supplantings — — — Q

Unit of measurements considered-load =lb

Distance=inches

## Design & A ; Analysis Solution

## Nodal co-ordinates

Node

Ten

Yttrium

1

0

0

2

40

0

3

40

30

4

0

30

## Element connectivity tabular array

Component

1

2

1

1

2

2

3

2

3

1

3

4

4

3

## Directional cosines- ,

Where, =effective length

ten, y are co-ordinates

Component

lupus erythematosus

cubic decimeter

m

1

40

1

0

2

30

0

-1

3

50

0.8

0.6

4

40

1

0

## Stiffness matrix-k

Here we calculate the K for each component and assemble for full job based on element connectivity.

Calculating the K for country of cross subdivision — — 1×1

Tocopherol — — 29.5e6

## For element-1

or

Here the top numerical, 1234-dof indicate the grades of freedom

## For element-2

Or

## For Element -3

Or

## For element-4

Or

## Assembling K matrix

Or

As, Q1=Q2=Q4=Q7=Q8=0, can be seen from the fig.

Therefore merely Q3, Q5, Q6 possess force or supplanting.

Reducing the above assembled matrix

We get,

Solving the above matrix, we get

## Stresss

Calculating the emphasis in elements 1 and 2

=20000 pounds per square inch

=-21880 pounds per square inch

## Strains

=20000/29.5e6

=0.00676

=-21880/29.5e6

=-0.000268

## Component considered for analysis in ansys

## Beam2D- elastic 3

Figure-Beam3 geometry

BEAM3 is a uniaxial component with tenseness, compaction, and flexing capablenesss. The component has three grades of freedom at each node: interlingual renditions in the nodal ten and y waies and rotary motion about the nodal z-axis.

Figure -BEAM3 Geometry shows the geometry, node locations, and the co-ordinate system for this component. The component is defined by two nodes, the cross-sectional country, the country minute of inactiveness, the tallness, and the stuff belongingss. The initial strain in the component ( ISTRN ) is given by I”/L, where I” is the difference between the component length, L ( as defined by the I and J node locations ) , and the nothing strain length. The initial strain is besides used in ciphering the emphasis stiffness matrix, if any, for the first cumulative loop.

## BEAM3 Stress Output

## Figure-BEAM3 Stress Output

## For 1×1 cross subdivision

Defined job theoretical account in ansys with two views-oblique and forepart

Boundary conditions

Boundary conditions and burden application on the model-oblique and front position

Deformed and Displacements figures for 1x1cs prob

Q5, Q3, Q6 values and at their respective deformed locations

Stress and strain diagrams for 1×1 Cs job

## For 2×2 Cs job

Deformed form and supplanting value for 2×2 Cs job

Stress and strain diagrams for 2×2 Cs job

## For 3×3 Cs job

Deformed, emphasis and strain figures for 3×3 Cs job

## Comparative tabular array among the values for different transverse subdivisions of frame-truss

## A

1×1

2×2

3×3

Q3

0.027099

0.00676

0.002993

Q5

0.005658

0.001421

0.000636

Q6

-0.02224

-0.00555

-0.002463

I?1A

19985

4985

2208

I?2A

-21867

-5460

-2422

A Iµ1

0.000677

0.000169

0.000074

Iµ2A

-0.00074

-0.00019

-0.0000821

## Consequences

Maximal Stress in all instances is below the output emphasis of the steel, so the design of frame truss is safe.

As the country cross subdivision of the frame truss additions, the emphasis value decreases hence factor of safety additions.

The distortion of the frame truss decreasing as the cross subdivision of the frame truss is increasing. Hence the frame trusses possess good stiffness.

## Seat belt lingua

Mechanical belongingss of aluminium metal, E=71.1e3 N/mm2, =0.34

Thickness=2.5mm and 5mm.

## Design & A ; Analysis Solution

Seat belt lingua is considered to be in plane emphasis status with thickness option. One terminal of the place belt lingua is fixed as boundary status ( shown in ansys figure ) .

Plane emphasis status

— — -D

Jacobian matrix, J=

B=displacement matrix,

KQ=F

I?=DBq

Iµ=Bq

## Component considered for analysis in ansys

## Solid-quad 4node 42 ( plane 42 )

## Figure-PLANE42 Geometry

PLANE42 is used for 2-D mold of solid constructions. The component can be used either as a plane component ( plane emphasis or plane strain ) or as an axisymmetric component. The component is defined by four nodes holding two grades of freedom at each node: interlingual renditions in the nodal ten and y waies. The component has malleability, weirdo, swelling, emphasis stiffening, big warp, and big strain capablenesss.

Seat belt tongue theoretical account in ansys

Seat belt tongue theoretical account in ansys-meshed

Seat belt tongue theoretical account in ansys-boundary conditions and burden application and reaction forces ( shown in pink coloring material )

## For 2.5mm thickness

Stress, =1000/ ( 50×2.5 ) =8 N/mm2

Strain, =1.11e-4

Seat belt lingua in ansys-stress consequences

Seat belt lingua in ansys-strain consequences

## For 5mm thickness

Stress, =1000/ ( 5×50 ) =4 N/mm2

Strain, =4/71.7e3=5.57e-5

Seat belt lingua in ansys-stress consequences

Seat belt lingua in ansys-strain consequences

## Comparison

Thickness

emphasis N/mm2

strain

2.5

8

1.11E-04

5

4

5.57E-05

## Consequences

Maximal Stress in both instances is below the output emphasis of the aluminum alloys, so the design of the place belt lingua is safe.

Maximum emphasis is found in the locality of crisp corners, so crisp corners can be avoided to cut down the emphasis concentration in those peculiar countries to avoid failure.

As the thickness of the place belt lingua additions, the emphasis value decreases hence factor of safety additions.

The distortion of the place belt lingua is diminishing as the thickness is increasing. Hence the place belt tongue possess good stiffness.

## Shaft

A round shaft given axial burden of 2000N, changing its radius,25mm, 35mm. its mechanical belongingss, E=2e5 N/mm2, =0.3

## Design & A ; Analysis Solution

The round shaft is considered to be a line section to transport on the analysis on the shaft. Load is applied axially.

[ K ] [ Q ] = [ F ]

Iµ=I?/E

## Component considered for analysis in ansys

## Beam -3D-2node 188

## Figure-BEAM188 Geometry

BEAM188 is suited for analysing slender to reasonably stubby/thick beam constructions. This component is based on Timoshenko beam theory. Shear distortion effects are included.

BEAM188 is a additive ( 2-node ) or a quadratic beam component in 3-D. BEAM188 has six or seven grades of freedom at each node, with the figure of grades of freedom depending on the value of KEYOPT ( 1 ) . When KEYOPT ( 1 ) = 0 ( the default ) , six grades of freedom occur at each node. These include interlingual renditions in the ten, Y, and omega waies and rotary motions about the ten, Y, and omega waies. When KEYOPT ( 1 ) = 1, a 7th grade of freedom ( falsifying magnitude ) is besides considered. This component is well-suited for additive, big rotary motion, and/or big strain nonlinear applications.

shaft line theoretical account in ansys

shaft theoretical account in ansys

shaft theoretical account in ansys-boundary conditions and burden application

## for shaft radius=25mm

emphasis, N/mm2

strain, =5×10-6

shaft theoretical account in ansys-stress consequences

shaft theoretical account in ansys-strain consequences

## for shaft radius=35mm

emphasis, N/mm2

strain, =2.595 x10-6

Shaft theoretical account in ansys-stress consequences

shaft theoretical account in ansys-strain consequences

## Comparison

radius of shaft

emphasis N/mm2

strain

25

1.018

5×10-6

35

0.519

2.595×10-6

## Consequences

Maximal Stress in both instances is below the output emphasis of steel, so the design of the shaft is safe.

Since the burden is applied axially the emphasis distribution is same through out the line section.

As the radius of the shaft additions, the emphasis value decreases hence factor of safety additions.

The distortion of the shaft is diminishing with the addition in radius of the shaft. Hence the shaft possess good stiffness

## Bracket

A bracket fixed to the wall, supports the perpendicular and horizontal burden.

Material belongingss are,

E=2.1e5MPa

=0.3

Area of cross subdivision considered for the bracket

35 ten 70 sq.mm

35 ten 35 sq.mm

## Design & A ; Analysis Solution

The bracket is assumed to be fixed to the wall to back up the perpendicular and inclined tonss. Inclined tonss are resolved in to constituents and assigned as perpendicular and horizontal tonss. The bracket is represented in the signifier of line sections in ansys to transport on analysis.

[ K ] [ Q ] = [ F ]

Iµ=I?/E

## Component considered for analysis in ansys

## Beam2D- elastic 3

Figure-Beam3 geometry

BEAM3 is a uniaxial component with tenseness, compaction, and flexing capablenesss. The component has three grades of freedom at each node: interlingual renditions in the nodal ten and y waies and rotary motion about the nodal z-axis.

Figure -BEAM3 Geometry shows the geometry, node locations, and the co-ordinate system for this component. The component is defined by two nodes, the cross-sectional country, the country minute of inactiveness, the tallness, and the stuff belongingss. The initial strain in the component ( ISTRN ) is given by I”/L, where I” is the difference between the component length, L ( as defined by the I and J node locations ) , and the nothing strain length. The initial strain is besides used in ciphering the emphasis stiffness matrix, if any, for the first cumulative loop.

## BEAM3 Stress Output

## Figure-BEAM3 Stress Output

Bracket- line theoretical account in ansys

Bracket theoretical account in ansys

Bracket component theoretical account in ansys

Bracket component theoretical account in ansys- boundary conditions and burden application

## For cs=35×70

Stress, =1.7673 N/mm2

Strain, =8.415×10-6

Bracket component theoretical account in ansys- emphasis consequences

Bracket component theoretical account in ansys- strain consequences

## For cs=35×35

Stress, =3.535 N/mm2

Strain, =1.683×10-5

Bracket component theoretical account in ansys- emphasis consequences

Bracket component theoretical account in ansys- strain consequences

## Comparison

country of cross subdivision

emphasis N/mm2

strain

35×35

3.535

1.683×10-5

35×70

1.7673

8.415×10-6

## Consequences

Maximal Stress in all instances is below the output emphasis of the steel, so the design of the bracket is safe.

As the country cross subdivision of the bracket additions, the emphasis value decreases hence factor of safety additions.

The distortion of the bracket is diminishing as the country of cross subdivision is increasing. Hence the bracket possess good stiffness.

## Chapter-5

## Decisions

In all the instances the maximal emphasiss are under their several output strengths. So, their designs are safe under their several applied loading conditions.

The distortion of all the constituents are diminishing as the country of their several cross subdivision or thickness is increasing. Hence the constituents possess good stiffness.

The factor of safety is tolerably high sing the distortion to the tonss in all the instances.

## Recommendation

The emphasiss are really below to the output strength of their several stuffs. Material optimisation i.e. diminishing the dimensions can be done to the same working tonss i.e. applied tonss.

Crisp corners induce high emphasiss which leads failure due to high emphasis concentration, which is a major factor for the break of the constituents.

## Chapter-6

## General process carried to work out the jobs in ansys.

The undermentioned process is followed to work out the job in ansys.

Pre-processor & gt ; element type-required component is selected

Pre-processor & gt ; existent constants-areas of cross subdivision, minute of inactiveness is selected.

Pre-processor & gt ; material properties-material belongingss are selected.

Pre-processor & gt ; modelling-the modeling of the needed geometry is created.

Pre-processor & gt ; meshing-full theoretical account is made into finite elements utilizing the engagement.

Solution & gt ; define loads-boundary conditions and burden are applied.

Solution & gt ; solve-the defined job is solved.

General station processor & gt ; plot results-to read and plot the consequences.