Structural dynamics
The purpose of this project was to perform static analysis on two models of plate with holes using SolidWorks. In the first model, a plate with a single hole in centre was created and a static analysis was performed on it. In the second model, a plate with three holes (one in centre & other two at some distance from the centre) was created and static analysis was performed on it. Further; stress, displacement, strain & factor of safety plots of both the analysis was compared and a conclusion was made from the analysis results.
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CONTENTS:
1. Introduction
- Static Analysis
- Stress
- Displacement
- Strain
- Factor of Safety
2. Static Analysis
- Case 1: Metal Plate with single hole
- Geometry Model
- Material Condition
- Boundary Condition
- Load Condition
- Mesh Parameter
- Result
- Case 2: Metal Plate with three holes
- Geometry Model
- Material Condition
- Boundary Condition
- Load Condition
- Mesh Parameter
- Result
3. Overall Result
4. Evaluation
5. Conclusion
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1. INTRODUCTION:
Static Analysis
Static FEA is based on the assumption that time does not play important role and its influence on the results can be ignored. In case of solid mechanics simulations, it means that load and response to it are static. In case of fluid mechanics and heat transfer analyses it means that we only get the stationary solution - when there are no more temperature/velocity/pressure differences and no flow (fluid or heat) occurs. So basically, all static analyses search for equilibrium state, be it mechanical, thermodynamics etc.
Stress
Stress is the force per unit area on a body that tends to cause it to change shape.
Stress is a measure of the internal forces in a body between its particles. These internal forces are a reaction to the external forces applied on the body that cause it to separate, compress or slide. External forces are either surface forces or body forces. Stress is the average force per unit area that a particle of a body exerts on an adjacent particle, across an imaginary surface that separates them.
The formula for uniaxial normal stress is: σ = F/A
where σ is the stress, F is the force and A is the surface area.
In SI units, force is measured in newtons and area in square metres. This means stress is newtons per square meter, or N/m2. However, stress has its own SI unit, called the pascal. 1 pascal (symbol Pa) is equal to 1 N/m2.
Displacement
Displacement is the distance moved by a particle or body in a specific direction. It can also be defined as the amount to which a particular point in a body is displayed.
Strain
Strain, represented by the Greek letter ε, is a term used to measure the deformation or extension of a body that is subjected to a force or set of forces. The strain of a body is generally defined as the change in length divided by the initial length.
ε = ΔL/L
Factor of Safety
The ratio of a structure's absolute strength (structural capability) to actual applied load; this is a measure of the reliability of a particular design. In engineering, a factor of safety (FoS), also known as safety factor (SF), expresses how much stronger a system is than it needs to be for an intended load. Safety factors are often calculated using detailed analysis because comprehensive testing is impractical on many projects, such as bridges and buildings, but the structure's ability to carry a load must be determined to a reasonable accuracy.
Many systems are intentionally built much stronger than needed for normal usage to allow for emergency situations, unexpected loads, misuse, or degradation (reliability).
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2. STATIC ANALYSIS
Case 1: Metal Plate with single hole
Geometry Model:
The model was created in SolidWorks as per the given dimensions.
Length=300mm
Height=120mm
Thickness=30mm
Circular Hole at the centre:
Diameter=60mm
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Material Condition:
Alloy Steel (Yield Strength = 620.42 MPa) was applied as a material to the beam.
Linear Elastic Isentropic was selected as a material model.
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Boundary Condition:
The plate was fixed from the shorter side.
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Load Condition:
Uniformly Distributed Load (UDL) of 1000 Newton was applied on the face having shorter side of the plate.
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Mesh Parameter:
The beam was refined with standard triangular mesh of size 20 mm.
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Result:
The result consists of four plots (Stress Plot, Displacement Plot, Strain Plot & Factor of Safety Plot).
The below 3 figures represents plots with deformed geometry which indicates how the part will fail if it exceeds the yield strength. In this analysis, the design is safe.
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Since, the applied load is very less as compared to critical load and induced stresses are also less than the yield strength. Therefore, the design is safe and can be better understood by the true plots. The below four figures represent the true plots.
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Case 2: Metal Plate with three holes
Geometry Model:
The model was created in SolidWorks as per the given dimensions.
Length=300mm
Height=120mm
Thickness=30mm
Circular Hole at the centre:
Diameter=60mm
Additionally, two holes of 30 mm diameter which are placed 90mm away from the central hole on both sides.
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Material Condition:
Alloy Steel (Yield Strength = 620.42 MPa) was applied as a material to the beam.
Linear Elastic Isentropic was selected as a material model.
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Boundary Condition:
The plate was fixed from the shorter side.
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Load Condition:
Uniformly Distributed Load (UDL) of 1000 Newton was applied on the face having shorter side of the plate.
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Mesh Parameter:
The beam was refined with standard triangular mesh of size 20 mm.
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Result:
The result consists of four plots (Stress Plot, Displacement Plot, Strain Plot & Factor of Safety Plot).
The below 3 figures represents plots with deformed geometry which indicates how the part will fail if it exceeds the yield strength. In this analysis, the design is safe.
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Since, the applied load is very less as compared to critical load and induced stresses are also less than the yield strength. Therefore, the design is safe and can be better understood by the true plots. The below four figures represent the true plots.
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OVERALL RESULT:
The 2nd case i.e. plate with three holes is the best as the induced stresses, displacement, strain & weight are less while both the minimum & maximum values of factor of safety are more in comparison with the plate with single hole.From the above table, we can observe that in the 1st case the first four values are quite more as compared to the 2nd case. In practical, for first four properties, minimum values are desired for an optimum design due to which 2nd case is preferred here. For the remaining two properties, the 2nd case has high values as compared to 1st case and as high factor of safety is always preferred; the 2nd case proved to be the best.
This happens due to the fact that stress lines gets contracted & concentrated due to single hole while multiple holes tends to uniformly distribute the stress lines over the geometry resulting in less stresses & increased strength.
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EVALUATION:
Through static analysis; stress, displacement, strain & more analysis can be performed for the required part or object. In this project, the analysis of plate with holes was performed to observe the behaviour of plate when under tensile load. These kind of basic FEA problems are necessary to understand how the component behaviour changes due to the changes in its geometry. The holes are basically provided either due to the requirement or to reduce the weight & sometimes also to improve the strength & life of the component. Overall, this project helped in polishing the concepts related to static analysis.
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CONCLUSION: