Finite Element Analysis And Mechanincal Elements Engineering Essay Example

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 belts play a critical function in cars, particularly in autos. Seat belts prevent the auto driver from clashing with the maneuvering other co-travelers hitting from the front board, at the time of an accident.The seat belt is equipped with a locking system that operates based on the principle of whip lash action. This locking mechanism is crucial in preventing accidents, and failure of these locks can lead to loss of life. The importance of these locks is demonstrated in the figures above.

A shaft is a mechanical component used for transmitting torsion and rotary motion. It serves to connect other components of a drivetrain that cannot be directly connected due to distance or the need for relative motion between them. Drive shafts are designed to withstand torsion and shear stress, equivalent to the difference between the input torque and the load. They must be strong enough to handle this stress while avoiding excessive weight, which would increase their inertia. The figures above depict various types of shafts, such as axles, drive shafts, and ventilation shafts.

A bracket is a metal or metal alloy

component that extends from a wall to provide support or carry weight. It can also be used to support statues, the spring of an arch, a beam, or a shelf. Brackets can come in the form of coils and can be carved, cast, or molded.Brackets are used as a component in systems that mount modern facade cladding systems onto the exterior and interior of buildings. In Chapter 3, we will define the problem of each mechanical component. Let's start with the frame truss, which has specific dimensions and loads. The thickness of the cross section varies, and the material used is steel. The frame is fixed and provided with loads as shown in the figure. We will design and analyze the frame by considering these loads and adjusting the thickness.

Moving on to the seat belt tongue, it has its own dimensions and a specific load applied. The thickness of the tongue varies, and the material used is aluminium metal. Due to sudden burden moments, we need to design and analyze the seat belt tongue by considering this load and adjusting the thickness.

Lastly, we have the shaft, which also has specific dimensions and loads. The radius of the shaft varies, and the material used is steel. The shaft is fixed at one end and supports axial loads. We will design and analyze the shaft by considering this load and adjusting the shaft radius.

Bracket

Bracket figure with dimensions (millimeter)
Loads: perpendicular = 2500N, horizontal = 4330N
Thickness of the cross section: (35x35) mm2, (35x70) mm2
Material considered: steel, E=2.1e5MPa, v=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 loads). Design and analysis is done by considering these loads and changing the thickness.

Chapter-4

Design and analysis of each mechanical constituent

Frame-truss

Mechanical properties: E=29.5E6 pounds per square inch, v=0.3
Area of cross subdivision considered: 1X1 sq.in, 2X2 sq.in, and 3x3 sq.in
Element Number -- --
Supplantings -- -- -- Q
Unit of measurements considered-load = lb
Distance = inches

Design & Analysis Solution

Nodal co-ordinates

Element connectivity table

Directional cosines-

Where, =effective length
x, 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 the full job based on element connectivity.

Calculating the K for country of cross subdivision -- -- 1x1 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 also used in calculating the stress stiffness matrix for the first cumulative loop.

BEAM3 Stress Output

Figure-BEAM3 Stress Output

For 1x1 cross subdivision

Defined job model in ANSYS with two views - oblique and front.
Boundary conditions and load application on the model - oblique and front view.
Deformed and displacement figures for 1x1cs problem.
Q5, Q3, Q6 values and their respective deformed locations.
Stress and strain diagrams for 1x1 Cs job.

For 2x2 Cs job

Deformed shape and displacement values for 2x2 Cs

job.
Stress and strain diagrams for 2x2 Cs job.

For 3x3 Cs job

Deformed, stress, and strain figures for 3x3 Cs job.

Comparative table among the values for different transverse subdivisions of frame-truss

A

1x1 2x2 3x3
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

Results

The maximum stress in all cases is below the ultimate stress of the steel, indicating that the design of the frame truss is safe. As the area cross-section of the frame truss increases, the stress value decreases, leading to an increase in the factor of safety. The deformation of the frame truss decreases as the cross-section of the frame truss increases.Therefore, the frame trusses exhibit good stiffness.

Seat belt tongue

The mechanical properties of aluminum metal are as follows: E=71.1e3 N/mm2, ?=0.34 Thickness=2.5mm and 5mm.

Design & Analysis Solution

The seat belt tongue is assumed to be in a plane stress condition with thickness options. One end of the seat belt tongue is fixed as a boundary condition (shown in the ansys figure).

FEM related equations to compute the stress and strain

In a plane stress condition: Jacobian matrix, J= B=displacement matrix, KQ=F I?=DB? I?=B?

Component considered for analysis in ansys

Solid-quad 4node 42 ( plane 42 )

Figure-PLANE42 Geometry

PLANE42 is utilized for 2-D modeling of solid structures. The component can be used for either plane stress or plane strain analysis, as well as axisymmetric analysis. The component has four nodes with two degrees of freedom at each node: translations in the nodal x and y directions. It has capabilities for elasticity, bending, swelling, stress stiffening, large deflection, and large strain.Seat belt tongue theoretical model in Ansys:
- Meshed model
- Boundary conditions and burden application and reaction forces (shown in pink color)

For 2.5mm thickness:

Stress = 1000 / (50 x 2.5) = 8 N/mm2
Strain = 1.11e-4

Seat belt tongue in Ansys - Stress results
Seat belt tongue in Ansys - Strain results

For 5mm thickness:

Stress = 1000 / (5 x 50) = 4 N/mm2
Strain = 4 / 71.7e3 = 5.57e-5

Seat belt tongue in Ansys - Stress results
Seat belt tongue in Ansys - Strain results

Comparison:

Thickness | Stress N/mm2 | Strain
2.5 | 8 |1.11E-04
5 | 4 |5.57E-05

Consequences:

The maximum stress in both cases is below the output stress of the aluminum alloys, ensuring the safety of the design of the seat belt tongue.
The highest stress is found in the areas with sharp corners, so avoiding sharp corners reduces stress concentration and prevents failure.
As the thickness of the seat belt tongue increases, the stress value decreases, resulting in an increase in the factor of safety.
The distortion of the seat belt tongue decreases

as the thickness increases, indicating good stiffness.

Shaft:

A round shaft with an axial burden of 2000N, varying its radius from 25mm to 35mm.
Its mechanical properties: E=2e5 N/mm2, Poisson's ratio (v) = 0.3.

Design & Analysis

Analysis Solution

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

Fem related equations to cipher the emphasis and strain

[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.The theoretical model of the shaft in ANSYS includes boundary conditions and load application. For a shaft with a radius of 25mm, the stress and strain are specified as follows: emphasis = N/mm2, strain = 5x10-6. The ANSYS analysis also provides stress and strain results for the shaft.

Similarly, for a shaft with a radius of 35mm, the stress and strain values are: emphasis = N/mm2, strain = 2.595 x10-6. The ANSYS analysis provides stress and strain results for this

shaft as well.

Comparing the two shafts, the following information is obtained:
- Radius of shaft:
- For 25mm radius: emphasis = 1.018 N/mm2, strain = 5x10-6
- For 35mm radius: emphasis = 0.519 N/mm2, strain = 2.595 x10-6

The results show that the maximum stress in both cases is below the output stress of steel, indicating that the design of the shaft is safe. Since the load is applied axially, the stress distribution is uniform throughout the shaft.

As the radius of the shaft increases, the stress value decreases, leading to an increase in factor of safety. Additionally, as the radius increases, the distortion of the shaft decreases, indicating better stiffness.

Moving on to the bracket fixed to the wall, it supports both vertical and horizontal loads. The material properties considered are: E=2.1e5MPa and ?=0.3. The cross-sectional area considered for the bracket is either 35x70 sq.mm or 35x35 sq.mm.

The design and analysis solution assumes that the bracket is fixed to the wall to support both vertical and inclined loads.The text below isand unified, keeping the and their contents:

Inclined loads are divided into perpendicular and horizontal loads. The brackets are represented as line segments in ANSYS for analysis.

Equations related to Finite Element Method (FEM) are used to calculate stress and strain: [ K ] [ Q ] = [ F ], Iµ = I?/E.

ANSYS considers the following components for analysis:

- Beam2D- elastic 3.

Figure-Beam3 geometry shows the geometry, node locations, and coordinate system for the BEAM3 component. BEAM3 is a uniaxial component capable of withstanding tension, compression, and bending. Each node of the component has three degrees of freedom: translations in the x and y

directions, and rotation about the z-axis.

The geometry of the component is defined by two nodes, cross-sectional area, area moment of inertia, height, and material properties. The initial strain (ISTRN) in the component is calculated as I/L, where I is the difference between the component length (defined by node locations I and J) and the zero strain length.

The initial strain is also used to calculate the stress stiffness matrix 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=35x70

Stress, =1.7673 N/mm2
Strain, =8.415x10-6

Bracket component theoretical account in ansys- emphasis consequences

Bracket component theoretical account in ansys- strain consequences

For cs=35x35

Stress, =3.535 N/mm2
Strain, =1.683x10-5

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 35x35 3.535 1.683x10-5 35x70 1.7673 8.415x10-6

Consequences

Maximal Stress in all instances is below the output emphasis of the steel, so the design of the bracket is safe. As the area cross subdivision of the bracket increases, the emphasis value decreases hence factor of safety increases. The distortion of the bracket is diminishing as the area of cross subdivision is increasing. Hence the bracket possess good stiffness.

Chapter-5

Decisions

In all the instances the maximal stresses are under their respective output strengths. So, their designs are safe under their respective applied loading conditions.The stiffness of the

constituents is improved when the country or thickness of their respective cross subdivisions increases, resulting in a reduction of distortion. Consequently, the factor of safety is reasonably high for all load cases.

Recommendation

The stresses exerted on the materials are well below their output strength. Material optimization can be achieved by reducing the dimensions while maintaining the same applied loads. Sharp corners should be avoided as they lead to high stress concentrations, which can cause component failure.

Chapter-6

General process for problem solving in ANSYS

The following steps are followed to solve problems in ANSYS:

Pre-processor ;gt; Select element type and required components.
Pre-processor ;gt; Select existing constants for cross-section areas and moments of inertia.
Pre-processor ;gt; Select material properties.
Pre-processor ;gt; Create the necessary geometry.
Pre-processor ;gt; Generate finite elements using meshing techniques.
Solution ;gt; Define loads and apply boundary conditions.
Solution ;gt; Solve the defined problem.
General post-processor ;gt; Plot and interpret the results.