Week 1 Stress Concentration on a Plate with hole

Challenge 1: Plate with Hole/s

Problem statements:

1. Compare the performance of 2 separate plates with different hole geometries by performing a static structural analysis using ANSYS Workbench and determine the maximum deformation and Stresses developed in each model.
2. From an analysis standpoint, which of the design should be selected and why?
3. From a manufacturing standpoint, which of the designs should be selected and why?

The 2 models below are referred to case 1 and case 2 respectively.

Figure 1: Drawings of the parts to be analyzed

Tools used:

ANSYS Workbench 2020 R1

Boundary conditions (Same for both models):

Part type = Plate with hole/s

Material = Structural Steel

Tensile load = 500 N (pulling on one of the shorter side of the plate – 120 mm X 30 mm surface)

Case 1: Rectangular plate with 1X 60 mm hole

• Setup: A new Static Structural study was created in ANSYS Workbench.
• Boundary conditions: Structural steel was applied as the material; one of the 120 mm X 30 mm face is fixed and a tensile load is applied on the opposite 120 mm X 30 mm face so that it stretches the plate.
• Mesh: A mesh size of 10 mm is chosen and applied.
• Results: The mesh is generated and Stress and Deformation as chosen as the solutions to be evaluated. The results are tabulated in the results section of the report.

Figure 2: Results for Stress analysis on a plate with a single hole

Figure 3: Results for Deformation analysis on a plate with a single hole

Case 2: Rectangular plate with 1X 60 mm and 2X 30 mm hole

• Setup: A new Static Structural study was created in ANSYS Workbench.
• Boundary conditions: Structural steel was applied as the material; one of the 120 mm X 30 mm face is fixed and a tensile load is applied on the opposite 120 mm X 30 mm face so that it stretches the plate.
• Mesh: A mesh size of 10 mm is chosen and applied.
• Results: The mesh is generated and Stress and Deformation as chosen as the solutions to be evaluated. The results are tabulated in the results section of the report.

Figure 4: Results for Stress analysis on a plate with three holes

Figure 5: Results for Deformation analysis on a plate with three holes

Results:

1. The following table compares the results between the 2 models.

Sl. No	Description	Rectangular Plate with 1X hole	Rectangular Plate with 3X hole
1	Max. Von Mises Stresses (MPa)	0.584	0.561
2	Max. Displacement (mm)	0.00027	0.00029
3	Mass (g)	7662.86	7336.29

2. From an analysis standpoint, the plate with a single hole should be chosen because of a higher stress value and simplicity of analysis. This is a simple analytical experiment to understand the effect of tensile forces on a plate with a relief feature such as a hole. As far as deformation is concerned, the total difference in deformation is 20 nm i.e. the plate with 1 hole deforms 20 nm less than the plate with 3 holes. This value is so negligible that it should not play a factor in making this decision. For the purpose of analysis, we are not concerned about the weight, cost, and manufacturing aspects of the design.

3. From a manufacturing standpoint, the plate with 3 holes should be chosen because it has less stress acting on it. In the case of a manufacturing decision, material cost, weight, and machinability are critical to the decision-making process. This plate is lighter, uses less material, and has the same manufacturability (if cast) as the plate with 1 hole and therefore is more cost-efficient with better stress properties.

Inference:

The 2 rectangular plates have very similar characteristics as far as maximum Von-Mises stresses and maximum deformation are considered. The plate with 3 holes has an almost negligibly higher displacement value by the order of 0.00002 mm. The plate with one-hole experiences more stresses and this leads us to conclude that the increased number of holes acts as stress relief features.