Aim: -

The study of the behavior of a plate having holes under tension or stretching conditions is the main aim of this study.

Introduction: -

Stress concentration: -

Stress Concentration is the location of an area of the element where the stress is significantly greater than its surrounding areas. The areas where the stress is concentrated in an element is known as stress concentration. Stress concentrations occur when there are irregularities in the geometry or material of a structural component that cause an interruption to the flow of stress.

Stress concentration at holes: -

The holes are made on any part to satisfy functional requirements, reduce weight, achieve the economic benefits, etc. As holes create an irregularity in geometry, stress concentration often occurs at these holes. The stress concentration might fail the part. This is not desirable in any case. Thus, analysis is run to study the stress concentration and get the FOS of the element. In our case, there are holes on a rectangular metal plate. The plate is stretched from one side while the other side is fixed. Thus, it will result in the stress concentration around the holes due to irregularities in geometry which causes interruption to the flow of stress.

Objective/Tasks: -

1. To create a model of a plate having a circular hole at its center and then, run a static analysis.
2. To create a model of a plate having a circular hole at its center and two more holes at a certain distance from the central holes then, run a static analysis.
3. Compare the results and suggest the best one.

Common analysis settings for all analysis: -

Following are the details of all the analysis: -

Material Selection: -

The material used for all the analyses is Steel Alloy. The properties of the alloy steel are shown in figure 1.

Figure 1. Properties of alloy steel.

Mesh Parameters: -

Figure 2 shows the parameters used for the fine mesh. The mesh parameters were the same for all the analysis models.

Figure 2. Mesh parameters.

Case 1: Static Analysis of plate having a circular hole at its centre.

Procedure: -

The procedure used for the analysis is as follows

1. Create a sketch of the model having a circular hole at its center and extrude it to 30 mm.
2. Start a new study. Under it select Static analysis and name it as the plate with one hole.
3. Apply the Alloy Steel Material
4. Apply the fixtures.
5. Apply the loads
6. Generate a mesh with appropriate parameters.
7. Run the study.

Analysis Setup: -

Model: -

First of all, a sketch was made from the dimensions given below as shown in figure 3.

• Length = 300mm
• Height = 120 mm
• Thickness = 30 mm.
• A circular hole at the center: Diameter = 60 mm.

Figure 3. Sketch of the plate.

The sketch was then extruded up to 30 mm (it’s the thickness of the plate). The 3 – Dimensional model is shown in figure 4.

figure 4.

Model of the plate.

Fixture: -

The plate was supposed to be fixed at one of the smaller ends of the plate. Figure 5 shows the fixed geometry on the plate.

Figure 5. Fixed geometry on the plate.

Loads: -

The load was applied to the other smaller face of the plate such that it is stretched. This means that the direction of the force must be outward i.e. the plate is pulled. A load of 1000 N is applied which is shown in figure 6.

Figure 6. A 1000 N load applied such that the plate is stretched.

Mesh: -

The mesh was done using the parameters shown earlier in figure 2. The meshed model of the plate with one hole is shown in figure 7.

Figure 7. Meshed model of the plate with one hole.

Analysis Results: -

The analysis results are obtained in terms of strain, stress, and displacement plots.

Von Misses Stress Plot:

The Von Misses Stress plot for the plate with a circular hole at its center. It is shown in figure 8. The maximum and minimum stress obtained are 1.212e+06 and 2.643e+04. The maximum stress is obtained at the hole as it is a stress concentration area.

Figure 8. Von Misses stress plot.

Equivalent Strain Plot:

The equivalent strain plot is shown in figure 9. The maximum and minimum strain values are 4.502e-06 and 2.183e-07. The intensity of strain is more at the hole of the plate.

Figure 9. Equivalent Strain Plot.

Displacement Plot:

As the plate is stretched from one side, the displacement is shown in figure 10.

Figure 10. Displacement Plot.

Case 2: Static Analysis of plate having three circular holes.

Procedure: -

The procedure used for the analysis is as follows

1. Create a sketch of the model having the three holes and extrude it to 30 mm.
2. Start a new study. Under it select Static analysis and name it as the plate with one hole.
3. Apply the Alloy Steel Material
4. Apply the fixtures.
5. Apply the loads
6. Generate a mesh with appropriate parameters.
7. Run the study.

Analysis Setup: -

Model: -

First of all, a sketch was made from the dimensions given below as shown in figure 11.

• Length = 300mm
• Height = 120 mm
• Thickness = 30 mm.
• A circular hole at the center: Diameter = 60 mm.
• Two holes of 30 mm diameter are placed 90mm away from the central hole on both sides.

Figure 11. Sketch of the plate.

The sketch was then extruded up to 30 mm (it’s the thickness of the plate). The 3 – Dimensional model is shown in figure 12.

Figure 12. Model of the plate.

Fixture: -

The plate was supposed to be fixed at one of the smaller ends of the plate. Figure 13 shows the fixed geometry on the plate.

Figure 13. Fixed Geometry on the plate.

Loads: -

The load was applied to the other smaller face of the plate such that it is stretched. This means that the direction of the force must be outward i.e. the plate is pulled. A load of 1000 N is applied which is shown in figure 14.

Figure 14. A 1000 N load applied such that the plate is stretched.

Mesh: -

The mesh was done using the parameters shown earlier in figure 2. The meshed model of the plate with one hole is shown in figure 15.

Figure 15. Meshed model of the plate with one hole.

Analysis Results: -

The analysis results are obtained in terms of strain, stress, and displacement plots.

Von Misses Stress Plot:

The Von Misses Stress plot for the plate with a circular hole at its center. It is shown in figure 16. The maximum and minimum stress obtained are 1.169e+06 and 3.674e+04. The maximum stress is obtained at the central hole similar to that of the previous analysis. The holes are the stress concentration areas.

Figure 16. Von Misses stress plot.

Equivalent Strain Plot:

The equivalent strain plot is shown in figure 17. The maximum and minimum strain values are 4.312e-06 and 1.768e-08. The intensity of strain is more at the central hole of the plate similar to that of the previous analysis.

Figure 17. Equivalent Strain Plot.

Displacement Plot:

As the plate is stretched from one side, the displacement is shown in figure 18.

Figure 18. Displacement Plot.

Comparison of Results: -

The results are summarized in a tabular form as shown in table 1. The table contains the details about the stress, strain, and displacement of the plates.

Table 1. Comparison of the Analysis results.

Analysis	Max. Von misses Stress (MPa)	Max. Displacement (mm)	Max. Equivalent strain (MPa)	Factor of Safety
1 holed plate	1212000	0.0005241	0.000004502	512
3 holed plate	1169000	0.0005666	0.000004312	530.55

Observation: -

From table 1, it is clear that the stress and strain have decreased in the plate with 3 holes, whereas the displacement and Factor of Safety (FOS) have increased. It can also be seen in the stress plots of both cases that the maximum stress occurs at the circular hole and it is indeed a stress concentrated area. In the plate with 3 holes, it can be seen that the stress is more distributed than in the plate with a central circular hole.

Conclusion: -

In this study, two models of a plate were created. One with a single central circular hole and another one with three holes. The static analysis was done on both of them having a 1000 N load on one of its smaller faces. The results obtained showed that the plate with three holes had less stress and strain than the plate with one hole. While the displacement and Factor of safety are less than that of the plate with one hole. From a purely analytical point of view, the plate with three holes is better. From the manufacturing point of view, the plate with one hole is better as it requires less manufacturing cost.