ANALYSIS OF PLATE WITH HOLES
AIM
Performing a static analysis on two models of plate with holes.
THEORY
The story or history of the analysis of stress concentrations begins in 1898 with Ernst Gustav Kirsch's linear elastic solution for stresses around a hole in an infinite plate. The stress concentration can in fact vary from two to four for more complex loading conditions, i.e. stress states different from uniaxial tension.
Stress concentration
Stress Concentration is the area of the element where the stress is significantly greater compared to other position on the element. The areas where the stress is increased in an element is known as stress concentration. It occurs when there are irregularities in the geometry or material of a structural component that cause an interruption to the flow line of stress. The holes are made to satisfy process requirements, reduce weight, economics etc. Due to irregularity in geometry, stress concentration occurs around the irregularity, due to this factor the material may fail due to large stress near the holes. This is not desirable in any case. Thus, analysis is run to study the stress concentration and knowing the FOS of the element is very important to design the component.
OBJECTIVE
Modelling the component as shown below
CASE 1
Length=300mm
Height=120mm
Thickness=30mm
Circular Hole at the center:
Diameter=60mm
The dimensions for the second case is as follows:
CASE 2
Length=300mm
Height=120mm
Thickness=30mm
Circular Hole at the center:
Diameter=60mm
Two holes of 30 mm diameter which are placed 90mm away from the central hole on both sides.
Applying a fixed relation to one of the short side of the plate and applying a force of 1000N on the other such that the plate is stretched.
Running the analysis and compare the results for stress, strain and displacement
PROCEDURE
CASE 1
1. Creating the model with centre circular hole
2. Run the static analysis.
CASE 2
1. Creating the model of a plate having a circular hole at its center and two more holes at a certain distance away from the central holes then,
2. Run a static analysis.
3. Comparing the results and considering the best one.
MATERIAL- ALLOY STEEL
MESHING (same for both cases)
size=3mm
tolerance=0.25mm
CASE 1
ANALYSIS OF PLATE WITH SINGLE HOLE AT CENTRE
Following steps are done
1. Create a model with required dimensions.
2. Run the Static analysis.
3. Apply the material as Alloy Steel.
4. Apply the fixtures.
5. Apply the loads
6. Generate a mesh with appropriate parameters.
7. Run the study.
CONSTRAINTS and LOADING
Now the model is created , we will setup the static analysis and apply the constraints and loads
MESH GENERATION
RESULTS
1. STRESS DISTRIBUTION (ACCORDING TO VON MISES)
2. DISPLACEMENT
3. STRAIN DISTRIBUTION
CASE 2
ANALYSIS OF PLATE WITH 3 HOLES AT DIFFERENT POSITION
Following steps are done
1. Create a model with required dimensions.
2. Run the Static analysis.
3. Apply the material as Alloy Steel.
4. Apply the fixtures.
5. Apply the loads
6. Generate a mesh with appropriate parameters.
7. Run the study.
CONSTRAINTS and LOADING
Now the model is created , we will setup the static analysis and apply the constraints and loads
MESH GENERATION
RESULTS
1. STRESS DISTRIBUTION (ACCORDING TO VON MISES)
2. DISPLACEMENT
3. STRAIN DISTRIBUTION
RESULT COMPARISION
| GEOMETRY | MAX VON MISES STRESS | MAX DISPLACEMENT | MAXIMUM STRAIN |
| With centre hole in a plate | 1.194 | 0.001 | 4.269e-06 |
| Three holes in a plate | 1.128 | 0.001 |
3.980e-06 |
CONCLUSION
- Stress and strain values are less in a plate with three holes compared to plate with single hole. This is due to smooth flow line of stress in case of plate with 3 holes were as in case of plate with single hole the flow lines are suddenly restrictrd by the centre hole there by increasing the stress at that specified area around the hole
- The displacement in both cases is almost same.
- Maximum stress is observed around the circular hole and that itself is a stress concentrated area.
- In case of plate with 3 holes, it can be observed that the stress is more distributed than in the plate with a centre hole.
- So, plate with three holes is better option because the stress lines are almost distributed evenly.